Indentation of Ellipsoidal and Cylindrical Elastic Shells

KAUST Repository

Vella, Dominic

2012-10-01

Thin shells are found in nature at scales ranging from viruses to hens\\' eggs; the stiffness of such shells is essential for their function. We present the results of numerical simulations and theoretical analyses for the indentation of ellipsoidal and cylindrical elastic shells, considering both pressurized and unpressurized shells. We provide a theoretical foundation for the experimental findings of Lazarus etal. [following paper, Phys. Rev. Lett. 109, 144301 (2012)PRLTAO0031-9007] and for previous work inferring the turgor pressure of bacteria from measurements of their indentation stiffness; we also identify a new regime at large indentation. We show that the indentation stiffness of convex shells is dominated by either the mean or Gaussian curvature of the shell depending on the pressurization and indentation depth. Our results reveal how geometry rules the rigidity of shells. © 2012 American Physical Society.

Nonlinear theory of elastic shells

International Nuclear Information System (INIS)

Costa Junior, J.A.

1979-08-01

Nonlinear theory of elastic shells is developed which incorporates both geometric and physical nonlinearities and which does not make use of the well known Love-Kirchhoff hypothesis. The resulting equations are formulated in tensorial notation and are reduced to the ones of common use when simplifying assumptions encountered in the especific litterature are taken. (Author) [pt

Random three-dimensional jammed packings of elastic shells acting as force sensors

Science.gov (United States)

Jose, Jissy; van Blaaderen, Alfons; Imhof, Arnout

2016-06-01

In a jammed solid of granular particles, the applied stress is in-homogeneously distributed within the packing. A full experimental characterization requires measurement of all the interparticle forces, but so far such measurements are limited to a few systems in two and even fewer in three dimensions. Particles with the topology of (elastic) shells are good local force sensors as relatively large deformations of the shells result from relatively small forces. We recently introduced such fluorescent shells as a model granular system in which force distributions can be determined in three dimensions using confocal microscopy and quantitative image analysis. An interesting aspect about these shells that differentiates them from other soft deformable particles is their buckling behavior at higher compression. This leads to deformations that do not conserve the inner volume of the particle. Here we use this system to accurately measure the contact forces in a three-dimensional packing of shells subjected to a static anisotropic compression and to shear. At small deformations forces are linear, however, for a buckled contact, the restoring force is related to the amount of deformation by a square root law, as follows from the theory of elasticity of shells. Near the unjamming-jamming transition (point J ), we found the probability distribution of the interparticle forces P (f ) to decay nearly exponentially at large forces, with little evidence of long-range force chains in the packings. As the packing density is increased, the tail of the distribution was found to crossover to a Gaussian, in line with other experimental and simulation studies. Under a small shear strain, up to 0.216, applied at an extremely low shear rate, we observed a shear-induced anisotropy in both the pair correlation function and contact force network; however, no appreciable change was seen in the number of contacts per particle.

Uniqueness theorems in linear elasticity

CERN Document Server

Knops, Robin John

1971-01-01

The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...

Theory of elastic thin shells solid and structural mechanics

CERN Document Server

Gol'Denveizer, A L; Dryden, H L

1961-01-01

Theory of Elastic Thin Shells discusses the mathematical foundations of shell theory and the approximate methods of solution. The present volume was originally published in Russian in 1953, and remains the only text which formulates as completely as possible the different sets of basic equations and various approximate methods of shell analysis emphasizing asymptotic integration. The book is organized into five parts. Part I presents the general formulation and equations of the theory of shells, which are based on the well-known hypothesis of the preservation of the normal element. Part II is

Elastic-plastic-creep analysis of shells

International Nuclear Information System (INIS)

Pai, D.H.

1979-01-01

This paper presents the recent experience of a designer/fabricator of nuclear heat transport components in the area of elastic-plastic-creep analysis of shell-like structures. A brief historical perspective is first given to highlight the evolution leading to the present industry practice. The ASME elevated temperature design criteria will be discussed followed by examples of actual computations performed to support the design/analysis and fabrication of a breeder reactor component in which a substantial amount of elastic-plastic-creep analysis was performed. Mathematical challenges encountered by the design analyst in these problems will be highlighted. Developmental needs and future trends will then be given

Nanoscale elasticity mappings of micro-constituents of abalone shell by band excitation-contact resonance force microscopy

Science.gov (United States)

Li, Tao; Zeng, Kaiyang

2014-01-01

The macroscopic mechanical properties of the abalone shell have been studied extensively in the literature, but the in situ nanoscale elasticity of various micro-constituents in the shell have not been characterized and reported yet. In this study, the nanoscale elasticity mappings including different micro-constituents in abalone shell were observed by using the Contact Resonance Force Microscopy (CR-FM) technique. CR-FM is one of the advanced scanning probe microscopy techniques that is able to quantify the local elastic moduli of various materials in a non-destructive manner. Instead of an average value, an elasticity mapping that reveals the nanoscale variations of elastic moduli with location can be extracted and correlated with the topography of the structure. Therefore in this study, by adopting the CR-FM technique that is incorporated with the band excitation technique, the elasticity variations of the abalone shell caused by different micro-constituents and crystal orientations are reported, and the elasticity values of the aragonite and calcite nanograins are quantified.The macroscopic mechanical properties of the abalone shell have been studied extensively in the literature, but the in situ nanoscale elasticity of various micro-constituents in the shell have not been characterized and reported yet. In this study, the nanoscale elasticity mappings including different micro-constituents in abalone shell were observed by using the Contact Resonance Force Microscopy (CR-FM) technique. CR-FM is one of the advanced scanning probe microscopy techniques that is able to quantify the local elastic moduli of various materials in a non-destructive manner. Instead of an average value, an elasticity mapping that reveals the nanoscale variations of elastic moduli with location can be extracted and correlated with the topography of the structure. Therefore in this study, by adopting the CR-FM technique that is incorporated with the band excitation technique, the

Modeling complicated rheological behaviors in encapsulating shells of lipid-coated microbubbles accounting for nonlinear changes of both shell viscosity and elasticity.

Science.gov (United States)

Li, Qian; Matula, Thomas J; Tu, Juan; Guo, Xiasheng; Zhang, Dong

2013-02-21

It has been accepted that the dynamic responses of ultrasound contrast agent (UCA) microbubbles will be significantly affected by the encapsulating shell properties (e.g., shell elasticity and viscosity). In this work, a new model is proposed to describe the complicated rheological behaviors in an encapsulating shell of UCA microbubbles by applying the nonlinear 'Cross law' to the shell viscous term in the Marmottant model. The proposed new model was verified by fitting the dynamic responses of UCAs measured with either a high-speed optical imaging system or a light scattering system. The comparison results between the measured radius-time curves and the numerical simulations demonstrate that the 'compression-only' behavior of UCAs can be successfully simulated with the new model. Then, the shell elastic and viscous coefficients of SonoVue microbubbles were evaluated based on the new model simulations, and compared to the results obtained from some existing UCA models. The results confirm the capability of the current model for reducing the dependence of bubble shell parameters on the initial bubble radius, which indicates that the current model might be more comprehensive to describe the complex rheological nature (e.g., 'shear-thinning' and 'strain-softening') in encapsulating shells of UCA microbubbles by taking into account the nonlinear changes of both shell elasticity and shell viscosity.

Modeling complicated rheological behaviors in encapsulating shells of lipid-coated microbubbles accounting for nonlinear changes of both shell viscosity and elasticity

International Nuclear Information System (INIS)

Li Qian; Tu Juan; Guo Xiasheng; Zhang Dong; Matula, Thomas J

2013-01-01

It has been accepted that the dynamic responses of ultrasound contrast agent (UCA) microbubbles will be significantly affected by the encapsulating shell properties (e.g., shell elasticity and viscosity). In this work, a new model is proposed to describe the complicated rheological behaviors in an encapsulating shell of UCA microbubbles by applying the nonlinear ‘Cross law’ to the shell viscous term in the Marmottant model. The proposed new model was verified by fitting the dynamic responses of UCAs measured with either a high-speed optical imaging system or a light scattering system. The comparison results between the measured radius–time curves and the numerical simulations demonstrate that the ‘compression-only’ behavior of UCAs can be successfully simulated with the new model. Then, the shell elastic and viscous coefficients of SonoVue microbubbles were evaluated based on the new model simulations, and compared to the results obtained from some existing UCA models. The results confirm the capability of the current model for reducing the dependence of bubble shell parameters on the initial bubble radius, which indicates that the current model might be more comprehensive to describe the complex rheological nature (e.g., ‘shear-thinning’ and ‘strain-softening’) in encapsulating shells of UCA microbubbles by taking into account the nonlinear changes of both shell elasticity and shell viscosity. (paper)

Elastic-plastic failure analysis of pressure burst tests of thin toroidal shells

International Nuclear Information System (INIS)

Jones, D.P.; Holliday, J.E.; Larson, L.D.

1998-07-01

This paper provides a comparison between test and analysis results for bursting of thin toroidal shells. Testing was done by pressurizing two toroidal shells until failure by bursting. An analytical criterion for bursting is developed based on good agreement between structural instability predicted by large strain-large displacement elastic-plastic finite element analysis and observed burst pressure obtained from test. The failures were characterized by loss of local stability of the membrane section of the shells consistent with the predictions from the finite element analysis. Good agreement between measured and predicted burst pressure suggests that incipient structural instability as calculated by an elastic-plastic finite element analysis is a reasonable way to calculate the bursting pressure of thin membrane structures

Enhancement and prediction of modulus of elasticity of palm kernel shell concrete

International Nuclear Information System (INIS)

Alengaram, U. Johnson; Mahmud, Hilmi; Jumaat, Mohd Zamin

2011-01-01

Research highlights: → Micro-pores of size 16-24 μm were found on the outer surface of palm kernel shell. → Infilling of pores by mineral admixtures was evident. → Sand content influenced both modulus of elasticity and compressive strength. → Proposed equation predicts modulus of elasticity within ±1.5 kN/mm 2 of test results. -- Abstract: This paper presents results of an investigation conducted to enhance and predict the modulus of elasticity (MOE) of palm kernel shell concrete (PKSC). Scanning electron microscopic (SEM) analysis on palm kernel shell (PKS) was conducted. Further, the effect of varying sand and PKS contents and mineral admixtures (silica fume and fly ash) on compressive strength and MOE was investigated. The variables include water-to-binder (w/b) and sand-to-cement (s/c) ratios. Nine concrete mixes were prepared, and tests on static and dynamic moduli of elasticity and compressive strength were conducted. The SEM result showed presence of large number of micro-pores on PKS. The mineral admixtures uniformly filled the micro-pores on the outer surface of PKS. Further, the increase in sand content coupled with reduction in PKS content enhanced the compressive strength and static MOE: The highest MOE recorded in this investigation, 11 kN/mm 2 , was twice that previously published. Moreover, the proposed equation based on CEB/FIP code formula appears to predict the MOE close to the experimental values.

Transient Response of a Fluid-Filled, Thick-Walled Spherical Shell Embedded in an Elastic Medium

Directory of Open Access Journals (Sweden)

Bahari Ako

2016-01-01

Full Text Available The paper addresses the problem of transient elastodynamics analysis of a thick-walled, fluid-filled spherical shell embedded in an elastic medium with an analytical approach. This configuration is investigated at first step for a full-space case. Different constitutive relations for the elastic medium, shell material and filling fluid can be considered, as well as different excitation sources (including S/P wave or plane/spherical incident wave at different locations. With mapmaking visualisation, the wave propagation phenomena can be described and better understood. The methodology is going to be applied to analysis of the tunnels or other shell like structures under the effect of nearby underground explosion.

Non-linear realizations of supersymmetry with off-shell central charges

International Nuclear Information System (INIS)

Santos Filho, P.B.; Oliveira Rivelles, V. de.

1985-01-01

A new class of non-linear realizations of the extended supersymmetry algebra with central charges is presented. They were obtained by applying the technique of dimensional reduction by Legendre transformation to a non-linear realization without central charges in one higher dimension. As a result an off-shell central charge is obtained. The non-linear lagrangian is the same as is the case of vanishing central charge. On-shell the central charge vanishes so this non-linear realization differs from that without central charges only off-shell. It is worked in two dimensions and its extension to higher dimensions is discussed. (Author) [pt

On the use of elastic-plastic material characteristics for linear-elastic component assessments

International Nuclear Information System (INIS)

Kussmaul, K.; Silcher, H.; Eisele, U.

1995-01-01

In this paper the procedure of safety assessment of components by fracture mechanics analysis as recommended in TECDOC 717 is applied to two standard specimens of ductile cast iron. It is shown that the use of a pseudo-elastic K IJ -value in linear elastic safety analysis may lead to non-conservative results, when elastic-plastic material behaviour can be expected. (author)

Asymptotic expansions for high-contrast linear elasticity

KAUST Repository

Poveda, Leonardo A.; Huepo, Sebastian; Calo, Victor M.; Galvis, Juan

2015-01-01

We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.

Asymptotic expansions for high-contrast linear elasticity

KAUST Repository

Poveda, Leonardo A.

2015-03-01

We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.

Determining characteristics of oscillations of elastic spherical shell filled using semiconductor laser autodyne

Science.gov (United States)

Dobdin, S. Yu.; Usanov, D. A.; Skripal, A. V.

2012-06-01

The experimental results to determine the motion characteristics of oscillations of elastic spherical shell filled under the pneumopulse action have been presented. The required characteristics of motion were determined by analysis of the autodyne signal. The relationship between the parameters of motion of the spherical shell and the internal pressure measured using a contact tonometer has been shown.

Enhanced linear photonic nanojet generated by core-shell optical microfibers

Science.gov (United States)

Liu, Cheng-Yang; Yen, Tzu-Ping; Chen, Chien-Wen

2017-05-01

The generation of linear photonic nanojet using core-shell optical microfiber is demonstrated numerically and experimentally in the visible light region. The power flow patterns for the core-shell optical microfiber are calculated by using the finite-difference time-domain method. The focusing properties of linear photonic nanojet are evaluated in terms of length and width along propagation and transversal directions. In experiment, the silica optical fiber is etched chemically down to 6 μm diameter and coated with metallic thin film by using glancing angle deposition. We show that the linear photonic nanojet is enhanced clearly by metallic shell due to surface plasmon polaritons. The large-area superresolution imaging can be performed by using a core-shell optical microfiber in the far-field system. The potential applications of this core-shell optical microfiber include micro-fluidics and nano-structure measurements.

A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories

Directory of Open Access Journals (Sweden)

V. V. Zozulya

2013-01-01

Full Text Available A high order theory for linear thermoelasticity and heat conductivity of shells has been developed. The proposed theory is based on expansion of the 3-D equations of theory of thermoelasticity and heat conductivity into Fourier series in terms of Legendre polynomials. The first physical quantities that describe thermodynamic state have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity and heat conductivity including generalized Hooke's and Fourier's laws have been transformed to the corresponding equations for coefficients of the polynomial expansion. Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. First approximation theory is considered in more detail. The obtained equations for the first approximation theory are compared with the corresponding equations for Timoshenko's and Kirchhoff-Love's theories. Special case of plates and cylindrical shell is also considered, and corresponding equations in displacements are presented.

Calculation of elastic-plastic strain ranges for fatigue analysis based on linear elastic stresses

International Nuclear Information System (INIS)

Sauer, G.

1998-01-01

Fatigue analysis requires that the maximum strain ranges be known. These strain ranges are generally computed from linear elastic analysis. The elastic strain ranges are enhanced by a factor K e to obtain the total elastic-plastic strain range. The reliability of the fatigue analysis depends on the quality of this factor. Formulae for calculating the K e factor are proposed. A beam is introduced as a computational model for determining the elastic-plastic strains. The beam is loaded by the elastic stresses of the real structure. The elastic-plastic strains of the beam are compared with the beam's elastic strains. This comparison furnishes explicit expressions for the K e factor. The K e factor is tested by means of seven examples. (orig.)

TWO-DIMENSIONAL APPROXIMATION OF EIGENVALUE PROBLEMS IN SHELL THEORY: FLEXURAL SHELLS

Institute of Scientific and Technical Information of China (English)

无

2000-01-01

The eigenvalue problem for a thin linearly elastic shell, of thickness 2e, clamped along its lateral surface is considered. Under the geometric assumption on the middle surface of the shell that the space of inextensional displacements is non-trivial, the authors obtain, as ε→0,the eigenvalue problem for the two-dimensional"flexural shell"model if the dimension of the space is infinite. If the space is finite dimensional, the limits of the eigenvalues could belong to the spectra of both flexural and membrane shells. The method consists of rescaling the variables and studying the problem over a fixed domain. The principal difficulty lies in obtaining suitable a priori estimates for the scaled eigenvalues.

Non-linear theory of elasticity and optimal design

CERN Document Server

Ratner, LW

2003-01-01

In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it

Discriminative Elastic-Net Regularized Linear Regression.

Science.gov (United States)

Zhang, Zheng; Lai, Zhihui; Xu, Yong; Shao, Ling; Wu, Jian; Xie, Guo-Sen

2017-03-01

In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zero-one matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.

Atomic mass formula with linear shell terms

International Nuclear Information System (INIS)

Uno, Masahiro; Yamada, Masami; Ando, Yoshihira; Tachibana, Takahiro.

1981-01-01

An atomic mass formula is constructed in the form of a sum of gross terms and empirical linear shell terms. Values of the shell parameters are determined after the statistical method of Uno and Yamada, Which is characterized by inclusion of the error inherent in the mass formula. The resulting formula reproduces the input masses with the standard deviation of 393 keV. A prescription is given for estimating errors of calculated masses. The mass formula is compared with recent experimental data of Rb, Cs and Fr isotopes, which are not included in the input data, and also with the constant-shell-term formula of Uno and Yamada. (author)

Mechanical properties of two-way grid shells optimized considering roundness and elastic stiffness

International Nuclear Information System (INIS)

Ogawa, Toshiyuki; Yuta, Nishikawa; Rie, Tateishi; Ohsaki, Makoto

2002-01-01

A single-layer two-way grid shell defined by Bezier surface is optimized by coordinates of the control points as design variables. The purpose of this paper is to find optimal shapes considering roundness and elastic stiffness, and to investigate their mechanical properties. The distance of the center of curvature from the specified point is used for formulating the objective function for generating a round shape. Consider next a problem of minimizing the compliance as mechanical performance measure. The compliance is defined by the external work against the static loads applied to the nodes. The mechanically optimal shape is different from the round shape. Therefore, the multi objective optimization problem is formulated for optimizing the two objectives, which are roundness and the elastic stiffness defined by using the compliance. The constraint method is used for obtaining Pareto optimal solutions between the two objectives. We optimize single-layer two-way grid shells with square and rectangle plans. Mechanical properties of the optimal shapes are investigated by compliance and the distributions of axial force and bending moment. The round shape is significantly dominated by the bending moment and its compliance is large. The bending moment of the mechanically optimal shape is not very large, and the latticed shell has large stiffness through axial deformation. A trade-off shape is round enough, and the influence of the bending moment is smaller than that of the optimal round shape and the elastic stiffness is moderately large

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

Science.gov (United States)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

Vectorized Matlab Codes for Linear Two-Dimensional Elasticity

Directory of Open Access Journals (Sweden)

Jonas Koko

2007-01-01

Full Text Available A vectorized Matlab implementation for the linear finite element is provided for the two-dimensional linear elasticity with mixed boundary conditions. Vectorization means that there is no loop over triangles. Numerical experiments show that our implementation is more efficient than the standard implementation with a loop over all triangles.

Free vibration analysis of a magneto-electro-elastic doubly-curved shell resting on a Pasternak-type elastic foundation

International Nuclear Information System (INIS)

Razavi, Soheil; Shooshtari, Alireza

2014-01-01

Free vibration of a simply-supported magneto-electro-elastic doubly-curved thin shell resting on a Pasternak foundation is investigated based on Donnell theory. The rotary inertia effect is considered in the formulation. Maxwell equations for electrostatics and magnetostatics are used to model the electric and magnetic behavior. The partial differential equations of motion are reduced to a single ordinary differential equation and an analytical relation is obtained for the natural frequency. After validation of the present study, several numerical studies is done to investigate the effects of the electric and magnetic potentials, spring and shear coefficients of the Pasternak foundation, and the geometry of the shell on the vibration frequency. (paper)

SOUND FIELD SHIELDING BY FLAT ELASTIC LAYER AND THIN UNCLOSED SPHERICAL SHELL

Directory of Open Access Journals (Sweden)

G. Ch. Shushkevich

2014-01-01

Full Text Available An analytical solution of a boundary problem describing the process of penetration of a sound field of a spherical radiator located inside a thin unclosed spherical shell through a flat elastic layer is constructed. An influence of some parameters of the problem on the value of the attenuation coeffi-cient (screening of the sound field was studied by using a numerical simulation.

Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.

Energy Technology Data Exchange (ETDEWEB)

Preston, Leiph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-08-01

Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.

Analytical Investigation of Elastic Thin-Walled Cylinder and Truncated Cone Shell Intersection Under Internal Pressure

OpenAIRE

Zamani, J.; Soltani, B.; Aghaei, M.

2014-01-01

An elastic solution of cylinder-truncated cone shell intersection under internal pressure is presented. The edge solution theory that has been used in this study takes bending moments and shearing forces into account in the thin-walled shell of revolution element. The general solution of the cone equations is based on power series method. The effect of cone apex angle on the stress distribution in conical and cylindrical parts of structure is investigated. In addition, the effect of the inter...

Generalized theory of resonance excitation by sound scattering from an elastic spherical shell in a nonviscous fluid.

Science.gov (United States)

Mitri, Farid G

2012-08-01

This work presents the general theory of resonance scattering (GTRS) by an elastic spherical shell immersed in a nonviscous fluid and placed arbitrarily in an acoustic beam. The GTRS formulation is valid for a spherical shell of any size and material regardless of its location relative to the incident beam. It is shown here that the scattering coefficients derived for a spherical shell immersed in water and placed in an arbitrary beam equal those obtained for plane wave incidence. Numerical examples for an elastic shell placed in the field of acoustical Bessel beams of different types, namely, a zero-order Bessel beam and first-order Bessel vortex and trigonometric (nonvortex) beams are provided. The scattered pressure is expressed using a generalized partial-wave series expansion involving the beam-shape coefficients (BSCs), the scattering coefficients of the spherical shell, and the half-cone angle of the beam. The BSCs are evaluated using the numerical discrete spherical harmonics transform (DSHT). The far-field acoustic resonance scattering directivity diagrams are calculated for an albuminoidal shell immersed in water and filled with perfluoropropane gas, by subtracting an appropriate background from the total far-field form function. The properties related to the arbitrary scattering are analyzed and discussed. The results are of particular importance in acoustical scattering applications involving imaging and beam-forming for transducer design. Moreover, the GTRS method can be applied to investigate the scattering of any beam of arbitrary shape that satisfies the source-free Helmholtz equation, and the method can be readily adapted to viscoelastic spherical shells or spheres.

Non-linear elastic thermal stress analysis with phase changes

International Nuclear Information System (INIS)

Amada, S.; Yang, W.H.

1978-01-01

The non-linear elastic, thermal stress analysis with temperature induced phase changes in the materials is presented. An infinite plate (or body) with a circular hole (or tunnel) is subjected to a thermal loading on its inner surface. The peak temperature around the hole reaches beyond the melting point of the material. The non-linear diffusion equation is solved numerically using the finite difference method. The material properties change rapidly at temperatures where the change of crystal structures and solid-liquid transition occur. The elastic stresses induced by the transient non-homogeneous temperature distribution are calculated. The stresses change remarkably when the phase changes occur and there are residual stresses remaining in the plate after one cycle of thermal loading. (Auth.)

Thermal stress state of laminated shells of revolution made of isotropic and linearly orthotropic materials

International Nuclear Information System (INIS)

Savchenko, V.G.

1995-01-01

In this investigation, we will use a cylindrical coordinate system to study the stress state of laminated shells of revolution made of inelastically deforming isotropic materials and elastic materials with linear orthotropy. One of the principal directions of anisotropy coincides with the axis of revolution of the body. The shells will be subjected to nonaxisymmetric loading by body bar K (K Z , K r , K var-phi ) and surface bar t n (t nz , t nr , t nvar-phi ) forces and heating. The level of loading is such that the rheological properties of the materials of the layers are not a factor, although their thermomechanical characteristics depend on temperature. In addition, the loading and heating of the body occur in such a way that simple (or close to simple) deformation processes take place in its isotropic elements. These processes are accompanied by inelastic strains and the formation of unloading regions in which plastic strains having the sign opposite the initial strains develop. It is assumed that the layers of the body are secured to one another without interference and that conditions corresponding to ideal contact prevail at their interfaces

Linear and nonlinear symmetrically loaded shells of revolution approximated with the finite element method

International Nuclear Information System (INIS)

Cook, W.A.

1978-10-01

Nuclear Material shipping containers have shells of revolution as a basic structural component. Analytically modeling the response of these containers to severe accident impact conditions requires a nonlinear shell-of-revolution model that accounts for both geometric and material nonlinearities. Present models are limited to large displacements, small rotations, and nonlinear materials. This report discusses a first approach to developing a finite element nonlinear shell of revolution model that accounts for these nonlinear geometric effects. The approach uses incremental loads and a linear shell model with equilibrium iterations. Sixteen linear models are developed, eight using the potential energy variational principle and eight using a mixed variational principle. Four of these are suitable for extension to nonlinear shell theory. A nonlinear shell theory is derived, and a computational technique used in its solution is presented

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part I: Linear Theory

Science.gov (United States)

Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

2014-01-01

Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports. The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness.

The Vibration Analysis of Tube Bundles Induced by Fluid Elastic Excitation in Shell Side of Heat Exchanger

Science.gov (United States)

Bao, Minle; Wang, Lu; Li, Wenyao; Gao, Tianze

2017-09-01

Fluid elastic excitation in shell side of heat exchanger was deduced theoretically in this paper. Model foundation was completed by using Pro / Engineer software. The finite element model was constructed and imported into the FLUENT module. The flow field simulation adopted the dynamic mesh model, RNG k-ε model and no-slip boundary conditions. Analysing different positions vibration of tube bundles by selecting three regions in shell side of heat exchanger. The results show that heat exchanger tube bundles at the inlet of the shell side are more likely to be failure due to fluid induced vibration.

Size effect of the elastic modulus of rectangular nanobeams: Surface elasticity effect

International Nuclear Information System (INIS)

Yao Hai-Yan; Fan Wen-Liang; Yun Guo-Hong

2013-01-01

The size-dependent elastic property of rectangular nanobeams (nanowires or nanoplates) induced by the surface elasticity effect is investigated by using a developed modified core-shell model. The effect of surface elasticity on the elastic modulus of nanobeams can be characterized by two surface related parameters, i.e., inhomogeneous degree constant and surface layer thickness. The analytical results show that the elastic modulus of the rectangular nanobeam exhibits a distinct size effect when its characteristic size reduces below 100 nm. It is also found that the theoretical results calculated by a modified core-shell model have more obvious advantages than those by other models (core-shell model and core-surface model) by comparing them with relevant experimental measurements and computational results, especially when the dimensions of nanostructures reduce to a few tens of nanometers. (condensed matter: structural, mechanical, and thermal properties)

Free and Forced Vibrations of Thick-Walled Anisotropic Cylindrical Shells

Science.gov (United States)

Marchuk, A. V.; Gnedash, S. V.; Levkovskii, S. A.

2017-03-01

Two approaches to studying the free and forced axisymmetric vibrations of cylindrical shell are proposed. They are based on the three-dimensional theory of elasticity and division of the original cylindrical shell with concentric cross-sectional circles into several coaxial cylindrical shells. One approach uses linear polynomials to approximate functions defined in plan and across the thickness. The other approach also uses linear polynomials to approximate functions defined in plan, but their variation with thickness is described by the analytical solution of a system of differential equations. Both approaches have approximation and arithmetic errors. When determining the natural frequencies by the semi-analytical finite-element method in combination with the divide and conqure method, it is convenient to find the initial frequencies by the finite-element method. The behavior of the shell during free and forced vibrations is analyzed in the case where the loading area is half the shell thickness

Analytical Investigation of Elastic Thin-Walled Cylinder and Truncated Cone Shell Intersection Under Internal Pressure.

Science.gov (United States)

Zamani, J; Soltani, B; Aghaei, M

2014-10-01

An elastic solution of cylinder-truncated cone shell intersection under internal pressure is presented. The edge solution theory that has been used in this study takes bending moments and shearing forces into account in the thin-walled shell of revolution element. The general solution of the cone equations is based on power series method. The effect of cone apex angle on the stress distribution in conical and cylindrical parts of structure is investigated. In addition, the effect of the intersection and boundary locations on the circumferential and longitudinal stresses is evaluated and it is shown that how quantitatively they are essential.

Geometrically nonlinear dynamic and static analysis of shallow spherical shell resting on two-parameters elastic foundations

International Nuclear Information System (INIS)

Civalek, Ö.

2014-01-01

In the present study nonlinear static and dynamic responses of shallow spherical shells resting on Winkler–Pasternak elastic foundations are carried out. The formulation of the shells is based on the Donnell theory. The nonlinear governing equations of motion of shallow shells are discretized in space and time domains using the discrete singular convolution and the differential quadrature methods, respectively. The validity of the present method is demonstrated by comparing the present results with those available in the open literature. The effects of the Winkler and Pasternak foundation parameters on nonlinear static and dynamic response of shells are investigated. Some results are also presented for circular plate as special case. Damping effect on nonlinear dynamic response of shells is studied. It is important to state that the increase in damping parameter causes decrease in the dynamic response of the shells. It is shown that the shear parameter of the foundation has a significant influence on the dynamic and static response of the shells. Also, the response of the shell is decreased with the increasing value of the shear parameter of the foundation. Parametric studies considering different geometric variables have also been investigated. -- Highlights: • Nonlinear responses of shallow spherical shells are presented. • The effects of foundation parameters are investigated. • Damping effect on nonlinear dynamic response of shells is also studied

Elasto/visco-plastic dynamic response of shells of revolution

International Nuclear Information System (INIS)

Takezono, S.; Tao, K.

1977-01-01

The authors study the large deflection elasto/visco-plastic dynamic response of shells of revolution to strong blast loads, where the viscosity of the material is considered in the plastic range. The equations of motion and the relations between the strain and the displacement are derived from the Sanders nonlinear theory for thin shells. The constitutive relation for shell response is linear elastic, visco-plastic. In the linear elastic range Hooke's law is used. In the plastic range the elasto/visco-plastic equations by Fyfe based on the model developed by Perzyna are employed. The criterion for yielding used in this analysis is the von Mises yield theory. The numerical method selected for integration of the equations of motion is a method using finite difference in both space and time. The differential equations are written in finite difference form on the basis of the parabola method. For the time integration of the equations of motion the second-order finite difference in time is used. The equations of motion are thus expressed in finite difference form if we divide the shell into segments along meridional length and around the circumference. Resultant forces and resultant moments are given from numerical integration by Simpson's 1/3 rule. The loadings which are considered in this paper may be either impulsive or of finite time duration. (Auth.)

Suppression of an acoustic mode by an elastic mode of a liquid-filled spherical shell resonator.

Science.gov (United States)

Lonzaga, Joel B; Raymond, Jason L; Mobley, Joel; Gaitan, D Felipe

2011-02-01

The purpose of this paper is to report on the suppression of an approximately radial (radially symmetric) acoustic mode by an elastic mode of a water-filled, spherical shell resonator. The resonator, which has a 1-in. wall thickness and a 9.5-in. outer diameter, was externally driven by a small transducer bolted to the external wall. Experiments showed that for the range of drive frequencies (19.7-20.6 kHz) and sound speeds in water (1520-1570 m/s) considered in this paper, a nonradial (radially nonsymmetric) mode was also excited, in addition to the radial mode. Furthermore, as the sound speed in the liquid was changed, the resonance frequency of the nonradial mode crossed with that of the radial one and the amplitude of the latter was greatly reduced near the crossing point. The crossing of the eigenfrequency curves of these two modes was also predicted theoretically. Further calculations demonstrated that while the radial mode is an acoustic one associated with the interior fluid, the nonradial mode is an elastic one associated with the shell. Thus, the suppression of the radial acoustic mode is apparently caused by the overlapping with the nonradial elastic mode near the crossing point.

Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of harmonic differential quadrature-finite difference methods

International Nuclear Information System (INIS)

Civalek, Oemer

2005-01-01

The nonlinear dynamic response of doubly curved shallow shells resting on Winkler-Pasternak elastic foundation has been studied for step and sinusoidal loadings. Dynamic analogues of Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by numerical examples. The shear parameter G of the Pasternak foundation and the stiffness parameter K of the Winkler foundation have been found to have a significant influence on the dynamic response of the shell. It is concluded from the present study that the HDQ-FD methodolgy is a simple, efficient, and accurate method for the nonlinear analysis of doubly curved shallow shells resting on two-parameter elastic foundation

Linear models of income patterns in consumer demand for foods and evaluation of its elasticity

Directory of Open Access Journals (Sweden)

Pavel Syrovátka

2005-01-01

Full Text Available The paper is focused on the use of the linear constructions for developing of Engel’s demand models in the field of the food-consumer demand. In the theoretical part of the paper, the linear approximations of this demand models are analysed on the bases of the linear interpolation. In the same part of this text, the hyperbolic elasticity function was defined for the linear Engel model. The behaviour of the hyperbolic elasticity function and its properties were consequently investigated too. The behaviour of the determined elasticity function was investigated according to the values of the intercept point and the direction parameter in the original linear Engel model. The obtained theoretical findings were tested using the real data of Czech Statistical Office. The developed linear Engel model was explicitly dynamised, because the achieved database was formed into the time series. With respect to the two variables definitions of the hyperbolic function in the theoretical part of the text, the determined dynamic model of the Engel demand for food was transformed into the form with parametric intercept point:ret* = At + 0.0946 · rmt*,where the values of absolute member are defined as:At = 1773.0973 + 9.3064 · t – 0.3023 · t2; (t = 1, 2, ... 32.The value of At in the parametric linear model of Engel consumer demand for food was during the observed period (1995–2002 always positive. Thus, the hyperbolic elasticity function achieved the elasticity coefficients from the interval:ηt ∈〈+0; +1.Within quantitative analysis of Engel demand for food in the Czech Republic during the given time period, it was founded, that income elasticity of food expenditures of the average Czech household was moved between +0.4080 and +0.4511. The Czech-household demand for food is thus income inelastic with the normal income reactions.

Elasto/visco-plastic dynamic response of multi-layered shells of revolution

International Nuclear Information System (INIS)

Takezono, S.; Tao, K.; Taguchi, T.

1989-01-01

Many investigations of the elasto/visco-plastic dynamic response of shells have been conducted. These investigations, however, have been mostly concerned with the case of single-layered shells, and few studies on multi-layered shells have been reported in spite of their importance in engineering. In this paper, the authors study the elasto/visco-plastic dynamic response of the multi-layered shells of revolution subjected to impulsive loads. The equations of motion and the relations between the strains and displacements are derived by extending Sanders' theory for elastic thin shells. As the constitutive relation, Hooke's law is used in the linear elastic range, and the elasto/visco-plastic equations are employed in the plastic range. The criterion for yielding used in the analysis is the von Mises yield theory. In the numerical analysis of the fundamental equations for incremental values an usual finite difference form is employed for the spatial derivatives and the inertia terms are treated with the backward difference formula. The solutions are obtained by summation of the incremental values

Viscous-elastic dynamics of power-law fluids within an elastic cylinder

Science.gov (United States)

Boyko, Evgeniy; Bercovici, Moran; Gat, Amir D.

2017-07-01

In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a tn/n +1 dependence on time (t ), suggesting the ability to indirectly measure the power-law index (n ) of shear-thinning liquids through measurements of elastic deformation.

Curvature Effects on the Vibration Characteristics of Doubly Curved Shallow Shells with General Elastic Edge Restraints

Directory of Open Access Journals (Sweden)

Hui Shi

2015-01-01

Full Text Available Effects of curvature upon the vibration characteristics of doubly curved shallow shells are assessed in this paper. Boundary conditions of the shell are generally specified in terms of distributed elastic restraints along the edges. The classical homogeneous boundary supports can be easily simulated by setting the stiffnesses of restraining springs to either zero or infinite. Vibration problems of the shell are solved by a modified Fourier series method that each of the displacements is invariably expressed as a simple trigonometric series which converges uniformly and acceleratedly over the solution domain. All the unknown expansion coefficients are treated equally as a set of independent generalized coordinates and solved using the Rayleigh-Ritz technique. The current method provides a unified solution to the vibration problems of curved shallow shells involving different geometric properties and boundary conditions with no need of modifying the formulations and solution procedures. Extensive tabular and graphical results are presented to show the curvature effects on the natural frequencies of the shell with various boundary conditions.

Designing Linear Feedback Controller for Elastic Inverted Pendulum with Tip Mass

Directory of Open Access Journals (Sweden)

Minh Hoang Nguyen

2016-12-01

Full Text Available This paper introduced a kind of cart and pole system. The pole in this system is not a solid beam but an elastic beam. The paper analyzed the dynamic equation of this complex system. Then, a linear feedback controller was designed to stabilize this model in order to keep the elastic beam balanced in the up-side position. The control results were proved to work well through simulation.

Four-dimensional Hooke's law can encompass linear elasticity and inertia

International Nuclear Information System (INIS)

Antoci, S.; Mihich, L.

1999-01-01

The question is examined whether the formally straightforward extension of Hooke's time-honoured stress-strain relation to the four dimensions of special and of general relativity can make physical sense. The four-dimensional Hooke law is found able to account for the inertia of matter; in the flat-space, slow-motion approximation the field equations for the displacement four-vector field ξ i can encompass both linear elasticity and inertia. In this limit one just recovers the equations of motion of the classical theory of elasticity

Non-linear elastic deformations

CERN Document Server

Ogden, R W

1997-01-01

Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.

Bi-orthogonality conditions for power flow analysis in fluid-loaded elastic cylindrical shells

DEFF Research Database (Denmark)

Ledet, Lasse; Sorokin, Sergey V.; Larsen, Jan Balle

2015-01-01

The paper addresses the classical problem of time-harmonic forced vibrations of a fluid-loaded cylindrical shell considered as a multi-modal waveguide carrying infinitely many waves. Firstly, a modal method for formulation of Green’s matrix is derived by means of modal decomposition. The method...... builds on the recent advances on bi-orthogonality conditions for multi-modal waveguides, which are derived here for an elastic fluid-filled cylindrical shell. Subsequently, modal decomposition is applied to the bi-orthogonality conditions to formulate explicit algebraic equations to express the modal...... vibro-acoustic waveguide is subjected to separate pressure and velocity acoustical excitations. Further, it has been found and justified that the bi-orthogonality conditions can be used as a ’root finder’ to solve the dispersion equation. Finally, it is discussed how to predict the response of a fluid...

Elastic stresses at reinforced nozzles in spherical shells with pressure and moment loading

International Nuclear Information System (INIS)

Rodabaugh, E.C.; Gwaltney, R.D.

1976-01-01

Calculated elastic stresses at reinforced nozzles in spherical shells with pressure and moment loading are presented. The models used in the calculations represent a wide variety of reinforced shapes; all meeting Code requirements. The results show Code stress indices for pressure loading for nozzles with local reinforcement are acceptable with some modification in coverage. Simple equations for stress indices for moment loading are developed. Potential application of the moment-loading stress indices is discussed. Several recommendations for Code changes are included

Simulation of nonlinear benchmarks and sheet metal forming processes using linear and quadratic solid–shell elements combined with advanced anisotropic behavior models

Directory of Open Access Journals (Sweden)

Wang Peng

2016-01-01

Full Text Available A family of prismatic and hexahedral solid‒shell (SHB elements with their linear and quadratic versions is presented in this paper to model thin 3D structures. Based on reduced integration and special treatments to eliminate locking effects and to control spurious zero-energy modes, the SHB solid‒shell elements are capable of modeling most thin 3D structural problems with only a single element layer, while describing accurately the various through-thickness phenomena. In this paper, the SHB elements are combined with fully 3D behavior models, including orthotropic elastic behavior for composite materials and anisotropic plastic behavior for metallic materials, which allows describing the strain/stress state in the thickness direction, in contrast to traditional shell elements. All SHB elements are implemented into ABAQUS using both standard/quasi-static and explicit/dynamic solvers. Several benchmark tests have been conducted, in order to first assess the performance of the SHB elements in quasi-static and dynamic analyses. Then, deep drawing of a hemispherical cup is performed to demonstrate the capabilities of the SHB elements in handling various types of nonlinearities (large displacements and rotations, anisotropic plasticity, and contact. Compared to classical ABAQUS solid and shell elements, the results given by the SHB elements show good agreement with the reference solutions.

Dynamics of pre-strained bi-material elastic systems linearized three-dimensional approach

CERN Document Server

Akbarov, Surkay D

2015-01-01

This book deals with dynamics of pre-stressed or pre-strained bi-material elastic systems consisting of stack of pre-stressed layers, stack of pre-stressed layers and pre-stressed half space (or half plane), stack of pre-stressed layers as well as absolute rigid foundation, pre-stressed compound solid and hollow cylinders and pre-stressed sandwich hollow cylinders. The problems considered in the book relate to the dynamics of a moving and oscillating moving load, forced vibration caused by linearly located or point located time-harmonic forces acting to the foregoing systems. Moreover, a considerable part of the book relate to the problems regarding the near surface, torsional and axisymmetric longitudinal waves propagation and dispersion in the noted above bi-material elastic systems. The book carries out the investigations within the framework of the piecewise homogeneous body model with the use of the Three-Dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies.

Theoretical assessment of a proposal for the simplified determination of critical loads of elastic shells

International Nuclear Information System (INIS)

Malmberg, T.

1986-08-01

Within the context of the stability analysis of the cryostat of a fusion reactor the question was raised whether or not the rather lengthy conventional stability analysis can be circumvented by applying a simplified strategy based on common linear Finite Element computer programs. This strategy involves the static linear deformation analysis of the structure with and without imperfections. For some simple stability problems this approach has been shown to be successful. The purpose of this study is to derive a general proof of the validity of this approach for thin shells with arbitrary geometry under hydrostatic pressure or dead loading along the boundary. This general assessment involves two types of analyses: 1) A general stability analysis for thin shells; this is based on a simple nonlinear shell theory and a stability criterion in form of the neutral (indifferent) equilibrium condition. This result is taken as reference solution. 2) A general linear deformation analysis for thin imperfect shells and the definition of a suitable scalar parameter (β-parameter) which should represent the reciprocal of the critical load factor. It is shown that the simplified strategy (=β-parameter approach'') generally is not capable to predict the actual critical load factor irrespective whether there is a hydrostatic pressure loading or dead loading along the edge of the shell. This general result is in contrast to the observations made for some simple stability problems. Nevertheless, the results of this study do not exclude the possibility that the simplified strategy will give reasonable approximate solutions at least for a restricted class of stability problems. (orig./HP) [de

A robust approach for analysing dispersion of elastic waves in an orthotropic cylindrical shell

Science.gov (United States)

Kaplunov, J.; Nobili, A.

2017-08-01

Dispersion of elastic waves in a thin orthotropic cylindrical shell is considered, within the framework of classical 2D Kirchhoff-Love theory. In contrast to direct multi-parametric analysis of the lowest propagating modes, an alternative robust approach is proposed that simply requires evaluation of the evanescent modes (quasi-static edge effect), which, at leading order, do not depend on vibration frequency. A shortened dispersion relation for the propagating modes is then derived by polynomial division and its accuracy is numerically tested against the full Kirchhoff-Love dispersion relation. It is shown that the same shortened relation may be also obtained from a refined dynamic version of the semi-membrane theory for cylindrical shells. The presented results may be relevant for modelling various types of nanotubes which, according to the latest experimental findings, possess strong material anisotropy.

Solution strategies for linear and nonlinear instability phenomena for arbitrarily thin shell structures

International Nuclear Information System (INIS)

Eckstein, U.; Harte, R.; Kraetzig, W.B.; Wittek, U.

1983-01-01

In order to describe nonlinear response and instability behaviour the paper starts with the total potential energy considering the basic kinematic equations of a consistent nonlinear shell theory for large displacements and moderate rotations. The material behaviour is assumed to be hyperelastic and isotropic. The incrementation and discretization of the total potential energy leads to the tangent stiffness relation, which is the central equation of computational algorithms based on combined incremental and iterative techniques. Here a symmetrized form of the RIKS/WEMPNER-algorithm for positive and negative load incrementation represents the basis of the nonlinear solution technique. To detect secondary equilibrium branches at points of neutral equilibrium within nonlinear primary paths a quadratic eigenvalue-problem has to be solved. In order to follow those complicated nonlinear response phenomena the RIKS/WEMPNER incrementation/iteration process is combined with a simultaneous solution of the linearized quadratic eigenvalue-problem. Additionally the essentials of a recently derived family of arbitrarily curved shell elements for linear (LACS) and geometrically nonlinear (NACS) shell problems are presented. The main advantage of these elements is the exact description of all geometric properties as well as the energy-equivalent representation of the applied loads in combination with an efficient algorithm to form the stiffness submatrices. Especially the NACS-elements are designed to improve the accuracy of the solution in the deep postbuckling range including moderate rotations. The derived finite elements and solution strategies are applied to a certain number of typical shell problems to prove the precision of the shell elements and to demonstrate the possibilities of tracing linear and nonlinear bifurcation problems as well as snap-through phenomena with and without secondary bifurcation branches. (orig.)

Three-dimensional thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers by differential quadrature method

Energy Technology Data Exchange (ETDEWEB)

Alashti, R. Akbari, E-mail: raalashti@nit.ac.ir [Mechanical Engineering Department, Babol University of Technology, P.O. Box 484, Shariati Avenue, Babol (Iran, Islamic Republic of); Khorsand, M. [Mechanical Engineering Department, Babol University of Technology, P.O. Box 484, Shariati Avenue, Babol (Iran, Islamic Republic of)

2011-05-15

Three-dimensional thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers under the effect of asymmetric thermo-electro-mechanical loads is carried out. Numerical results of displacement, stress and thermal fields are obtained using two versions of the differential quadrature methods, namely polynomial and Fourier quadrature methods. Material properties of the shell are assumed to be graded in the radial direction according to a power law but the Poisson's ratio is assumed to be constant. Shells are considered to be under the effect of the pressure loading in the form of cosine and ring pressure loads, electric potentials and temperature fields. Numerical results for various boundary conditions are obtained and the effects of the thickness of piezoelectric layers, grading index of material properties and the ratio of the thickness to the radius of the shell on these results is presented. - Highlights: > A numerical study of an FGM cylindrical shell with piezoelectric layers is made. > Governing equations are solved by two versions of differential quadrature methods. > The effect of layers thickness, grading index and geometrical ratios is presented.

Three-dimensional thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers by differential quadrature method

International Nuclear Information System (INIS)

Alashti, R. Akbari; Khorsand, M.

2011-01-01

Three-dimensional thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers under the effect of asymmetric thermo-electro-mechanical loads is carried out. Numerical results of displacement, stress and thermal fields are obtained using two versions of the differential quadrature methods, namely polynomial and Fourier quadrature methods. Material properties of the shell are assumed to be graded in the radial direction according to a power law but the Poisson's ratio is assumed to be constant. Shells are considered to be under the effect of the pressure loading in the form of cosine and ring pressure loads, electric potentials and temperature fields. Numerical results for various boundary conditions are obtained and the effects of the thickness of piezoelectric layers, grading index of material properties and the ratio of the thickness to the radius of the shell on these results is presented. - Highlights: → A numerical study of an FGM cylindrical shell with piezoelectric layers is made. → Governing equations are solved by two versions of differential quadrature methods. → The effect of layers thickness, grading index and geometrical ratios is presented.

Three-dimensional dynamo-thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers by DQ-FD coupled

International Nuclear Information System (INIS)

Akbari Alashti, R.; Khorsand, M.

2012-01-01

Three-dimensional elastic analysis is carried out for functionally graded cylindrical shells bonded with piezoelectric layers subjected to dynamic and thermal loads. Material properties are assumed to be graded in the radial direction obeying a simple power law with constant Poisson's ratio. Two versions of differential quadrature (DQ) method coupled with the finite difference (FD) method are employed to discretize the governing differential equations in space and time domains. The convergence is studied and results of the axisymmetric loadings are verified with reported results. Effects of the grading index of material properties, thermal gradient, boundary conditions, thickness of piezoelectric layers and electric excitation on stress, displacement, electric and temperature fields are presented. Highlights: ► Dynamo-thermo-elastic analysis of an FGM shell with piezoelectric layer is carried out. ► Governing equations are solved by DQ-FD coupled. ► Effects of grading index, temperature difference and piezoelectric thickness are presented.

A Lagrangian meshfree method applied to linear and nonlinear elasticity.

Science.gov (United States)

Walker, Wade A

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.

Damage detection strategies for aircraft shell-like structures based on propagation guided elastic waves

International Nuclear Information System (INIS)

Zak, A; Ostachowicz, W; Krawczuk, M

2011-01-01

Damage of aircraft structural elements in any form always present high risks. Failures of these elements can be caused by various reasons including material fatigue or impact leading to damage initiation and growth. Detection of these failures at their earliest stage of development, estimation of their size and location, are one of the most crucial factors for each damage detection method. Structural health monitoring strategies based on propagation of guided elastic waves in structures and wave interaction with damage related discontinuities are very promising tools that offer not only damage detection capabilities, but are also meant to provide precise information about the state of the structures and their remaining lifetime. Because of that various techniques are employed to simulate and mimic the wave-discontinuity interactions. The use of various types of sensors, their networks together with sophisticated contactless measuring techniques are investigated both numerically and experimentally. Certain results of numerical simulations obtained by the use of the spectral finite element method are presented by the authors and related with propagation of guided elastic waves in shell-type aircraft structures. Two types of structures are considered: flat 2D panels with or without stiffeners and 3D shell structures. The applicability of two different damage detection approaches is evaluated in order to detect and localise damage in these structures. Selected results related with the use of laser scanning vibrometry are also presented and discussed by the authors.

Quantification of local and global elastic anisotropy in ultrafine grained gradient microstructures, produced by linear flow splitting

DEFF Research Database (Denmark)

Niehuesbernd, Jörn; Müller, Clemens; Pantleon, Wolfgang

2013-01-01

. Consequently, the macroscopic elastic behavior results from the local elastic properties within the gradient. In the present investigation profiles produced by the linear flow splitting process were examined with respect to local and global elastic anisotropy, which develops during the complex forming process...

Linear Elastic Waves - Series: Cambridge Texts in Applied Mathematics (No. 26)

Science.gov (United States)

Harris, John G.

2001-10-01

Wave propagation and scattering are among the most fundamental processes that we use to comprehend the world around us. While these processes are often very complex, one way to begin to understand them is to study wave propagation in the linear approximation. This is a book describing such propagation using, as a context, the equations of elasticity. Two unifying themes are used. The first is that an understanding of plane wave interactions is fundamental to understanding more complex wave interactions. The second is that waves are best understood in an asymptotic approximation where they are free of the complications of their excitation and are governed primarily by their propagation environments. The topics covered include reflection, refraction, the propagation of interfacial waves, integral representations, radiation and diffraction, and propagation in closed and open waveguides. Linear Elastic Waves is an advanced level textbook directed at applied mathematicians, seismologists, and engineers. Aimed at beginning graduate students Includes examples and exercises Has application in a wide range of disciplines

DNA nanoparticles with core-shell morphology.

Science.gov (United States)

Chandran, Preethi L; Dimitriadis, Emilios K; Lisziewicz, Julianna; Speransky, Vlad; Horkay, Ferenc

2014-10-14

Mannobiose-modified polyethylenimines (PEI) are used in gene therapy to generate nanoparticles of DNA that can be targeted to the antigen-presenting cells of the immune system. We report that the sugar modification alters the DNA organization within the nanoparticles from homogenous to shell-like packing. The depth-dependent packing of DNA within the nanoparticles was probed using AFM nano-indentation. Unmodified PEI-DNA nanoparticles display linear elastic properties and depth-independent mechanics, characteristic of homogenous materials. Mannobiose-modified nanoparticles, however, showed distinct force regimes that were dependent on indentation depth, with 'buckling'-like response that is reproducible and not due to particle failure. By comparison with theoretical studies of spherical shell mechanics, the structure of mannobiosylated particles was deduced to be a thin shell with wall thickness in the order of few nanometers, and a fluid-filled core. The shell-core structure is also consistent with observations of nanoparticle denting in altered solution conditions, with measurements of nanoparticle water content from AFM images, and with images of DNA distribution in Transmission Electron Microscopy.

Finite element analysis program for shells of revolution: ISTRAN/SR, 4

International Nuclear Information System (INIS)

Chiba, Toshio

1980-01-01

The computational capabilities available in the current version of ISTRAN/SR for stress analysis of shells of revolution have been described in the 1st, 2nd and 3rd reports. This report describes the linear elastic dynamic analysis of shells of revolution under axisymmetric and asymmetric loadings. The shell, idealized as a curved element and cubic function for all displacements, is used. A method for solution of the equations of motion is described with special emphasis on the computational aspect of the solution. Three solution methods, which can be employed for the linear dynamic analysis, are possible - direct integration method, mode superposition method, and spectrum analysis method. Each method involves a numerical method which must be formulated in effective form for computer implementation - solution of linear equations, evaluation of eigenvalues and eigenvectors, and step-by-step numerical integration. In this program, the skyline method is employed for the solution of linear equations, and the subspace method and the determinant search method are employed for eigenproblem. The Newmark-Wilson method is employed for the step-by-step integration. The comparison of the solution of ISTRAN/SR and other numerical solution shows good agreement. (author)

Linear elastic properties derivation from microstructures representative of transport parameters.

Science.gov (United States)

Hoang, Minh Tan; Bonnet, Guy; Tuan Luu, Hoang; Perrot, Camille

2014-06-01

It is shown that three-dimensional periodic unit cells (3D PUC) representative of transport parameters involved in the description of long wavelength acoustic wave propagation and dissipation through real foam samples may also be used as a standpoint to estimate their macroscopic linear elastic properties. Application of the model yields quantitative agreement between numerical homogenization results, available literature data, and experiments. Key contributions of this work include recognizing the importance of membranes and properties of the base material for the physics of elasticity. The results of this paper demonstrate that a 3D PUC may be used to understand and predict not only the sound absorbing properties of porous materials but also their transmission loss, which is critical for sound insulation problems.

Neoclassical Solution of Transient Interaction of Plane Acoustic Waves with a Spherical Elastic Shell

Directory of Open Access Journals (Sweden)

Hanson Huang

1996-01-01

Full Text Available A detailed solution to the transient interaction of plane acoustic waves with a spherical elastic shell was obtained more than a quarter of a century ago based on the classical separation of variables, series expansion, and Laplace transform techniques. An eight-term summation of the time history series was sufficient for the convergence of the shell deflection and strain, and to a lesser degree, the shell velocity. Since then, the results have been used routinely for validation of solution techniques and computer methods for the evaluation of underwater explosion response of submerged structures. By utilizing modern algorithms and exploiting recent advances of computer capacities and floating point mathematics, sufficient terms of the inverse Laplace transform series solution can now be accurately computed. Together with the application of the Cesaro summation using up to 70 terms of the series, two primary deficiencies of the previous solution are now remedied: meaningful time histories of higher time derivative data such as acceleration and pressure are now generated using a sufficient number of terms in the series; and uniform convergence around the discontinuous step wave front is now obtained, completely eradicating spurious oscillations due to the Gibbs' phenomenon. New results of time histories of response items of interest are presented.

A reexamination of some puzzling results in linearized elasticity

Indian Academy of Sciences (India)

University of North Carolina at Charlotte, Charlotte, NC 28223-0001, USA e-mail: jogc@mecheng.iisc.ernet.in; ..... ˆT (F) = C[ϵ] + o(∇u), where ϵ = [∇u+(∇u)T ]/2, and C = D ˆT (I) is the elasticity tensor, and one also linearizes the body force vector to get b = QT [ b∗ − ¨c. ] − ˙ × X − × ( × X) − 2 × v,. (5) where X is the position ...

Analysis on Forced Vibration of Thin-Wall Cylindrical Shell with Nonlinear Boundary Condition

Directory of Open Access Journals (Sweden)

Qiansheng Tang

2016-01-01

Full Text Available Forced vibration of thin-wall cylindrical shell under nonlinear boundary condition was discussed in this paper. The nonlinear boundary was modeled as supported clearance in one end of shell and the restraint was assumed as linearly elastic in the radial direction. Based on Sanders’ shell theory, Lagrange equation was utilized to derive the nonlinear governing equations of cylindrical shell. The displacements in three directions were represented by beam functions and trigonometric functions. In the study of nonlinear dynamic responses of thin-wall cylindrical shell with supported clearance under external loads, the Newmark method is used to obtain time history, frequency spectrum plot, phase portraits, Poincare section, bifurcation diagrams, and three-dimensional spectrum plot with different parameters. The effects of external loads, supported clearance, and support stiffness on nonlinear dynamics behaviors of cylindrical shell with nonlinear boundary condition were discussed.

Bulk solitary waves in elastic solids

Science.gov (United States)

Samsonov, A. M.; Dreiden, G. V.; Semenova, I. V.; Shvartz, A. G.

2015-10-01

A short and object oriented conspectus of bulk solitary wave theory, numerical simulations and real experiments in condensed matter is given. Upon a brief description of the soliton history and development we focus on bulk solitary waves of strain, also known as waves of density and, sometimes, as elastic and/or acoustic solitons. We consider the problem of nonlinear bulk wave generation and detection in basic structural elements, rods, plates and shells, that are exhaustively studied and widely used in physics and engineering. However, it is mostly valid for linear elasticity, whereas dynamic nonlinear theory of these elements is still far from being completed. In order to show how the nonlinear waves can be used in various applications, we studied the solitary elastic wave propagation along lengthy wave guides, and remarkably small attenuation of elastic solitons was proven in physical experiments. Both theory and generation for strain soliton in a shell, however, remained unsolved problems until recently, and we consider in more details the nonlinear bulk wave propagation in a shell. We studied an axially symmetric deformation of an infinite nonlinearly elastic cylindrical shell without torsion. The problem for bulk longitudinal waves is shown to be reducible to the one equation, if a relation between transversal displacement and the longitudinal strain is found. It is found that both the 1+1D and even the 1+2D problems for long travelling waves in nonlinear solids can be reduced to the Weierstrass equation for elliptic functions, which provide the solitary wave solutions as appropriate limits. We show that the accuracy in the boundary conditions on free lateral surfaces is of crucial importance for solution, derive the only equation for longitudinal nonlinear strain wave and show, that the equation has, amongst others, a bidirectional solitary wave solution, which lead us to successful physical experiments. We observed first the compression solitary wave in the

The local response of elastic tubes and shells to spherical pressure pulse loading

International Nuclear Information System (INIS)

Thompson, J.J.; Holy, Z.J.

1977-01-01

This paper develops a formulation and numerical solution technique for calculating the peak transient stresses developed in tubes or shells with external and internal acoustic media, as a result of shock loadings which may be represented as originating from external or internal point symmetric or dipole sources. The field of application is intended to be the local peak response of the cylindrical fuel cans, core barrels, pressure vessels, pipes and containment shells of Nuclear Reactor Technology, subjected to transient pressure shock loadings for a variety of operational or accident conditions, which cannot adequately be described as one dimensional plane shocks, for which elastic shell responses have been presented by other workers. The work reported here concerns the basic problem of an infinite static fluid filled hollow cylinder of arbitrary thickness, in an infinite static fluid medium, with a source at an arbitrary internal or external radial location. An acoustic model is used, with acoustic damping due to radiation as the only possible damping mechanism. The formulation and solution technique is based on the availability of the multi-dimensional Fast Fourier Transform algorithm. The basic result is the representation, in cylindrical co-ordinates, of the two dimensional (time and axial co-ordinate) Fourier Transform of the infinite medium frequency response function for outgoing waves from a point symmetrical source, as a series of azimuthal Fourier harmonics, from which the result for a dipole source of arbitrary orientation follows. Where possible numerical results will be presented

Contribution to the study of heavy-ion induced quasi-elastic processes in the 2s-1d shell

International Nuclear Information System (INIS)

Greiner, A.

1982-06-01

In the first part of this thesis, we present a study of the charge exchange reaction 28 Si( 18 O, 18 F) 28 Al at 56 MeV. This reaction can be easily understood in terms of a one-step direct charge exchange mechanism. With a very simple shell model, it can be interpreted that a neutron of the 18 O in the Jsup(π)=0 + , T=1 state interacts with a proton in the dsub(5/2) shell of 28 Si and they exchange their spin and charge forming Jsup(π)=1 + , T=0 18 F, and Jsup(π)=3 + or 2 + , T=1 28 Al. In the present analysis of data, we have first performed the direct charge exchange DWBA calculations. These results are compared with the exact-finite-range (EFR) second order DWBA calculations which take into account the successive one-nucleon stripping and pickup, and pickup and stripping process. In the second part, we wish to report results and analysis concerning the 24 Mg+ 12 C system. The 180 0 c.m. angle scattering excitation functions were measured between 12- and 27-MeV c.m. corresponding to a range in the compound 36 Ar excitation energy of 28.3 to 43.3 MeV. Several angular distributions for the elastic and inelastic scattering have been measured on the top of the bumps of the elastic scattering excitation function. These elastic scattering angular distributions cannot be fitted by a single squared Legendre polynomial of order L. A complete phase shift analysis is presented. We discuss also the shapes of the first 24 Mg 2 + inelastic scattering angular distributions with respect to the shape of the elastic scattering differential cross section [fr

Indentation of Ellipsoidal and Cylindrical Elastic Shells

KAUST Repository

Vella, Dominic; Ajdari, Amin; Vaziri, Ashkan; Boudaoud, Arezki

2012-01-01

Thin shells are found in nature at scales ranging from viruses to hens' eggs; the stiffness of such shells is essential for their function. We present the results of numerical simulations and theoretical analyses for the indentation of ellipsoidal

Astronomical optics and elasticity theory

CERN Document Server

Lemaitre, Gerard Rene

2008-01-01

Astronomical Optics and Elasticity Theory provides a very thorough and comprehensive account of what is known in this field. After an extensive introduction to optics and elasticity, the book discusses variable curvature and multimode deformable mirrors, as well as, in depth, active optics, its theory and applications. Further, optical design utilizing the Schmidt concept and various types of Schmidt correctors, as well as the elasticity theory of thin plates and shells are elaborated upon. Several active optics methods are developed for obtaining aberration corrected diffraction gratings. Further, a weakly conical shell theory of elasticity is elaborated for the aspherization of grazing incidence telescope mirrors. The very didactic and fairly easy-to-read presentation of the topic will enable PhD students and young researchers to actively participate in challenging astronomical optics and instrumentation projects.

Triggered Snap-Through of Bistable Shells

Science.gov (United States)

Cai, Yijie; Huang, Shicheng; Trase, Ian; Hu, Nan; Chen, Zi

Elastic bistable shells are common structures in nature and engineering, such as the lobes of the Venus flytrap or the surface of a toy jumping poppers. Despite their ubiquity, the parameters that control the bistability of such structures are not well understood. In this study, we explore how the geometrical features of radially symmetric elastic shells affect the shape and potential energy of a shell's stable states, and how to tune certain parameters in order to generate a snap-through transition from a convex semi-stable state to concave stable state. We fabricated a series of elastic shells with varying geometric parameters out of silicone rubber and measured the resulting potential energy in the semi-stable state. Finite element simulations were also conducted in order to determine the deformation and stress in the shells during snap-through. It was found that the energy of the semi-stable state is controlled by only two geometric parameters and a dimensionless ratio. We also noted two distinct transitions during snap-through, one between monostability and semi-bistability (the state a popper toy is in before it snaps-through and jumps), and a second transition between semi-bistability and true bistability. This work shows that it is possible to use a set of simple parameters to tailor the energy landscape of an elastic shell in order to generate complex trigger motions for their potential use in smart applications. Z.C. acknowledge support from Society in Science-Branco Weiss Fellowship, administered by ETH Zurich.

Compact solitary waves in linearly elastic chains with non-smooth on-site potential

Energy Technology Data Exchange (ETDEWEB)

Gaeta, Giuseppe [Dipartimento di Matematica, Universita di Milano, Via Saldini 50, 20133 Milan (Italy); Gramchev, Todor [Dipartimento di Matematica e Informatica, Universita di Cagliari, Via Ospedale 72, 09124 Cagliari (Italy); Walcher, Sebastian [Lehrstuhl A Mathematik, RWTH Aachen, 52056 Aachen (Germany)

2007-04-27

It was recently observed by Saccomandi and Sgura that one-dimensional chains with nonlinear elastic interaction and regular on-site potential can support compact solitary waves, i.e. travelling solitary waves with strictly compact support. In this paper, we show that the same applies to chains with linear elastic interaction and an on-site potential which is continuous but non-smooth at minima. Some different features arise; in particular, the speed of compact solitary waves is not uniquely fixed by the equation. We also discuss several generalizations of our findings.

HANFORD DOUBLE-SHELL TANK THERMAL AND SEISMIC PROJECT-SENSITIVITY OF DOUBLE-SHELL DYNAMIC RESPONSE TO THE WASTE ELASTIC PROPERTIES

International Nuclear Information System (INIS)

Mackey, T.C.; Abatt, F.G.; Johnson, K.I.

2009-01-01

The purpose of this study was to determine the sensitivity of the dynamic response of the Hanford double-shell tanks (DSTs) to the assumptions regarding the constitutive properties of the contained waste. In all cases, the waste was modeled as a uniform linearly elastic material. The focus of the study was on the changes in the modal response of the tank and waste system as the extensional modulus (elastic modulus in tension and compression) and shear modulus of the waste were varied through six orders of magnitude. Time-history analyses were also performed for selected cases and peak horizontal reaction forces and axial stresses at the bottom of the primary tank were evaluated. Because the analysis focused on the differences in the responses between solid-filled and liquid-filled tanks, it is a comparative analysis rather than an analysis of record for a specific tank or set of tanks. The shear modulus was varied between 4 x 10 3 Pa and 4.135 x 10 9 Pa. The lowest value of shear modulus was sufficient to simulate the modal response of a liquid-containing tank, while the higher values are several orders of magnitude greater than the upper limit of expected properties for tank contents. The range of elastic properties used was sufficient to show liquid-like response at the lower values, followed by a transition range of semi-solid-like response to a clearly identifiable solid-like response. It was assumed that the mechanical properties of the tank contents were spatially uniform. Because sludge-like materials are expected only to exist in the lower part of the tanks, this assumption leads to an exaggeration of the effects of sludge-like materials in the tanks. The results of the study show that up to a waste shear modulus of at least 40,000 Pa, the modal properties of the tank and waste system are very nearly the same as for the equivalent liquid-containing tank. This suggests that the differences in critical tank responses between liquid-containing tanks and tanks

HANFORD DOUBLE SHELL TANK THERMAL AND SEISMIC PROJECT SENSITIVITY OF DOUBLE SHELL DYNAMIC RESPONSE TO THE WASTE ELASTIC PROPERTIES

Energy Technology Data Exchange (ETDEWEB)

MACKEY TC; ABATT FG; JOHNSON KI

2009-01-16

The purpose of this study was to determine the sensitivity of the dynamic response of the Hanford double-shell tanks (DSTs) to the assumptions regarding the constitutive properties of the contained waste. In all cases, the waste was modeled as a uniform linearly elastic material. The focus of the study was on the changes in the modal response of the tank and waste system as the extensional modulus (elastic modulus in tension and compression) and shear modulus of the waste were varied through six orders of magnitude. Time-history analyses were also performed for selected cases and peak horizontal reaction forces and axial stresses at the bottom of the primary tank were evaluated. Because the analysis focused on the differences in the responses between solid-filled and liquid-filled tanks, it is a comparative analysis rather than an analysis of record for a specific tank or set of tanks. The shear modulus was varied between 4 x 10{sup 3} Pa and 4.135 x 10{sup 9} Pa. The lowest value of shear modulus was sufficient to simulate the modal response of a liquid-containing tank, while the higher values are several orders of magnitude greater than the upper limit of expected properties for tank contents. The range of elastic properties used was sufficient to show liquid-like response at the lower values, followed by a transition range of semi-solid-like response to a clearly identifiable solid-like response. It was assumed that the mechanical properties of the tank contents were spatially uniform. Because sludge-like materials are expected only to exist in the lower part of the tanks, this assumption leads to an exaggeration of the effects of sludge-like materials in the tanks. The results of the study show that up to a waste shear modulus of at least 40,000 Pa, the modal properties of the tank and waste system are very nearly the same as for the equivalent liquid-containing tank. This suggests that the differences in critical tank responses between liquid-containing tanks

A two-dimensional linear elasticity problem for anisotropic materials, solved with a parallelization code

Directory of Open Access Journals (Sweden)

Mihai-Victor PRICOP

2010-09-01

Full Text Available The present paper introduces a numerical approach of static linear elasticity equations for anisotropic materials. The domain and boundary conditions are simple, to enhance an easy implementation of the finite difference scheme. SOR and gradient are used to solve the resulting linear system. The simplicity of the geometry is also useful for MPI parallelization of the code.

The Simulation and Correction to the Brain Deformation Based on the Linear Elastic Model in IGS

Institute of Scientific and Technical Information of China (English)

MU Xiao-lan; SONG Zhi-jian

2004-01-01

@@ The brain deformation is a vital factor affecting the precision of the IGS and it becomes a hotspot to simulate and correct the brain deformation recently.The research organizations, which firstly resolved the brain deformation with the physical models, have the Image Processing and Analysis department of Yale University, Biomedical Modeling Lab of Vanderbilt University and so on. The former uses the linear elastic model; the latter uses the consolidation model.The linear elastic model only needs to drive the model using the surface displacement of exposed brain cortex,which is more convenient to be measured in the clinic.

Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

Directory of Open Access Journals (Sweden)

Humberto Breves Coda

2009-01-01

Full Text Available This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples.

On the application of the procedure of dynamic relaxation for the calculation of an elastical bedded hushy sperical shell

International Nuclear Information System (INIS)

Thiede, R.

1980-01-01

In the treatment of elastically embeded shells by finite element methods, a calculation of the rigid body deformations before each iteration essentially improves the convergence of the method. This is also the case when calculating with fictitions densities instead of the real material densities. Some evidence has been obtained for the choice of a damping factor by empirical evaluation of several model calculations. (GL) [de

Plastic buckling of cylindrical shells

International Nuclear Information System (INIS)

Bandyopadhyay, K.; Xu, J.; Shteyngart, S.; Eckert, H.

1994-01-01

Cylindrical shells exhibit buckling under axial loads at stresses much less than the respective theoretical critical stresses. This is due primarily to the presence of geometrical imperfections even though such imperfections could be very small (e.g., comparable to thickness). Under internal pressure, the shell regains some of its buckling strength. For a relatively large radius-to-thickness ratio and low internal pressure, the effect can be reasonably estimated by an elastic analysis. However, for low radius-to-thickness ratios and greater pressures, the elastic-plastic collapse controls the failure load. in order to quantify the elastic-plastic buckling capacity of cylindrical shells, an analysis program was carried out by use of the computer code BOSOR5 developed by Bushnell of Lockheed Missiles and Space Company. The analysis was performed for various radius-to-thickness ratios and imperfection amplitudes. The purpose of the analytical program was to compute the buckling strength of underground cylindrical tanks, that are used for storage of nuclear wastes, for realistic geometric imperfections and internal pressure loads. This paper presents the results of the elastic-plastic analyses and compares them with other available information for various pressure loads

Integrodifferential relations in linear elasticity

CERN Document Server

Kostin, Georgy V

2012-01-01

This work treats the elasticity of deformed bodies, including the resulting interior stresses and displacements.It also takes into account that some of constitutive relations can be considered in a weak form. To discuss this problem properly, the method of integrodifferential relations is used, and an advanced numerical technique for stress-strain analysis is presented and evaluated using various discretization techniques. The methods presented in this book are of importance for almost all elasticity problems in materials science and mechanical engineering.

Non-linear theory of elasticity

CERN Document Server

Lurie, AI

2012-01-01

This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.

Influence of time-dependent elastic-plastic material behaviour on the load-carrying capacity of shells of revolution

International Nuclear Information System (INIS)

Schnabel, F.

1987-01-01

The present report deals with the influence of time-dependent material behavior on the load-carrying capacity of thin-walled shells of revolution. In the first part various creep-hardening hypotheses as well as the spatial and temporal discretization procedures employed are described. The adaptation of a well-tested finite element method based on ring elements to the treatment of creep problems and several time-integration procedures, in particular the iterative treatment of the coupling between creep and elastic-plastic strains as well as the important aspect of time-step-control are discussed in detail. In the second part several typical shell configurations are analyzed and a comparison with available theoretical and experimental results is made. Finally, the time-dependent load-carrying behavior of torispherical pressure vessel ends subjected to internal and external pressure is investigated and design aids for the determination of creep collapse times are proposed. (orig.) [de

On the mechanics of elastic lines in thin shells

Science.gov (United States)

Benet, Eduard; Vernerey, Franck

The deformation of soft shells in nature and engineering is often conditioned by the presence of lines whose mechanical properties are different from the shell. For instance, the deformation of tree leaves is conditioned by the presence of harder stems, and cell mitosis is driven by a stiffening line along its membrane. From an experimental standpoint, many groups have taken advantage of this feature to develop self-actuated shells with prescribed deformations. Examples include the polymerization of gels along certain lines, or the inclusion of stiffer lines via 3D printing. However, there is not yet a general continuum theory that accounts for this type of discontinuity within the membrane. Hence, we extend the general shell theory to account for the inclusion of a line that potentially induces jumps in stresses, couple stresses and moments, across its thickness. This is achieved via coupling the rod and the membrane deformations, and ensuring continuity of displacements. The model is then applied to three important problems: a constriction disc inside a shell of revolution, the induced twisting of a shell via the torsion of an embedded line, and the effect of an helicoidal line on the uni-axial deformation of a cylindrical shell. National Science Foundation CAREER award 1350090.

Amorphous TiO2 Shells: A Vital Elastic Buffering Layer on Silicon Nanoparticles for High-Performance and Safe Lithium Storage.

Science.gov (United States)

Yang, Jianping; Wang, Yunxiao; Li, Wei; Wang, Lianjun; Fan, Yuchi; Jiang, Wan; Luo, Wei; Wang, Yang; Kong, Biao; Selomulya, Cordelia; Liu, Hua Kun; Dou, Shi Xue; Zhao, Dongyuan

2017-12-01

Smart surface coatings of silicon (Si) nanoparticles are shown to be good examples for dramatically improving the cyclability of lithium-ion batteries. Most coating materials, however, face significant challenges, including a low initial Coulombic efficiency, tedious processing, and safety assessment. In this study, a facile sol-gel strategy is demonstrated to synthesize commercial Si nanoparticles encapsulated by amorphous titanium oxide (TiO 2 ), with core-shell structures, which show greatly superior electrochemical performance and high-safety lithium storage. The amorphous TiO 2 shell (≈3 nm) shows elastic behavior during lithium discharging and charging processes, maintaining high structural integrity. Interestingly, it is found that the amorphous TiO 2 shells offer superior buffering properties compared to crystalline TiO 2 layers for unprecedented cycling stability. Moreover, accelerating rate calorimetry testing reveals that the TiO 2 -encapsulated Si nanoparticles are safer than conventional carbon-coated Si-based anodes. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Parity dependence in the optical potential of sd-shell nuclei

International Nuclear Information System (INIS)

Ferrero, J.L.; Ruiz, J.A.; Bilwes, B.; Bilwes, R.

1989-01-01

Elastic scattering between sd-shell nuclei differing by one, two, three and four nucleons has been measured. The oscillating pattern of the angular distributions, when it is observed, is attributed to the interference between direct elastic scattering and elastic transfer. Explicit DWBA treatment of the elastic transfer or parity dependent real potential analysis allow both a good reproduction of the data. The sign and the importance of the parity potential deduced by fitting the data are in good agreement with the predictions of microscopic calculations in the two centre shell-model

Force sensing using 3D displacement measurements in linear elastic bodies

Science.gov (United States)

Feng, Xinzeng; Hui, Chung-Yuen

2016-07-01

In cell traction microscopy, the mechanical forces exerted by a cell on its environment is usually determined from experimentally measured displacement by solving an inverse problem in elasticity. In this paper, an innovative numerical method is proposed which finds the "optimal" traction to the inverse problem. When sufficient regularization is applied, we demonstrate that the proposed method significantly improves the widely used approach using Green's functions. Motivated by real cell experiments, the equilibrium condition of a slowly migrating cell is imposed as a set of equality constraints on the unknown traction. Our validation benchmarks demonstrate that the numeric solution to the constrained inverse problem well recovers the actual traction when the optimal regularization parameter is used. The proposed method can thus be applied to study general force sensing problems, which utilize displacement measurements to sense inaccessible forces in linear elastic bodies with a priori constraints.

Compressible convection in a rotating spherical shell. II. A linear anelastic model

International Nuclear Information System (INIS)

Glatzmaier, G.A.; Gilman, P.A.

1981-01-01

We study the onset of convection for a compressible fluid in a rotating spherical shell via linear anelastic fluid equations for a depth of 40% of the radius, constant kinematic viscosity and thermometric diffusivity, Taylor numbers up to 10 5 , and density stratifications up to seven e-folds across the zone. The perturbations are expanded in spherical harmonics, and the radially dependent equations are solved with a Newton-Raphson relaxation method

Linear analysis using secants for materials with temperature dependent nonlinear elastic modulus and thermal expansion properties

Science.gov (United States)

Pepi, John W.

2017-08-01

Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.

The homogeneous boundary value problem of the thick spherical shell

International Nuclear Information System (INIS)

Linder, F.

1975-01-01

With the aim to solve boundary value problems in the same manner as it is attained at thin shell theory (Superposition of Membrane solution to solution of boundary values), one has to search solutions of the equations of equilibrium of the three dimensional thick shell which produce tensions at the cut edge and are zero on the whole shell surface inside and outside. This problem was solved with the premissions of the linear theory of Elasticity. The gained solution is exact and contains the symmetric and non-symmetric behaviour and is described in relatively short analytical expressions for the deformations and tensions, after the problem of the coupled system had been solved. The static condition of the two surfaces (zero tension) leads to a homogeneous system of complex equations with the index of the Legendre spherical function as Eigenvalue. One symmetrical case is calculated numerically and is compared with the method of finite elements. This comparison results in good accordance. (Auth.)

Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads

Directory of Open Access Journals (Sweden)

Donald Mark Santee

2006-01-01

Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.

Elastic-plastic analysis of part-through crack propagation in piping and pressure vessels

International Nuclear Information System (INIS)

Souza, L.A. de; Ebecken, N.F.F.

1986-01-01

The shell structures, often used in the construction of reservoirs, pipings, pressure vessels, nuclear power plants, etc, with part-through crack along its thickness, are analysed, using a computer system developed by the finite element method. The surface is discretized with three-dimensional quadratic elements, degenerated in its mid-surface, such the fracture is simulated by scalar elements (non linear springs). The results are analysed by the stress intensity factor K Sub(I) and the strain energy release rate, which is known as J-integral. The analysis is performed in the elastic and elastic-plastic regime. The basic hipothesis and the formulation adopted in the derivation of the scalar elements are also shown. (Author) [pt

Dispersion of axially symmetric waves in fluid-filled cylindrical shells

DEFF Research Database (Denmark)

Bao, X.L.; Überall, H.; Raju, P. K.

2000-01-01

Acoustic waves normally incident on an elastic cylindrical shell can cause the excitation of circumferential elastic waves on the shell. These shells may be empty and fluid immersed, or fluid filled in an ambient medium of air, or doubly fluid loaded inside and out. Circumferential waves...... on such shells have been investigated for the case of aluminum shells, and their phase-velocity dispersion curves have been obtained for double fluid loading [Bao, Raju, and Überall, J. Acoust. Soc. Am. 105, 2704 (1999)]. Similar results were obtained for empty or fluid-filled brass shells [Kumar, Acustica 27......, 317 (1972)]. We have extended the work of Kumar to the case of fluid-filled aluminum shells and steel shells imbedded in air. These cases demonstrate the existence of circumferential waves traveling in the filler fluid, exhibiting a certain simplicity of the dispersion curves of these waves...

Boundary value problems of the circular cylinders in the strain-gradient theory of linear elasticity

International Nuclear Information System (INIS)

Kao, B.G.

1979-11-01

Three boundary value problems in the strain-gradient theory of linear elasticity are solved for circular cylinders. They are the twisting of circular cylinder, uniformly pressuring of concentric circular cylinder, and pure-bending of simply connected cylinder. The comparisons of these solutions with the solutions in classical elasticity and in couple-stress theory reveal the differences in the stress fields as well as the apparent stress fields due to the influences of the strain-gradient. These aspects of the strain-gradient theory could be important in modeling the failure behavior of structural materials

Muscle shear elastic modulus is linearly related to muscle torque over the entire range of isometric contraction intensity.

Science.gov (United States)

Ateş, Filiz; Hug, François; Bouillard, Killian; Jubeau, Marc; Frappart, Thomas; Couade, Mathieu; Bercoff, Jeremy; Nordez, Antoine

2015-08-01

Muscle shear elastic modulus is linearly related to muscle torque during low-level contractions (torque over the entire range of isometric contraction and (ii) the influence of the size of the region of interest (ROI) used to average the shear modulus value. Ten healthy males performed two incremental isometric little finger abductions. The joint torque produced by Abductor Digiti Minimi was considered as an index of muscle torque and elastic modulus. A high coefficient of determination (R(2)) (range: 0.86-0.98) indicated that the relationship between elastic modulus and torque can be accurately modeled by a linear regression over the entire range (0% to 100% of MVC). The changes in shear elastic modulus as a function of torque were highly repeatable. Lower R(2) values (0.89±0.13 for 1/16 of ROI) and significantly increased absolute errors were observed when the shear elastic modulus was averaged over smaller ROI, half, 1/4 and 1/16 of the full ROI) than the full ROI (mean size: 1.18±0.24cm(2)). It suggests that the ROI should be as large as possible for accurate measurement of muscle shear modulus. Copyright © 2015 Elsevier Ltd. All rights reserved.

Evaluating and interpreting the chemical relevance of the linear response kernel for atoms II: open shell.

Science.gov (United States)

Boisdenghien, Zino; Fias, Stijn; Van Alsenoy, Christian; De Proft, Frank; Geerlings, Paul

2014-07-28

Most of the work done on the linear response kernel χ(r,r') has focussed on its atom-atom condensed form χAB. Our previous work [Boisdenghien et al., J. Chem. Theory Comput., 2013, 9, 1007] was the first effort to truly focus on the non-condensed form of this function for closed (sub)shell atoms in a systematic fashion. In this work, we extend our method to the open shell case. To simplify the plotting of our results, we average our results to a symmetrical quantity χ(r,r'). This allows us to plot the linear response kernel for all elements up to and including argon and to investigate the periodicity throughout the first three rows in the periodic table and in the different representations of χ(r,r'). Within the context of Spin Polarized Conceptual Density Functional Theory, the first two-dimensional plots of spin polarized linear response functions are presented and commented on for some selected cases on the basis of the atomic ground state electronic configurations. Using the relation between the linear response kernel and the polarizability we compare the values of the polarizability tensor calculated using our method to high-level values.

Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem

Energy Technology Data Exchange (ETDEWEB)

Yoo, Jaechil [Univ. of Wisconsin, Madison, WI (United States)

1996-12-31

Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we prove the convergence of a multigrid (W-cycle) method. This multigrid is robust in that the convergence is uniform as the parameter, v, goes to 1/2 Computational experiments are included.

Extensions to a nonlinear finite-element axisymmetric shell model based on Reissner's shell theory

International Nuclear Information System (INIS)

Cook, W.A.

1981-01-01

Extensions to shell analysis not usually associated with shell theory are described in this paper. These extensions involve thick shells, nonlinear materials, a linear normal stress approximation, and a changing shell thickness. A finite element shell-of-revolution model has been developed to analyze nuclear material shipping containers under severe impact conditions. To establish the limits for this shell model, the basic assumptions used in its development were studied; these are listed in this paper. Several extensions were evident from the study of these limits: a thick shell, a plastic hinge, and a linear normal stress

The CEASEMT system (Calculation and Analysis of Structures in Mechanics and Thermics). Program TRICO. Analysis of tridimensionnal structures made of shells and beams. Statics - Dynamics - Elasticity - Plasticity - Collapse - Large displacements

International Nuclear Information System (INIS)

Hoffmann, Alain; Jeanpierre, Francoise.

1976-01-01

The TRICO subroutine of the CEASEMT system is especially intended for elastic or plastic computation of structures made of thin shells and beams. TRICO involves the finite element method for shells and beams, and is also suitable for a dynamic structural analysis: eigenmode and eigenfrequency analysis, and analysis of the response to various sinusoidal excitations, or time dependent elastic and plastic loading. Structures may have various shapes composed of a number of materials. Data are distributed between different optional commands having a precise physical sense, corresponding to a sequential program. A dynamic memory control provides the adaptation of the size of the program to that of the problem to be solved [fr

Isogeometric BDDC deluxe preconditioners for linear elasticity

KAUST Repository

Pavarino, L. F.

2018-03-14

Balancing Domain Decomposition by Constraints (BDDC) preconditioners have been shown to provide rapidly convergent preconditioned conjugate gradient methods for solving many of the very ill-conditioned systems of algebraic equations which often arise in finite element approximations of a large variety of problems in continuum mechanics. These algorithms have also been developed successfully for problems arising in isogeometric analysis. In particular, the BDDC deluxe version has proven very successful for problems approximated by Non-Uniform Rational B-Splines (NURBS), even those of high order and regularity. One main purpose of this paper is to extend the theory, previously fully developed only for scalar elliptic problems in the plane, to problems of linear elasticity in three dimensions. Numerical experiments supporting the theory are also reported. Some of these experiments highlight the fact that the development of the theory can help to decrease substantially the dimension of the primal space of the BDDC algorithm, which provides the necessary global component of these preconditioners, while maintaining scalability and good convergence rates.

Isogeometric BDDC deluxe preconditioners for linear elasticity

KAUST Repository

Pavarino, L. F.; Scacchi, S.; Widlund, O. B.; Zampini, Stefano

2018-01-01

Balancing Domain Decomposition by Constraints (BDDC) preconditioners have been shown to provide rapidly convergent preconditioned conjugate gradient methods for solving many of the very ill-conditioned systems of algebraic equations which often arise in finite element approximations of a large variety of problems in continuum mechanics. These algorithms have also been developed successfully for problems arising in isogeometric analysis. In particular, the BDDC deluxe version has proven very successful for problems approximated by Non-Uniform Rational B-Splines (NURBS), even those of high order and regularity. One main purpose of this paper is to extend the theory, previously fully developed only for scalar elliptic problems in the plane, to problems of linear elasticity in three dimensions. Numerical experiments supporting the theory are also reported. Some of these experiments highlight the fact that the development of the theory can help to decrease substantially the dimension of the primal space of the BDDC algorithm, which provides the necessary global component of these preconditioners, while maintaining scalability and good convergence rates.

Rectangular Shell Plating Under Uniformly Distributed Hydrostatic Pressure

Science.gov (United States)

Neubert, M; Sommer, A

1940-01-01

A check of the calculation methods used by Foppl and Henky for investigating the reliability of shell plating under hydrostatic pressure has proved that the formulas yield practical results within the elastic range of the material. Foppl's approximate calculation leaves one on the safe side. It further was found on the basis of the marked ductility of the shell plating under tensile stress that the strength is from 50 to 100 percent higher in the elastic range than expected by either method.

Study on modal characteristics of perforated shell using effective Young's modulus

International Nuclear Information System (INIS)

Jhung, Myung Jo; Yu, Seon Oh

2011-01-01

Research highlights: → The effective Young's modulus of perforated shell is proposed for modal analysis. → The penetration pattern is almost negligible for effective elastic constants. → The frequency of perforated shell decreases significantly due to the hole effect. - Abstract: For the perforated cylindrical shell submerged in fluid, it is almost impossible to develop a finite element model due to the necessity of the fine meshing of the shell and the fluid at the same time. This necessitates the use of solid shell with effective material properties. Unfortunately the effective elastic constants are not found in any references even though the ASME code is suggesting those for perforated plate. Therefore in this study the effective material properties of perforated shell are suggested by performing several finite element analyses with respect to the ligament efficiencies.

New non-linear model of groundwater recharge: Inclusion of memory, heterogeneity and visco-elasticity

Directory of Open Access Journals (Sweden)

Spannenberg Jescica

2017-09-01

Full Text Available Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.

Experiment study and FEM simulation on erythrocytes under linear stretching of optical micromanipulation

Science.gov (United States)

Liu, Ying; Song, Huadong; Zhu, Panpan; Lu, Hao; Tang, Qi

2017-08-01

The elasticity of erythrocytes is an important criterion to evaluate the quality of blood. This paper presents a novel research on erythrocytes' elasticity with the application of optical tweezers and the finite element method (FEM) during blood storage. In this work, the erythrocytes with different in vitro times were linearly stretched by trapping force using optical tweezers and the time dependent elasticity of erythrocytes was investigated. The experimental results indicate that the membrane shear moduli of erythrocytes increased with the increasing in vitro time, namely the elasticity was decreasing. Simultaneously, an erythrocyte shell model with two parameters (membrane thickness h and membrane shear modulus H) was built to simulate the linear stretching states of erythrocytes by the FEM, and the simulations conform to the results obtained in the experiment. The evolution process was found that the erythrocytes membrane thicknesses were decreasing. The analysis assumes that the partial proteins and lipid bilayer of erythrocyte membrane were decomposed during the in vitro preservation of blood, which results in thin thickness, weak bending resistance, and losing elasticity of erythrocyte membrane. This study implies that the FEM can be employed to investigate the inward mechanical property changes of erythrocyte in different environments, which also can be a guideline for studying the erythrocyte mechanical state suffered from different diseases.

Generalized linear elastic fracture mechanics: an application to a crack touching the bimaterial interface

Czech Academy of Sciences Publication Activity Database

Náhlík, Luboš; Šestáková, L.; Hutař, Pavel; Knésl, Zdeněk

2011-01-01

Roč. 452-453, - (2011), s. 445-448 ISSN 1013-9826 R&D Projects: GA AV ČR(CZ) KJB200410803; GA ČR GA101/09/1821 Institutional research plan: CEZ:AV0Z20410507 Keywords : generalized stress intensity factor * bimaterial interface * composite materials * strain energy density factor * fracture criterion * generalized linear elastic fracture mechanics Subject RIV: JL - Materials Fatigue, Friction Mechanics

Elastic-plastic analysis of high speed rotors with no plane of symmetry

International Nuclear Information System (INIS)

Anantha Ramu, S.

1981-01-01

A general method of analysis of elastic plastic shells has been developed. The material of the shell is assumed to obey von Mises yield condition and a stress strain law on the basis of deformation theory of plasticity. The method permits an easy iterative solution of the complete set of coupled nonlinear differential equations. The iterative procedure is essentially the solution of the elastic problem several times with different sets of loads. The solution finally yields among other things, the location of the elastic-plastic boundary in the shell wall. The second approach suggested is a three-dimensional hexahedral isoparametric solid element. The computer program developed is capable of modelling perfectly plastic, bilinear as well as nonlinear strain hardening behaviour of materials. As an example, a radial impeller is analysed by both the approaches by idealizing it as a rotating conical shell. The complete history of plastification of the shell wall as the speed increases is determined. The results of both approaches are found to be in good agreement with each other. (orig./HP)

Analysis of two colliding fractionally damped spherical shells in modelling blunt human head impacts

Science.gov (United States)

Rossikhin, Yury A.; Shitikova, Marina V.

2013-06-01

The collision of two elastic or viscoelastic spherical shells is investigated as a model for the dynamic response of a human head impacted by another head or by some spherical object. Determination of the impact force that is actually being transmitted to bone will require the model for the shock interaction of the impactor and human head. This model is indended to be used in simulating crash scenarios in frontal impacts, and provide an effective tool to estimate the severity of effect on the human head and to estimate brain injury risks. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. It is assumed that the viscoelastic features of the shells are exhibited only in the contact domain, while the remaining parts retain their elastic properties. In this case, the contact spot is assumed to be a plane disk with constant radius, and the viscoelastic features of the shells are described by the fractional derivative standard linear solid model. In the case under consideration, the governing differential equations are solved analytically by the Laplace transform technique. It is shown that the fractional parameter of the fractional derivative model plays very important role, since its variation allows one to take into account the age-related changes in the mechanical properties of bone.

The application of linear elastic fracture mechanics to thermally stressed welded components

International Nuclear Information System (INIS)

Green, D.

1981-01-01

Linear Elastic Fracture Mechanics techniques are applied to components constructed from brittle materials and operating at low or ambient temperatures. It is argued that these techniques can justifiably be applied to components at high temperature provided that stresses are thermally induced, self-equilibrating and cyclic. Such loading conditions occur for example in an LMFBR and a simple welded detail containing a crevice is taken as an example. Theoretical and experimental estimates of crack growth in this component are compared and good agreement is shown. (author)

Evaluation of linear polymerization shrinkage, flexural strength and modulus of elasticity of dental composites

Directory of Open Access Journals (Sweden)

Gabriela Queiroz de Melo Monteiro

2010-03-01

Full Text Available Linear polymerization shrinkage (LPS, flexural strength (FS and modulus of elasticity (ME of 7 dental composites (Filtek Z350™, Filtek Z250™/3M ESPE; Grandio™, Polofil Supra™/VOCO; TPH Spectrum™, TPH3™, Esthet-X™/Denstply were measured. For the measurement of LPS, composites were applied to a cylindrical metallic mold and polymerized (n = 8. The gap formed at the resin/mold interface was observed using scanning electron microscopy (1500×. For FS and ME, specimens were prepared according to the ISO 4049 specifications (n = 10. Statistical analysis of the data was performed with one-way ANOVA and the Tukey test. TPH Spectrum presented significantly higher LPS values (29.45 µm. Grandio had significantly higher mean values for FS (141.07 MPa and ME (13.91 GPa. The relationship between modulus of elasticity and polymerization shrinkage is the main challenge for maintenance of the adhesive interface, thus composites presenting high shrinkage values, associated with a high modulus of elasticity tend to disrupt the adhesive interface under polymerization.

Role of interstitial atoms in the microstructure and non-linear elastic deformation behavior of Ti–Nb alloy

Energy Technology Data Exchange (ETDEWEB)

Tahara, Masaki [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Kim, Hee Young, E-mail: heeykim@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Inamura, Tomonari; Hosoda, Hideki [Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Miyazaki, Shuichi, E-mail: miyazaki@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Center of Excellence for Advanced Materials Research, King Abdulaziz University, P.O. Box 80203, Jeddah 21589 (Saudi Arabia); School of Materials Science and Engineering and ERI, Gyeongsang National University, 900 Gazwadong, Jinju, Gyeongnam 660-701 (Korea, Republic of)

2013-11-15

Highlights: ► {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉{sub β}* rel rods and {1 1 1}{sub β}* rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation.

Role of interstitial atoms in the microstructure and non-linear elastic deformation behavior of Ti–Nb alloy

International Nuclear Information System (INIS)

Tahara, Masaki; Kim, Hee Young; Inamura, Tomonari; Hosoda, Hideki; Miyazaki, Shuichi

2013-01-01

Highlights: ► {110} β 〈11 ¯ 0〉 β transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉 β * rel rods and {1 1 1} β * rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110} β 〈11 ¯ 0〉 β transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation

Elasticity theory and applications

CERN Document Server

Saada, Adel S; Hartnett, James P; Hughes, William F

2013-01-01

Elasticity: Theory and Applications reviews the theory and applications of elasticity. The book is divided into three parts. The first part is concerned with the kinematics of continuous media; the second part focuses on the analysis of stress; and the third part considers the theory of elasticity and its applications to engineering problems. This book consists of 18 chapters; the first of which deals with the kinematics of continuous media. The basic definitions and the operations of matrix algebra are presented in the next chapter, followed by a discussion on the linear transformation of points. The study of finite and linear strains gradually introduces the reader to the tensor concept. Orthogonal curvilinear coordinates are examined in detail, along with the similarities between stress and strain. The chapters that follow cover torsion; the three-dimensional theory of linear elasticity and the requirements for the solution of elasticity problems; the method of potentials; and topics related to cylinders, ...

Anticavitation and Differential Growth in Elastic Shells

KAUST Repository

Moulton, Derek E.; Goriely, Alain

2010-01-01

infinite growth or resorption is imposed at the inner surface of the shell. However, void collapse can occur in a limiting sense when radial and circumferential growth are properly balanced. Growth functions which diverge or vanish at a point arise

On the bi-orthogonality conditions for multi-modal elastic waveguides

DEFF Research Database (Denmark)

Sorokin, Sergey

2013-01-01

The bi-orthogomality conditions in terms of generalised forces and displacements are derived from the reciprocity relations for a hierarchy of elastic waveguides, which support several travelling and evanescent modes (free waves). In the simple cases of waves in a straight beam and axisymmetric...... waves in a thin elastic cylindrical shell, these conditions are formulated as identities in an explicit form via wavenumbers. The forced vibrations of these waveguides under localised excitation are also considered with these identities being employed. The bi-orthogonality conditions in more advanced...... cases, specifically, for non-axisymmetric waves in an elastic cylindrical shell and for waves in an elastic helical spring, are derived, but not presented in an explicit form via wavenumbers. The results obtained for the hierarchy of waveguides are discussed in view of the classical bi...

A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials

Science.gov (United States)

Li, Chen; Liao, Yufei

2018-03-01

Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.

Two-dimensional linear elasticity theory of magneto-electro-elastic plates considering surface and nonlocal effects for nanoscale device applications

Science.gov (United States)

Wang, Wenjun; Li, Peng; Jin, Feng

2016-09-01

A novel two-dimensional linear elastic theory of magneto-electro-elastic (MEE) plates, considering both surface and nonlocal effects, is established for the first time based on Hamilton’s principle and the Lee plate theory. The equations derived are more general, suitable for static and dynamic analyses, and can also be reduced to the piezoelectric, piezomagnetic, and elastic cases. As a specific application example, the influences of the surface and nonlocal effects, poling directions, piezoelectric phase materials, volume fraction, damping, and applied magnetic field (i.e., constant applied magnetic field and time-harmonic applied magnetic field) on the magnetoelectric (ME) coupling effects are first investigated based on the established two-dimensional plate theory. The results show that the ME coupling coefficient has an obvious size-dependent characteristic owing to the surface effects, and the surface effects increase the ME coupling effects significantly when the plate thickness decreases to its critical thickness. Below this critical thickness, the size-dependent effect is obvious and must be considered. In addition, the output power density of a magnetic energy nanoharvester is also evaluated using the two-dimensional plate theory obtained, with the results showing that a relatively larger output power density can be achieved at the nanoscale. This study provides a mathematical tool which can be used to analyze the mechanical properties of nanostructures theoretically and numerically, as well as evaluating the size effect qualitatively and quantitatively.

Recent developments in anisotropic heterogeneous shell theory

CERN Document Server

Grigorenko, Alexander Ya; Grigorenko, Yaroslav M; Vlaikov, Georgii G

2016-01-01

This volume focuses on the relevant general theory and presents some first applications, namely those based on classical shell theory. After a brief introduction, during which the history and state-of-the-art are discussed, the first chapter presents the mechanics of anisotropic heterogeneous shells, covering all relevant assumptions and the basic relations of 3D elasticity, classical and refined shell models. The second chapter examines the numerical techniques that are used, namely discrete orthogonalization, spline-collocation and Fourier series, while the third highlights applications based on classical theory, in particular, the stress-strain state of shallow shells, non-circular shells, shells of revolution, and free vibrations of conical shells. The book concludes with a summary and an outlook bridging the gap to the second volume.

Study on modal characteristics of perforated shell using effective Young's modulus

Energy Technology Data Exchange (ETDEWEB)

Jhung, Myung Jo, E-mail: mjj@kins.re.kr [Korea Institute of Nuclear Safety, 19 Guseong-dong, Yuseong-gu, Daejeon 305-338 (Korea, Republic of); Yu, Seon Oh [Korea Institute of Nuclear Safety, 19 Guseong-dong, Yuseong-gu, Daejeon 305-338 (Korea, Republic of)

2011-06-15

Research highlights: > The effective Young's modulus of perforated shell is proposed for modal analysis. > The penetration pattern is almost negligible for effective elastic constants. > The frequency of perforated shell decreases significantly due to the hole effect. - Abstract: For the perforated cylindrical shell submerged in fluid, it is almost impossible to develop a finite element model due to the necessity of the fine meshing of the shell and the fluid at the same time. This necessitates the use of solid shell with effective material properties. Unfortunately the effective elastic constants are not found in any references even though the ASME code is suggesting those for perforated plate. Therefore in this study the effective material properties of perforated shell are suggested by performing several finite element analyses with respect to the ligament efficiencies.

Relating Cohesive Zone Model to Linear Elastic Fracture Mechanics

Science.gov (United States)

Wang, John T.

2010-01-01

The conditions required for a cohesive zone model (CZM) to predict a failure load of a cracked structure similar to that obtained by a linear elastic fracture mechanics (LEFM) analysis are investigated in this paper. This study clarifies why many different phenomenological cohesive laws can produce similar fracture predictions. Analytical results for five cohesive zone models are obtained, using five different cohesive laws that have the same cohesive work rate (CWR-area under the traction-separation curve) but different maximum tractions. The effect of the maximum traction on the predicted cohesive zone length and the remote applied load at fracture is presented. Similar to the small scale yielding condition for an LEFM analysis to be valid. the cohesive zone length also needs to be much smaller than the crack length. This is a necessary condition for a CZM to obtain a fracture prediction equivalent to an LEFM result.

Rotation, inversion and perversion in anisotropic elastic cylindrical tubes and membranes

KAUST Repository

Goriely, A.

2013-03-06

Cylindrical tubes and membranes are universal structural elements found in biology and engineering over a wide range of scales.Working in the framework of nonlinear elasticity, we consider the possible deformations of elastic cylindrical shells reinforced by one or two families of fibres. We consider both small and large deformations and the reduction from thick cylindrical shells (tubes) to thin shells (cylindrical membranes). In particular, a number of universal parameter regimes can be identified where the response behaviour of the cylinder is qualitatively different. This include the possibility of inversion of twist or axial strain when the cylinder is subject to internal pressure. Copyright © The Royal Society 2013.

On the accuracy of the asymptotic theory for cylindrical shells

DEFF Research Database (Denmark)

Niordson, Frithiof; Niordson, Christian

1999-01-01

We study the accuracy of the lowest-order bending theory of shells, derived from an asymptotic expansion of the three-dimensional theory of elasticity, by comparing the results of this shell theory for a cylindrical shell with clamped ends with the results of a solution to the three......-dimensional problem. The results are also compared with those of some commonly used engineering shell theories....

Interpolation problem for the solutions of linear elasticity equations based on monogenic functions

Science.gov (United States)

Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii

2017-11-01

Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.

Rotation, inversion and perversion in anisotropic elastic cylindrical tubes and membranes

KAUST Repository

Goriely, A.; Tabor, M.

2013-01-01

Cylindrical tubes and membranes are universal structural elements found in biology and engineering over a wide range of scales.Working in the framework of nonlinear elasticity, we consider the possible deformations of elastic cylindrical shells

Quadratic temporal finite element method for linear elastic structural dynamics based on mixed convolved action

International Nuclear Information System (INIS)

Kim, Jin Kyu; Kim, Dong Keon

2016-01-01

A common approach for dynamic analysis in current practice is based on a discrete time-integration scheme. This approach can be largely attributed to the absence of a true variational framework for initial value problems. To resolve this problem, a new stationary variational principle was recently established for single-degree-of-freedom oscillating systems using mixed variables, fractional derivatives and convolutions of convolutions. In this mixed convolved action, all the governing differential equations and initial conditions are recovered from the stationarity of a single functional action. Thus, the entire description of linear elastic dynamical systems is encapsulated. For its practical application to structural dynamics, this variational formalism is systemically extended to linear elastic multidegree- of-freedom systems in this study, and a corresponding weak form is numerically implemented via a quadratic temporal finite element method. The developed numerical method is symplectic and unconditionally stable with respect to a time step for the underlying conservative system. For the forced-damped vibration, a three-story shear building is used as an example to investigate the performance of the developed numerical method, which provides accurate results with good convergence characteristics

Quadratic temporal finite element method for linear elastic structural dynamics based on mixed convolved action

Energy Technology Data Exchange (ETDEWEB)

Kim, Jin Kyu [School of Architecture and Architectural Engineering, Hanyang University, Ansan (Korea, Republic of); Kim, Dong Keon [Dept. of Architectural Engineering, Dong A University, Busan (Korea, Republic of)

2016-09-15

A common approach for dynamic analysis in current practice is based on a discrete time-integration scheme. This approach can be largely attributed to the absence of a true variational framework for initial value problems. To resolve this problem, a new stationary variational principle was recently established for single-degree-of-freedom oscillating systems using mixed variables, fractional derivatives and convolutions of convolutions. In this mixed convolved action, all the governing differential equations and initial conditions are recovered from the stationarity of a single functional action. Thus, the entire description of linear elastic dynamical systems is encapsulated. For its practical application to structural dynamics, this variational formalism is systemically extended to linear elastic multidegree- of-freedom systems in this study, and a corresponding weak form is numerically implemented via a quadratic temporal finite element method. The developed numerical method is symplectic and unconditionally stable with respect to a time step for the underlying conservative system. For the forced-damped vibration, a three-story shear building is used as an example to investigate the performance of the developed numerical method, which provides accurate results with good convergence characteristics.

Impact loads on beams on elastic foundations

International Nuclear Information System (INIS)

Kameswara Rao, N.S.V.; Prasad, B.B.

1975-01-01

Quite often, complex structural components are idealised as beams in engineering analysis and design. Also, equations governing the responses of shallow shells are mathematically equivalent to the equations governing the responses of beams on elastic foundations. Hence with possible applications in several technical disciplines, the behaviour of beams on elastic foundations subjected to impact loads is studied in detail in the present investigation both analytically and experimentally. The analytical methods include analysis and energy method. The effect of foundation parameters (stiffness, and damping constants) on the dynamic responses of the beam-foundation system has been analysed. In modal analysis, the free-vibration equation has been solved by replacing the applied impulse by suitable initial conditions and the solution has been obtained as the linear combination of an infinite sequence of discrete eigen-vectors. In the energy method, the beam-foundation system is treated to be under forced vibrations and the forcing function has been obtained using the Hertz's law of impact. In the case of free-free end conditions of the beam, the rigid body modes and the elastic modes have been superposed to obtain the total response. The responses predicted using modal analysis are higher than those obtained using energy method. From the present study it is observed that model analysis is preferable to energy method. (Auth.)

Statistical Mechanics of Thin Spherical Shells

Directory of Open Access Journals (Sweden)

Andrej Košmrlj

2017-01-01

Full Text Available We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells. In flat membranes with a shear modulus, thermal fluctuations increase the bending rigidity and reduce the in-plane elastic moduli in a scale-dependent fashion. This is still true for spherical shells. However, the additional coupling between the shell curvature, the local in-plane stretching modes, and the local out-of-plane undulations leads to novel phenomena. In spherical shells, thermal fluctuations produce a radius-dependent negative effective surface tension, equivalent to applying an inward external pressure. By adapting renormalization group calculations to allow for a spherical background curvature, we show that while small spherical shells are stable, sufficiently large shells are crushed by this thermally generated “pressure.” Such shells can be stabilized by an outward osmotic pressure, but the effective shell size grows nonlinearly with increasing outward pressure, with the same universal power-law exponent that characterizes the response of fluctuating flat membranes to a uniform tension.

Dynamic plastic buckling of cylindrical and spherical shells

International Nuclear Information System (INIS)

Jones, N.; Okawa, D.M.

1975-01-01

A theoretical analysis is developed to predict the dynamic plastic buckling of a long, impulsively loaded cylindrical shell in order to examine various features of plastic buckling and to assess the importance of several approximations with previous authors have introduced in dynamic plastic buckling studies. The influence of a time-dependent circumferential membrane force, the sharpness of the peaks in the displacement and velocity amplification functions, the restrictions which are implicit when employing the Prandtl-Reuss equations in this class of problems, and the limitations due to elastic unloading are examined in some detail. A summary of all previously published theoretical investigations known to the authors is undertaken for the dynamic plastic behavior of cylindrical shells and rings which are made from rigid-plastic, rigid-visco-plastic, elastic-plastic and elastic-visco-plastic materials and subjected to initial axisymmetric impulsive velocity fields. The theoretical predictions of the dominant motions, critical mode numbers, and threshold impulses are compared and critically reviewed. An experimental investigation was also undertaken into the dynamic plastic buckling of circular rings subjected to uniformly distributed external impulsive velocities. It appears that no experiments have been reported previously on mild steel cylindrical shells with an axial length (L) less than four times the shell radius (R). The experimental values of the average final radial deflections, critical mode numbers and dimensions of the permanent wrinkles in the mild steel and some aliminium 6,061 T6 specimens are compared with all the previously published theoretical predictions and experimental results on cylindrical shells with various axial lengths. (orig./HP) [de

Dynamic acousto-elastic testing of concrete with a coda-wave probe: comparison with standard linear and nonlinear ultrasonic techniques.

Science.gov (United States)

Shokouhi, Parisa; Rivière, Jacques; Lake, Colton R; Le Bas, Pierre-Yves; Ulrich, T J

2017-11-01

The use of nonlinear acoustic techniques in solids consists in measuring wave distortion arising from compliant features such as cracks, soft intergrain bonds and dislocations. As such, they provide very powerful nondestructive tools to monitor the onset of damage within materials. In particular, a recent technique called dynamic acousto-elasticity testing (DAET) gives unprecedented details on the nonlinear elastic response of materials (classical and non-classical nonlinear features including hysteresis, transient elastic softening and slow relaxation). Here, we provide a comprehensive set of linear and nonlinear acoustic responses on two prismatic concrete specimens; one intact and one pre-compressed to about 70% of its ultimate strength. The two linear techniques used are Ultrasonic Pulse Velocity (UPV) and Resonance Ultrasound Spectroscopy (RUS), while the nonlinear ones include DAET (fast and slow dynamics) as well as Nonlinear Resonance Ultrasound Spectroscopy (NRUS). In addition, the DAET results correspond to a configuration where the (incoherent) coda portion of the ultrasonic record is used to probe the samples, as opposed to a (coherent) first arrival wave in standard DAET tests. We find that the two visually identical specimens are indistinguishable based on parameters measured by linear techniques (UPV and RUS). On the contrary, the extracted nonlinear parameters from NRUS and DAET are consistent and orders of magnitude greater for the damaged specimen than those for the intact one. This compiled set of linear and nonlinear ultrasonic testing data including the most advanced technique (DAET) provides a benchmark comparison for their use in the field of material characterization. Copyright © 2017 Elsevier B.V. All rights reserved.

The CEASEMT system (Computer analysis of the thermomechanical structure behavior). The TRICO code, for analysis of three-dimensional structures comprising shells and beams - Statics - Dynamics - Elasticity - Plasticity - Buckling - Large displacements

International Nuclear Information System (INIS)

1977-01-01

The TRICO part of the CEA-SEMT system is concerned with the elasticity or plasticity computation of structures made of thin shells and beams. TRICO uses the finite element method for shells and beams. TRICO also allows the dynamic computing of structures: search for eigenmodes and eigenfrequencies or response to any sinusoidal excitation, response to time dependent loads (direct integration) in elasticity or plasticity. The mechanical structures can offer any shape and be composed of a number of materials. A special effort has been put on data input (read without any format), the data being arranged in optional commands with a precise physical sense corresponding to an order for the program. A dynamic control of the memory allows the size of the program to be adapted to that the problem to be processed. Results are printed on listing, or many be described on a magnetic tape [fr

Dynamic analysis of aircraft impact using the linear elastic finite element codes FINEL, SAP and STARDYNE

International Nuclear Information System (INIS)

Lundsager, P.; Krenk, S.

1975-08-01

The static and dynamic response of a cylindrical/ spherical containment to a Boeing 720 impact is computed using 3 different linear elastic computer codes: FINEL, SAP and STARDYNE. Stress and displacement fields are shown together with time histories for a point in the impact zone. The main conclusions from this study are: - In this case the maximum dynamic load factors for stress and displacements were close to 1, but a static analysis alone is not fully sufficient. - More realistic load time histories should be considered. - The main effects seem to be local. The present study does not indicate general collapse from elastic stresses alone. - Further study of material properties at high rates is needed. (author)

Blocky inversion of multichannel elastic impedance for elastic parameters

Science.gov (United States)

Mozayan, Davoud Karami; Gholami, Ali; Siahkoohi, Hamid Reza

2018-04-01

Petrophysical description of reservoirs requires proper knowledge of elastic parameters like P- and S-wave velocities (Vp and Vs) and density (ρ), which can be retrieved from pre-stack seismic data using the concept of elastic impedance (EI). We propose an inversion algorithm which recovers elastic parameters from pre-stack seismic data in two sequential steps. In the first step, using the multichannel blind seismic inversion method (exploited recently for recovering acoustic impedance from post-stack seismic data), high-resolution blocky EI models are obtained directly from partial angle-stacks. Using an efficient total-variation (TV) regularization, each angle-stack is inverted independently in a multichannel form without prior knowledge of the corresponding wavelet. The second step involves inversion of the resulting EI models for elastic parameters. Mathematically, under some assumptions, the EI's are linearly described by the elastic parameters in the logarithm domain. Thus a linear weighted least squares inversion is employed to perform this step. Accuracy of the concept of elastic impedance in predicting reflection coefficients at low and high angles of incidence is compared with that of exact Zoeppritz elastic impedance and the role of low frequency content in the problem is discussed. The performance of the proposed inversion method is tested using synthetic 2D data sets obtained from the Marmousi model and also 2D field data sets. The results confirm the efficiency and accuracy of the proposed method for inversion of pre-stack seismic data.

On the accuracy of the asymptotic theory for cylindrical shells

DEFF Research Database (Denmark)

Niordson, Frithiof; Niordson, Christian

1999-01-01

We study the accuracy of the lowest-order bending theory of shells, derived from an asymptotic expansion of the three-dimensional theory of elasticity, by comparing the results of this theory for a cylindrical shell with clamped ends with the results of a solution to the three-dimensional problem....... The results are also compared with those of some commonly used engineering shell theories....

Form finding in elastic gridshells

Science.gov (United States)

Baek, Changyeob; Sageman-Furnas, Andrew O.; Jawed, Mohammad K.; Reis, Pedro M.

2018-01-01

Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We study elastic gridshells with a focus on the rational design of the final shapes. Our precision desktop experiments exhibit complex geometries, even from seemingly simple initial configurations and actuation processes. The numerical simulations capture this nonintuitive behavior with excellent quantitative agreement, allowing for an exploration of parameter space that reveals multistable states. We then turn to the theory of smooth Chebyshev nets to address the inverse design of hemispherical elastic gridshells. The results suggest that rod inextensibility, not elastic response, dictates the zeroth-order shape of an actuated elastic gridshell. As it turns out, this is the shape of a common household strainer. Therefore, the geometry of Chebyshev nets can be further used to understand elastic gridshells. In particular, we introduce a way to quantify the intrinsic shape of the empty, but enclosed regions, which we then use to rationalize the nonlocal deformation of elastic gridshells to point loading. This justifies the observed difficulty in form finding. Nevertheless, we close with an exploration of concatenating multiple elastic gridshell building blocks.

The effect of multi-directional nanocomposite materials on the vibrational response of thick shell panels with finite length and rested on two-parameter elastic foundations

Science.gov (United States)

Tahouneh, Vahid; Naei, Mohammad Hasan

2016-03-01

The main purpose of this paper is to investigate the effect of bidirectional continuously graded nanocomposite materials on free vibration of thick shell panels rested on elastic foundations. The elastic foundation is considered as a Pasternak model after adding a shear layer to the Winkler model. The panels reinforced by randomly oriented straight single-walled carbon nanotubes are considered. The volume fractions of SWCNTs are assumed to be graded not only in the radial direction, but also in axial direction of the curved panel. This study presents a 2-D six-parameter power-law distribution for CNTs volume fraction of 2-D continuously graded nanocomposite that gives designers a powerful tool for flexible designing of structures under multi-functional requirements. The benefit of using generalized power-law distribution is to illustrate and present useful results arising from symmetric, asymmetric and classic profiles. The material properties are determined in terms of local volume fractions and material properties by Mori-Tanaka scheme. The 2-D differential quadrature method as an efficient numerical tool is used to discretize governing equations and to implement boundary conditions. The fast rate of convergence of the method is shown and results are compared against existing results in literature. Some new results for natural frequencies of the shell are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The interesting results indicate that a graded nanocomposite volume fraction in two directions has a higher capability to reduce the natural frequency than conventional 1-D functionally graded nanocomposite materials.

Structure of 14C via elastic and inelastic neutron scattering from 13C: Measurement, R-matrix analysis, and shell model calculations

International Nuclear Information System (INIS)

Resler, D.A.

1987-03-01

The specific purpose of this work is to provide a better understanding of the 14 C level structure; the general purpose is to provide the details for using shell model calculations in R-matrix analyses. Using the TOF facilities of the Ohio University Accelerator Laboratory, the elastic and first 3 inelastic differential scattering cross sections for 13 C + n were measured at 69 energies for 4.5 ≤ E/sub n/ ≤ 11 MeV. A multiple scattering code was developed which provided a simulation of the experimental scattering process allowing accurate corrections to the small inelastic data. The integrated 13 C(n,α) 10 Be cross section is estimated. The sequential 2n-decay of 14 C states populated by 13 C + n was observed. A shell model code was developed. Normal and nonnormal parity calculations were made for the lithium isotopes using a new two-body interaction. The results for 5 Li predict the 2s/sub 1/2/ and 1d/sub 5/2/ single-particle states to be located below the 3/2 + state. Similar calculations were made for 13 C, 13 N, and 14 C. Results for 13 C and 13 N show for E/sub x/ 7 Li and 14 C, 2 h-barω calculations were done. Shell model calculations generated the R-matrix parameters for the elastic and first 3 inelastic channels of 13 C + n. After adjusting some energies, the predicted structure generally agrees with experiment for E/sub n/ 13 C + n data were refit to replace R 0 background terms by more realistic broad states and to get better agreement with model calculations. R-matrix fitting of the full data set produced new 14 C level information. For E/sub n/ > 4 MeV (E/sub x/ > 12 MeV), 5 states are given definite J/sup π/ assignments; 3, tentative assignments. 122 refs., 91 figs., 30 tabs

Stability of charged thin shells

International Nuclear Information System (INIS)

Eiroa, Ernesto F.; Simeone, Claudio

2011-01-01

In this article we study the mechanical stability of spherically symmetric thin shells with charge, in Einstein-Maxwell and Einstein-Born-Infeld theories. We analyze linearized perturbations preserving the symmetry, for shells around vacuum and shells surrounding noncharged black holes.

Dispersion properties of three-layered orthotropic shells

International Nuclear Information System (INIS)

Markus, S.

1995-01-01

This paper studies the harmonic wave propagation in thick, cylindrical, three-layered shells of infinite length. Both the outer layers and the core are composites made of short strand fiberglass and polyester resin. The randomly oriented fibers were approximately in parallel planes to constitute a transversely isotropic fibre composite. The planes of isotropy in the outer layers are orthogonal to the plane of isotropy at the core. A closed form solution of the exact linear equations of elasticity in sought in terms of a Frobenius series. The influence of the core thickness on the dynamics of the wave motion is estimated from numerically computed dispersion curves. Asymmetric wave motion is given prime consideration and the different types of waves which can occur are identified over a wide range of wave numbers

Symmetry-Free, p-Robust Equilibrated Error Indication for the hp-Version of the FEMin Nearly Incompressible Linear Elasticity

OpenAIRE

Dörsek, Philipp; Melenk, Jens M.

2017-01-01

We consider the extension of the p-robust equilibrated error estimator due to Braess, Pillwein and Schöberl to linear elasticity. We derive a formulation where the local mixed auxiliary problems do not require symmetry of the stresses. The resulting error estimator is p-robust, and the reliability estimate is also robust in the incompressible limit if quadratics are included in the approximation space. Extensions to other systems of linear second-order partial differential equations are discu...

Dynamics of Inhomogeneous Shell Systems Under Non-Stationary Loading (Survey)

Science.gov (United States)

Lugovoi, P. Z.; Meish, V. F.

2017-09-01

Experimental works on the determination of dynamics of smooth and stiffened cylindrical shells contacting with a soil medium under various non-stationary loading are reviewed. The results of studying three-layer shells of revolution whose motion equations are obtained within the framework of the hypotheses of the Timoshenko geometrically nonlinear theory are stated. The numerical results for shells with a piecewise or discrete filler enable the analysis of estimation of the influence of geometrical and physical-mechanical parameters of structures on their dynamics and reveal new mechanical effects. Basing on the classical theory of shells and rods, the effect of the discrete arrangement of ribs and coefficients of the Winkler or Pasternak elastic foundation on the normal frequencies and modes of rectangular planar cylindrical and spherical shells is studied. The number and shape of dispersion curves for longitudinal harmonic waves in a stiffened cylindrical shell are determined. The equations of vibrations of ribbed shells of revolution on Winkler or Pasternak elastic foundation are obtained using the geometrically nonlinear theory and the Timoshenko hypotheses. On applying the integral-interpolational method, numerical algorithms are developed and the corresponding non-stationary problems are solved. The special attention is paid to the statement and solution of coupled problems on the dynamical interaction of cylindrical or spherical shells with the soil water-saturated medium of different structure.

Non-linear elasticity of extracellular matrices enables contractile cells to communicate local position and orientation.

Directory of Open Access Journals (Sweden)

Jessamine P Winer

2009-07-01

Full Text Available Most tissue cells grown in sparse cultures on linearly elastic substrates typically display a small, round phenotype on soft substrates and become increasingly spread as the modulus of the substrate increases until their spread area reaches a maximum value. As cell density increases, individual cells retain the same stiffness-dependent differences unless they are very close or in molecular contact. On nonlinear strain-stiffening fibrin gels, the same cell types become maximally spread even when the low strain elastic modulus would predict a round morphology, and cells are influenced by the presence of neighbors hundreds of microns away. Time lapse microscopy reveals that fibroblasts and human mesenchymal stem cells on fibrin deform the substrate by several microns up to five cell lengths away from their plasma membrane through a force limited mechanism. Atomic force microscopy and rheology confirm that these strains locally and globally stiffen the gel, depending on cell density, and this effect leads to long distance cell-cell communication and alignment. Thus cells are acutely responsive to the nonlinear elasticity of their substrates and can manipulate this rheological property to induce patterning.

Elastic electron scattering from 14N, 15N, 16O and 18O at small momentum transfer

International Nuclear Information System (INIS)

Schuetz, W.

1973-01-01

At the Darmstadt linear accelerator, cross-sections for the elastic scattering of electrons on 14 N and 16 O relative to the proton and on 15 N and 18 O relative to 14 N and 16 O were measured at energies 30 MeV 0 0 (q 2 -2 ). The experiments were done with gas targets, the target containers being thin-walled aluminium cylinders. The data were evaluated by means of the partial-wave method assuming a charge distribution according to the shell model. (orig./WL) [de

Evaluation of thermal ratchetting on axisymmetric thin shells at the free level of sodium: Experimental results and elastic analysis

International Nuclear Information System (INIS)

Cabrillat, M.T.; Gatt, J.M.; Schoulguine, P.; Skiara, A.

1993-01-01

Startup operations and load variations for a FBR reactor (Fast Breeder Reactor) cause sodium level variations in the vessels which exert stresses on the emergent shells in the free level area. The loading of these shells is mainly linked to the axial thermal gradient, primary stresses being generally low or negligible as are the radial thermal gradients. Under the effect of these variable axial thermal gradients, there is a risk of progressive deformation even in the absence of primary type stresses. The simplified methods of analysis (Bree diagram, efficiency diagram) proposed in the design codes (Code Case and RCCMR) are not applicable in this specific case where primary type stresses are negligible. In recent years, many studies and experimental programmes have been undertaken in order to propose more reliable methods of analysis for these structures. This paper describes the experimental program, called VINIL, developed at the CEA at Cadarache. After a brief description of the experimental facility and of the experimental results, this paper proposes an evaluation of the risk of progressive deformation on an elastic basis: various simplified methods of analysis were used and are compared with experimental results

Aeroelastic Dynamics Simulation of Two BaffleBased Connected Shells

Directory of Open Access Journals (Sweden)

G. A. Shcheglov

2015-01-01

Full Text Available The present work is an extention study of aeroelastic vibrations of thin-walled structures with a spatial subsonic flow. An original algorithm for solving complex conjugated aeroelasticity problem, allowing to carry out direct numerical simulation of structural oscillations in the spatial flow of an incompressible medium are developed and tested. On the basis of this simulation study of the spectrum comes the driving forces acting on the flow in a spatial component elastic structure mounted on an impenetrable screen.Currently, updating the mathematical models of unsteady loads that act on the spacepurpose elastic designs such as launch vehicles, service tower installed on the launch pad is a challenge. We consider two thin-walled cantilevered rotating shells connected by a system of elastic couplings, installed next to the impenetrable baffle so that the axes of rotation are perpendicular to the baffle. Dynamics of elastic system is investigated numerically, using the vortex element method with the spatial separated flow of an incompressible medium. A feature of the algorithm is the common commercial complex MSC Patran / Nastran which is used in preparing data to calculate the shell dynamics thereby allowing to consider very complex dynamic schemes.The work performs the first calculations of the model problem concerning the forced oscillations of two coupled cylindrical shells in the flow of an incompressible medium. Comparing the load spectra for the elastic and absolutely rigid structure has shown that the frequency spectra vary slightly. Further calculations are required in which it will be necessary to increase the duration of the calculations, sampling in construction of design scheme, and given the large number of vibration modes that require increasing computing power.Experience in calculating aeroelastic dynamics of complex elastic structures taking into account the screen proved to be successful as a whole, thereby allowing to turn to

A new ceramic assemblage from Caution Bay, south coast of mainland PNG : the linear shell edge-impressed tradition from Bogi 1

International Nuclear Information System (INIS)

David, B.; McNiven, I.J.; Leavesley, M.; Barker, B.; Mandui, H.; Richards, T.; Skelly, R.

2012-01-01

This paper reports on the ceramics from Squares A and B of Bogi 1, a newly excavated site at Caution Bay, south coast of mainland Papua New Guinea. A dense cultural horizon dated from c. 2150 to c. 2100 calBP and preceded by earlier cultural deposits contains previously undescribed ceramics of limited decorative variability almost exclusively focused on Anadara shell edge impressions below finger-grooved lips, which we term the Linear Shell Edge-Impressed Tradition. Here we present the chrono-stratigraphic evidence for this decorative tradition and how it relates to previously described shell-impressed ceramics from the broader region. (author). 16 refs., 9 figs., 3 tabs.

Emergence of linear elasticity from the atomistic description of matter

Energy Technology Data Exchange (ETDEWEB)

Cakir, Abdullah, E-mail: acakir@ntu.edu.sg [Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University (Singapore); Pica Ciamarra, Massimo [Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University (Singapore); Dipartimento di Scienze Fisiche, CNR–SPIN, Università di Napoli Federico II, I-80126 Napoli (Italy)

2016-08-07

We investigate the emergence of the continuum elastic limit from the atomistic description of matter at zero temperature considering how locally defined elastic quantities depend on the coarse graining length scale. Results obtained numerically investigating different model systems are rationalized in a unifying picture according to which the continuum elastic limit emerges through a process determined by two system properties, the degree of disorder, and a length scale associated to the transverse low-frequency vibrational modes. The degree of disorder controls the emergence of long-range local shear stress and shear strain correlations, while the length scale influences the amplitude of the fluctuations of the local elastic constants close to the jamming transition.

Emergence of linear elasticity from the atomistic description of matter

International Nuclear Information System (INIS)

Cakir, Abdullah; Pica Ciamarra, Massimo

2016-01-01

We investigate the emergence of the continuum elastic limit from the atomistic description of matter at zero temperature considering how locally defined elastic quantities depend on the coarse graining length scale. Results obtained numerically investigating different model systems are rationalized in a unifying picture according to which the continuum elastic limit emerges through a process determined by two system properties, the degree of disorder, and a length scale associated to the transverse low-frequency vibrational modes. The degree of disorder controls the emergence of long-range local shear stress and shear strain correlations, while the length scale influences the amplitude of the fluctuations of the local elastic constants close to the jamming transition.

On reconstruction of an unknown polygonal cavity in a linearized elasticity with one measurement

International Nuclear Information System (INIS)

Ikehata, M; Itou, H

2011-01-01

In this paper we consider a reconstruction problem of an unknown polygonal cavity in a linearized elastic body. For this problem, an extraction formula of the convex hull of the unknown polygonal cavity is established by means of the enclosure method introduced by Ikehata. The advantages of our method are that it needs only a single set of boundary data and we do not require any a priori assumptions for the unknown polygonal cavity and any constraints on boundary data. The theoretical formula may have possibility of application in nondestructive evaluation.

Capillary micromechanics for core-shell particles

NARCIS (Netherlands)

Kong, T.; Wang, Liqiu; Wyss, H.M.; Shum, H.C.

2014-01-01

In this work, we have developed a facile, economical microfluidic approach as well as a simple model description to measure and predict the mechanical properties of composite core–shell microparticles made from materials with dramatically different elastic properties. By forcing the particles

Nonlinear problems of the theory of heterogeneous slightly curved shells

Science.gov (United States)

Kantor, B. Y.

1973-01-01

An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.

Elasto/visco-plastic analysis of orthotropic moderately thick shells of revolution

International Nuclear Information System (INIS)

Takezono, S.; Tao, K.

1985-01-01

This paper describes an analytical formulation and a numerical analysis on the elasto/visco-plastic problems of orthotropic moderately thick shells of revolution under axi-symmetrical loads with applications to a cylindrical shell, and with comparison to experimental results. The analytical formulation is developed by extension of the Reissner-Naghdi theory in elastic shells where a consideration on the effect of shear deformation is given. As the constitutive equation, Hooke's law for orthotropic materials is used in the elastic range, and equations based on the orthotropic visco-plastic theory derived from the orthotropic plastic theory by Hill are employed in the plastic range. The visco-plastic strain rates are related to the stresses by Perzyna's equation. In order to check up the adequacy of the numerical analysis, experiments on elasto/visco-plastic deformation of a titanium cylindrical shell subject to internal axi-symmetrical loads are performed. Good agreement is obtained between experimental results and analytical solution. (orig.)

The development of an algebraic multigrid algorithm for symmetric positive definite linear systems

Energy Technology Data Exchange (ETDEWEB)

Vanek, P.; Mandel, J.; Brezina, M. [Univ. of Colorado, Denver, CO (United States)

1996-12-31

An algebraic multigrid algorithm for symmetric, positive definite linear systems is developed based on the concept of prolongation by smoothed aggregation. Coarse levels are generated automatically. We present a set of requirements motivated heuristically by a convergence theory. The algorithm then attempts to satisfy the requirements. Input to the method are the coefficient matrix and zero energy modes, which are determined from nodal coordinates and knowledge of the differential equation. Efficiency of the resulting algorithm is demonstrated by computational results on real world problems from solid elasticity, plate blending, and shells.

A new technique for generating the isotropic and linearly anisotropic components of elastic and discrete inelastic transfer matrices

International Nuclear Information System (INIS)

Garcia, R.D.M.

1984-01-01

A new technique for generating the isotropic and linearly anisotropic componets of elastic and discrete inelastic transfer matrices is proposed. The technique allows certain angular integrals to be expressed in terms of functions that can be computed by recursion relations or series expansions alternatively to the use of numerical quadratures. (Author) [pt

CHILES, Singularity Strength of Linear Elastic Bodies by Finite Elements Method

International Nuclear Information System (INIS)

Benzley, S.E.; Beisinger, Z.E.

1981-01-01

1 - Description of problem or function: CHILES is a finite element computer program that calculates the strength of singularities in linear elastic bodies. Plane stress, plane strain, and axisymmetric conditions are treated. Crack tip singularity problems are solved by this version of the code, but any type of integrable singularity may be properly modeled by modifying selected subroutines in the program. 2 - Method of solution: A generalized, quadrilateral finite element that includes a singular point at a corner node is incorporated in the code. The displacement formulation is used and inter-element compatibility is maintained so that monotone convergence is preserved. 3 - Restrictions on the complexity of the problem: CHILES allows three singular points to be modeled in the body being analyzed and each singular point may have coupled Mode I and II deformations. 1000 nodal points may be used

Hydrostatic Pressurization of Lung Surfactant Microbubbles: Observation of a Strain-Rate Dependent Elasticity.

Science.gov (United States)

Thomas, Alec N; Borden, Mark A

2017-11-28

The microbubble offers a unique platform to study lung surfactant mechanics at physiologically relevant geometry and length scale. In this study, we compared the response of microbubbles (∼15 μm initial radius) coated with pure dipalmitoyl-phosphatidylcholine (DPPC) versus naturally derived lung surfactant (SURVANTA) when subjected to linearly increasing hydrostatic pressure at different rates (0.5-2.3 kPa/s) at room temperature. The microbubbles contained perfluorobutane gas and were submerged in buffered saline saturated with perfluorobutane at atmospheric pressure. Bright-field microscopy showed that DPPC microbubbles compressed spherically and smoothly, whereas SURVANTA microbubbles exhibited wrinkling and smoothing cycles associated with buckling and collapse. Seismograph analysis showed that the SURVANTA collapse amplitude was constant, but the collapse rate increased with the pressurization rate. An analysis of the pressure-volume curves indicated that the dilatational elasticity increased during compression for both shell types. The initial dilatational elasticity for SURVANTA was nearly twice that of DPPC at higher pressurization rates (>1.5 kPa/s), producing a pressure drop of up to 60 kPa across the film prior to condensation of the perfluorobutane core. The strain-rate dependent stiffening of SURVANTA shells likely arises from their composition and microstructure, which provide enhanced in-plane monolayer rigidity and lateral repulsion from surface-associated collapse structures. Overall, these results provide new insights into lung surfactant mechanics and collapse behavior during compression.

The effectiveness of a standardized rose hip powder, containing seeds and Shells of Rosa canina, on cell longevity, skin wrinkles, moisture, and elasticity 

DEFF Research Database (Denmark)

Phetcharat, L; Wongsuphasawat, K; Winther, Kaj

2015-01-01

Objective: To evaluate the effects of a rose hip powder (Hyben Vital®) made from seeds and shells on cell senescence, skin wrinkling, and aging. Methods: A total of 34 healthy subjects, aged 35–65 years, with wrinkles on the face (crow’s-feet) were subjected to a randomized and double-blinded cli...... hip product on cell membranes of stored erythrocyte cells observed in this study may contribute to improve the cell longevity and obstructing skin aging. Keywords: rose hip seed and shell powder, cell longevity, wrinkles, aging skin, moisture, elasticity......Objective: To evaluate the effects of a rose hip powder (Hyben Vital®) made from seeds and shells on cell senescence, skin wrinkling, and aging. Methods: A total of 34 healthy subjects, aged 35–65 years, with wrinkles on the face (crow’s-feet) were subjected to a randomized and double...... longevity was measured in terms of leakage of hemoglobin through red cell membranes (hemolytic index) in blood samples kept in a blood bank for 5 weeks. Significance of all values was attained with P#0.05. Results: In the double-blinded study, the rose hip group showed statistically significant improvements...

Elastic collisions of classical point particles on a finite frictionless linear track with perfectly reflecting endpoints

Science.gov (United States)

DeLuca, R.

2006-03-01

Repeated elastic collisions of point particles on a finite frictionless linear track with perfectly reflecting endpoints are considered. The problem is analysed by means of an elementary linear algebra approach. It is found that, starting with a state consisting of a projectile particle in motion at constant velocity and a target particle at rest in a fixed known position, the points at which collisions occur on track, when plotted versus progressive numerals, corresponding to the collisions themselves, show periodic patterns for a rather large choice of values of the initial position x(0) and on the mass ratio r. For certain values of these parameters, however, only regular behaviour over a large number of collisions is detected.

Structural shell analysis understanding and application

CERN Document Server

Blaauwendraad, Johan

2014-01-01

The mathematical description of the properties of a shell is much more elaborate than those of beam and plate structures. Therefore many engineers and architects are unacquainted with aspects of shell behaviour and design, and are not familiar with sufficiently reliable shell theories for the different shell types as derived in the middle of the 20th century. Rather than contributing to theory development, this university textbook focuses on architectural and civil engineering schools. Of course, practising professionals will profit from it as well. The book deals with thin elastic shells, in particular with cylindrical, conical and spherical types, and with elliptic and hyperbolic paraboloids. The focus is on roofs, chimneys, pressure vessels and storage tanks. Special attention is paid to edge bending disturbance zones, which is indispensable knowledge in FE meshing. A substantial part of the book results from research efforts in the mid 20th century at Delft University of Technology. As such, it is a valua...

Computer implementation of an elastic-plastic concrete relationship

International Nuclear Information System (INIS)

Murray, D.W.; Chitnuyanondh, L.; Wong, C.

1979-01-01

The purpose of this paper is to describe the difficulties that arose, and the strategies that were developed to overcome these difficulties, during the incorporation of a relatively complex elastic-plastic concrete constitutive relationship into an existing computer code for the analysis of axisymmetric loading acting on thin shells of revolution. The program had the capability of elastic-plastic analysis using a von-Mises yield curve prior to any modification by the writers. (orig.)

Off-shell distortions of multichannel atomic processes

Science.gov (United States)

Barrachina, R. O.; Clauser, C. F.

2017-10-01

Any multichannel problem can be reduced to a succession of two-body events. However, these basic building blocks of many-body theories do not correspond to elastic processes but are off-the-energy-shell. In view of this difficulty, the great majority of the Distorted-Wave models includes a subsidiary approximation where these off-shell terms are arbitrarily forced to lie on the energy shell. At a first glance, since the energy deficiency is negligible for high enough velocities, the on-shell assumption seems to be completely justified. However, for the case of Coulomb interactions, the two-body off-shell distortions have branch-point singularities on the on-shell limit. In this article we demonstrate that these singularities might produce sizeable distortions of multiple scattering amplitudes, mainly when dealing with ion-ion collisions. Finally, we propose a method of including these distortions that might lead to better results that removing them completely.

Colloidal InP/ZnS core-shell nanocrystals studied by linearly and circularly polarized photoluminescence

International Nuclear Information System (INIS)

Langof, L.; Fradkin, L.; Ehrenfreund, E.; Lifshitz, E.; Micic, O.I.; Nozik, A.J.

2004-01-01

The magneto-optical properties of InP/ZnS core-shell nanocrystals (NCs) were investigated by measuring the degree of linear and circular polarization of photoluminescence (PL) spectra, in the presence of an external magnetic field under resonant or non-resonant excitation. The linearly polarized PL data strongly indicate that InP/ZnS NCs have a prolongated shape. The resonant-excited circularly polarized PL decay curves indicate that the spin relaxation time of the studied samples is shorter than the radiative lifetime of their exciton. Furthermore, the magnetic field-induced circularly polarized PL process reveals an exciton g factor (g ex ) of 0.55. Thus, such studies may serve as a tool to directly estimate the NC's shape anisotropy and to determine the g-factor of charge carriers and excitons in those NCs

Colloidal InP/ZnS core shell nanocrystals studied by linearly and circularly polarized photoluminescence

Science.gov (United States)

Langof, L.; Fradkin, L.; Ehrenfreund, E.; Lifshitz, E.; Micic, O. I.; Nozik, A. J.

2004-02-01

The magneto-optical properties of InP/ZnS core-shell nanocrystals (NCs) were investigated by measuring the degree of linear and circular polarization of photoluminescence (PL) spectra, in the presence of an external magnetic field under resonant or non-resonant excitation. The linearly polarized PL data strongly indicate that InP/ZnS NCs have a prolongated shape. The resonant-excited circularly polarized PL decay curves indicate that the spin relaxation time of the studied samples is shorter than the radiative lifetime of their exciton. Furthermore, the magnetic field-induced circularly polarized PL process reveals an exciton g factor ( gex) of 0.55. Thus, such studies may serve as a tool to directly estimate the NC's shape anisotropy and to determine the g-factor of charge carriers and excitons in those NCs.

Coulomb excitations for a short linear chain of metallic shells

Energy Technology Data Exchange (ETDEWEB)

Zhemchuzhna, Liubov, E-mail: lzhemchuzhna@unm.edu [Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065 (United States); Center for High Technology Materials, University of New Mexico, Albuquerque, New Mexico 87106 (United States); Gumbs, Godfrey [Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065 (United States); Donostia International Physics Center (DIPC), P de Manuel Lardizabal, 4, 20018 San Sebastian, Basque Country (Spain); Iurov, Andrii [Center for High Technology Materials, University of New Mexico, Albuquerque, New Mexico 87106 (United States); Huang, Danhong [Air Force Research Laboratory, Space Vehicles Directorate, Kirtland Air Force Base, New Mexico 87117 (United States); Gao, Bo [Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065 (United States)

2015-03-15

A self-consistent-field theory is given for the electronic collective modes of a chain containing a finite number, N, of Coulomb-coupled spherical two-dimensional electron gases arranged with their centers along a straight line, for simulating electromagnetic response of a narrow-ribbon of metallic shells. The separation between nearest-neighbor shells is arbitrary and because of the quantization of the electron energy levels due to their confinement to the spherical surface, all angular momenta L of the Coulomb excitations, as well as their projections M on the quantization axis, are coupled. However, for incoming light with a given polarization, only one angular momentum quantum number is usually required. Therefore, the electromagnetic response of the narrow-ribbon of metallic shells is expected to be controlled externally by selecting different polarizations for incident light. We show that, when N = 3, the next-nearest-neighbor Coulomb coupling is larger than its value if they are located at opposite ends of a right-angle triangle forming the triad. Additionally, the frequencies of the plasma excitations are found to depend on the orientation of the line joining them with respect to the axis of quantization since the magnetic field generated from the induced oscillating electric dipole moment on one sphere can couple to the induced magnetic dipole moment on another. Although the transverse inter-shell electromagnetic coupling can be modeled by an effective dynamic medium, the longitudinal inter-shell Coulomb coupling, on the other hand, can still significantly modify the electromagnetic property of this effective medium between shells.

Finite element approximation of a new variational principle for compressible and incompressible linear isotropic elasticity

International Nuclear Information System (INIS)

Franca, L.P.; Stenberg, R.

1989-06-01

Stability conditions are described to analyze a variational formulation emanating from a variational principle for linear isotropic elasticity. The variational principle is based on four dependent variables (namely, the strain tensor, augmented stress, pressure and displacement) and is shown to be valid for any compressibility including the incompressible limit. An improved convergence error analysis is established for a Galerkin-least-squares method based upon these four variables. The analysis presented establishes convergence for a wide choice of combinations of finite element interpolations. (author) [pt

Elastic interaction of hydrogen atoms on graphene: A multiscale approach from first principles to continuum elasticity

Science.gov (United States)

Branicio, Paulo S.; Vastola, Guglielmo; Jhon, Mark H.; Sullivan, Michael B.; Shenoy, Vivek B.; Srolovitz, David J.

2016-10-01

The deformation of graphene due to the chemisorption of hydrogen atoms on its surface and the long-range elastic interaction between hydrogen atoms induced by these deformations are investigated using a multiscale approach based on first principles, empirical interactions, and continuum modeling. Focus is given to the intrinsic low-temperature structure and interactions. Therefore, all calculations are performed at T =0 , neglecting possible temperature or thermal fluctuation effects. Results from different methods agree well and consistently describe the local deformation of graphene on multiple length scales reaching 500 Å . The results indicate that the elastic interaction mediated by this deformation is significant and depends on the deformation of the graphene sheet both in and out of plane. Surprisingly, despite the isotropic elasticity of graphene, within the linear elastic regime, atoms elastically attract or repel each other depending on (i) the specific site they are chemisorbed; (ii) the relative position of the sites; (iii) and if they are on the same or on opposite surface sides. The interaction energy sign and power-law decay calculated from molecular statics agree well with theoretical predictions from linear elasticity theory, considering in-plane or out-of-plane deformations as a superposition or in a coupled nonlinear approach. Deviations on the exact power law between molecular statics and the linear elastic analysis are evidence of the importance of nonlinear effects on the elasticity of monolayer graphene. These results have implications for the understanding of the generation of clusters and regular formations of hydrogen and other chemisorbed atoms on graphene.

Structural aspects of elastic deformation of a metallic glass

International Nuclear Information System (INIS)

Hufnagel, T. C.; Ott, R. T.; Almer, J.

2006-01-01

We report the use of high-energy x-ray scattering to measure strain in a Zr 57 Ti 5 Cu 20 Ni 8 Al 10 bulk metallic glass in situ during uniaxial compression in the elastic regime up to stresses of approximately 60% of the yield stress. The strains extracted in two ways--directly from the normalized scattering data and from the pair correlation functions--are in good agreement with each other for length scales greater than 4 A. The elastic modulus calculated on the basis of this strain is in good agreement with that reported for closely related amorphous alloys based on macroscopic measurements. The strain measured for atoms in the nearest-neighbor shell, however, is smaller than that for more distant shells, and the effective elastic modulus calculated from the strain on this scale is therefore larger, comparable to crystalline alloys of similar composition. These observations are in agreement with previously proposed models in which the nominally elastic deformation of a metallic glass has a significant anelastic component due to atomic rearrangements in topologically unstable regions of the structure. We also observe that the distribution of the atomic-level stresses in the glass becomes more uniform during loading. This implies that the stiffness of metallic glasses may have an entropic contribution, analogous to the entropic contribution in rubber elasticity

Electrostatics-driven shape transitions in soft shells.

Science.gov (United States)

Jadhao, Vikram; Thomas, Creighton K; Olvera de la Cruz, Monica

2014-09-02

Manipulating the shape of nanoscale objects in a controllable fashion is at the heart of designing materials that act as building blocks for self-assembly or serve as targeted drug delivery carriers. Inducing shape deformations by controlling external parameters is also an important way of designing biomimetic membranes. In this paper, we demonstrate that electrostatics can be used as a tool to manipulate the shape of soft, closed membranes by tuning environmental conditions such as the electrolyte concentration in the medium. Using a molecular dynamics-based simulated annealing procedure, we investigate charged elastic shells that do not exchange material with their environment, such as elastic membranes formed in emulsions or synthetic nanocontainers. We find that by decreasing the salt concentration or increasing the total charge on the shell's surface, the spherical symmetry is broken, leading to the formation of ellipsoids, discs, and bowls. Shape changes are accompanied by a significant lowering of the electrostatic energy and a rise in the surface area of the shell. To substantiate our simulation findings, we show analytically that a uniformly charged disc has a lower Coulomb energy than a sphere of the same volume. Further, we test the robustness of our results by including the effects of charge renormalization in the analysis of the shape transitions and find the latter to be feasible for a wide range of shell volume fractions.

A Linear Theory for Pretwisted Elastic Beams

DEFF Research Database (Denmark)

Krenk, Steen

1983-01-01

contains a general system of differential equations and gives explicit solutions for homogenous extension, torsion, and bending. The theory accounts explicitly for the shear center, the elastic center, and the axis of pretwist. The resulting torsion-extension coupling is in agreement with a recent...

Linear dynamic analysis of arbitrary thin shells modal superposition by using finite element method

International Nuclear Information System (INIS)

Goncalves Filho, O.J.A.

1978-11-01

The linear dynamic behaviour of arbitrary thin shells by the Finite Element Method is studied. Plane triangular elements with eighteen degrees of freedom each are used. The general equations of movement are obtained from the Hamilton Principle and solved by the Modal Superposition Method. The presence of a viscous type damping can be considered by means of percentages of the critical damping. An automatic computer program was developed to provide the vibratory properties and the dynamic response to several types of deterministic loadings, including temperature effects. The program was written in FORTRAN IV for the Burroughs B-6700 computer. (author)

Determination of the buckling safety of reinforced concrete shells considering the nonlinear material-behavior

International Nuclear Information System (INIS)

Zerna, W.; Mungan, I.; Steffen, W.

1980-01-01

The equations of the bending and stability theories for the orthotropic shell are solved using the FEM. A biaxial material law for concrete and a nearly bilinear stress-strain diagram for reinforcing steel were considered. Taking a layered ring element the influence of bending moments together with the membrane forces can be followed under increasing load up to failure of concrete or steel. At each level the bucking factor can be calculated considering the stress dependent buckling stiffness. The method of calculation is applied to a cooling tower shell under dead load acting simultaneously with an axi-symmetric loading to compensate for the wind effect. Due to orthotropy and descending tangent modulus at the ultimate load the buckling load factor drops to the half of the value obtained assuming a linear elastic behaviour. Additional parametric studies demonstrate the effect of some hypothetic cracks of different position and depth of the bifurcation results. The variation of the safety factors against buckling and ultimate load is obtained by changing the shell thickness. For the shell investigated it turns out that the buckling safety is influenced much more than the safety against material failure if the wall thickness is varied. It is recommended to split the buckling analysis of reinforced concrete shells in two parts. For shells of parts of a shell under only slightly disturbed membrane stress state the buckling analysis governs, otherwise the ultimate state considering the geometric and material nonlinearities is decisive to obtain not only the wall thickness but also the amount of reinforced necessary. (orig./HP) [de

Control of the Speed of a Light-Induced Spin Transition through Mesoscale Core-Shell Architecture.

Science.gov (United States)

Felts, Ashley C; Slimani, Ahmed; Cain, John M; Andrus, Matthew J; Ahir, Akhil R; Abboud, Khalil A; Meisel, Mark W; Boukheddaden, Kamel; Talham, Daniel R

2018-05-02

The rate of the light-induced spin transition in a coordination polymer network solid dramatically increases when included as the core in mesoscale core-shell particles. A series of photomagnetic coordination polymer core-shell heterostructures, based on the light-switchable Rb a Co b [Fe(CN) 6 ] c · mH 2 O (RbCoFe-PBA) as core with the isostructural K j Ni k [Cr(CN) 6 ] l · nH 2 O (KNiCr-PBA) as shell, are studied using temperature-dependent powder X-ray diffraction and SQUID magnetometry. The core RbCoFe-PBA exhibits a charge transfer-induced spin transition (CTIST), which can be thermally and optically induced. When coupled to the shell, the rate of the optically induced transition from low spin to high spin increases. Isothermal relaxation from the optically induced high spin state of the core back to the low spin state and activation energies associated with the transition between these states were measured. The presence of a shell decreases the activation energy, which is associated with the elastic properties of the core. Numerical simulations using an electro-elastic model for the spin transition in core-shell particles supports the findings, demonstrating how coupling of the core to the shell changes the elastic properties of the system. The ability to tune the rate of optically induced magnetic and structural phase transitions through control of mesoscale architecture presents a new approach to the development of photoswitchable materials with tailored properties.

Buckling analysis of a cylindrical shell, under neutron radiation environment

International Nuclear Information System (INIS)

Arani, A. Ghorbanpour; Ahmadi, M.; Ahmadi, A.; Rastgoo, A.; Sepyani, H.A.

2012-01-01

Highlights: ► The work investigates the buckling of a shell in the neutron radiation environment. ► Radiation induced porosity in elastic materials affects the material's properties. ► The data based technique was used to determine the volume fraction porosity. ► The theoretical formulations are presented based on the classical shell theory (CST). ► It was concluded that both T and neutron induced swelling have significant effects. - Abstract: This research investigates the buckling of a cylindrical shell in the neutron radiation environment, subjected to combined static and periodic axial forces. Radiation induced porosity in elastic materials affects the thermal, electrical and mechanical properties of the materials. In this study, the data based technique was used to determine the volume fraction porosity, P, of shell material. A least-squares fit of the Young's module data yielded the estimated Young's modulus. The shell assumed made of iron irradiated in the range of 2–15e−7 dPa/s at 345–650 °C and theoretical formulations are presented based on the classical shell theory (CST). The research deals with the problem theoretically; keeping in mind that one means of generating relevant design data is to investigate prototype structures. A parametric study is followed and the stability of shell is discussed. It is concluded that both temperature and neutron induced swelling have significant effects on the buckling load.

Elastic scattering of low energy γ-rays

International Nuclear Information System (INIS)

Whittingham, I.B.

1978-05-01

Theoretical cross sections for the elastic scattering of 245, 334, 444, 779, 1086, 1112 and 1408 keV γ-rays by Pb are obtained for scattering angles up to 150 degrees. Three sets of Rayleigh scattering amplitudes have been computed using (1) the calculations of Johnson and Cheng, (2) the K shell calculations of Brown and co-workers supplemented by form factors amplitudes for higher shells, and (3) form factor amplitudes for all shells. Nuclear Thomson amplitudes have been included for all energies and, for 1408 keV, Delbruck scattering based upon the calculations of Papatzacos and Mork has been included. Nuclear resonance scattering is show to be negligble for all energies

Extensions to a nonlinear finite element axisymmetric shell model based on Reissner's shell theory

International Nuclear Information System (INIS)

Cook, W.A.

1981-01-01

A finite element shell-of-revolution model has been developed to analyze shipping containers under severe impact conditions. To establish the limits for this shell model, I studied the basic assumptions used in its development; these are listed in this paper. Several extensions were evident from the study of these limits: a thick shell, a plastic hinge, and a linear normal stress. (orig./HP)

Three dimensional vibration and bending analysis of carbon nanotubes embedded in elastic medium based on theory of elasticity

Directory of Open Access Journals (Sweden)

M. Shaban

Full Text Available This paper studies free vibration and bending behavior of singlewalled carbon nanotubes (SWCNTs embedded on elastic medium based on three-dimensional theory of elasticity. To accounting the size effect of carbon nanotubes, non-local theory is adopted to shell model. The nonlocal parameter is incorporated into all constitutive equations in three dimensions. The surrounding medium is modeled as two-parameter elastic foundation. By using Fourier series expansion in axial and circumferential direction, the set of coupled governing equations are reduced to the ordinary differential equations in thickness direction. Then, the state-space method as an efficient and accurate method is used to solve the resulting equations analytically. Comprehensive parametric studies are carried out to show the influences of the nonlocal parameter, radial and shear elastic stiffness, thickness-to-radius ratio and radiusto-length ratio.

The lifetime of a long cylindrical shell under external pressure at elevated temperature

CERN Document Server

Bargmann, H W

1972-01-01

This paper is concerned with creep collapse of a long, thin walled, circular, cylindrical shell subjected to external pressure. The problem has been studied by Hoff et al. (1959), where elasticity has been neglected in the material equations. In the present paper it is pointed out that elasticity must not be neglected in stability problems as it may reduce the lifetime considerably. The improved equation for the lifetime of the shell is presented. Moreover, a procedure is indicated to derive the necessary creep parameters easily from usually available creep data. Numerical values of the lifetime of thin-walled, circular, cylindrical shells under external atmospheric pressure are presented for a wide range of shells of different geometrical characteristics for a number of high-temperature alloys and the temperature range up to 1000 degrees C. Experimental results are reported which are in good agreement with the theoretical prediction. (11 refs).

The region of influence of significant defects and the mechanical vibrations of linear elastic solids

International Nuclear Information System (INIS)

Suarez Antola, R.

2004-12-01

The presence of cracks, voids or fields of pores, and their growth under applied forces or environmental actions, can produce a meaningful lowering in the proper frequencies of normal modes of mechanical vibration in machines and structures. A quite general expression for the square of modes proper frequency as a functional of displacement field, density field and elastic moduli fields is used as a starting point. The effect of defects on frequency are modeled as equivalent changes in density and elastic moduli fields, introducing the concept of region of influence of each defect. This region of influence is derived from the relation between the stress field of flawed components in machines or structures, and the elastic energy released from a suitable reference state, due to the presence of significant defects in the above mentioned mechanical components. An approximate analytical expression is obtained, which relates the relative variation in the square of mode s proper frequency with position, size, shape and orientation of defects in mode displacement field. Some simple mathematical models of machine and structural elements with cracks or fields of pores are considered as examples. The connections between the relative lowering in the square of mode s proper frequency and the stress intensity factor of a defect are discussed : the concept of region of influence of a defect is used as a bridge between (low frequency and low amplitude) vibration dynamics and linear elastic fracture mechanics. Some limitations of the present approach are discussed as well as the possibility of applying the region of influence of defects to the damping of normal modes of vibration

Thermal Shock In Periodic Edge-Cracked Plate Supported By Elastic Foundation

OpenAIRE

Abd El-Fattah A. Rizk

2012-01-01

The study of the transient thermal stress problem for a periodic edge cracks in an elastic plate on an elastic foundations is investigated. This study may also be applied for circumferentially periodic cracked hollow cylinder under transient thermal stresses. Based on previous studies, the cylindrical shell may be modeled by a plate on an elastic foundation. The thermal stresses are generated due to sudden convective cooling on the boundary containing the edge cracks while the other boundary ...

The impact of ice I rheology on interior models of Ganymede: The elastic vs. the visco-elastic case

Science.gov (United States)

Steinbrügge, Gregor; Hussmann, Hauke; Sohl, Frank; Oberst, Jürgen

2015-04-01

Many investigations on key processes of icy satellites are driven by the rheological behavior of planetary ices. Future missions to Jupiter's icy moons (e.g. JUICE / Europa clipper) aimed at constraining the thickness of the outer ice shell using radio science and/or laser altimetry will have to address this problem. We investigate for the case of Ganymede under which conditions the ice I viscosity could be constrained by measuring the phase-lag of the tidal response using laser altimetry. In the absence of seismic data, interior structure models are constrained by the satellite's mean density and mean moment-of-inertia factor. One key observable to reduce the ambiguity of the corresponding structural models is the measurement of the dynamic response of the satellite's outer ice shells to tidal forces exerted by Jupiter and characterized by the body tide surface Love numbers h2 and k2. The Love number k2 measures the variation of the gravitational potential due to tidally induced internal redistribution of mass and can be inferred from radio science experiments. The Love number h2 is a measure for the tide-induced radial displacement of the satellite's surface. It is an advantage that Ganymede's surface displacement Love number h2 can be expected to be measured with a high accuracy using laser altimetry (Steinbrügge et al., 2014). However, the determination of the resulting ice thickness further depends on the possible existence of a liquid subsurface water ocean and on the tidally effective rheology of the outer ice shell (Moore and Schubert, 2003). Here, we distinguish between an elastic, visco-elastic or even fluid behavior in the sense of the Maxwell model and alternative rheological models. In the case of Ganymede the fluid case would imply high ice temperatures which are at odds with thermal equilibrium models calculated by Spohn and Schubert (2003). However the visco-elastic case is still possible. Laboratory measurements of ice I (e.g. Sotin et al., 1998

Colloidal InP/ZnS core-shell nanocrystals studied by linearly and circularly polarized photoluminescence

Energy Technology Data Exchange (ETDEWEB)

Langof, L.; Fradkin, L.; Ehrenfreund, E.; Lifshitz, E.; Micic, O.I.; Nozik, A.J

2004-02-16

The magneto-optical properties of InP/ZnS core-shell nanocrystals (NCs) were investigated by measuring the degree of linear and circular polarization of photoluminescence (PL) spectra, in the presence of an external magnetic field under resonant or non-resonant excitation. The linearly polarized PL data strongly indicate that InP/ZnS NCs have a prolongated shape. The resonant-excited circularly polarized PL decay curves indicate that the spin relaxation time of the studied samples is shorter than the radiative lifetime of their exciton. Furthermore, the magnetic field-induced circularly polarized PL process reveals an exciton g factor (g{sub ex}) of 0.55. Thus, such studies may serve as a tool to directly estimate the NC's shape anisotropy and to determine the g-factor of charge carriers and excitons in those NCs.

Modeling deformation and chaining of flexible shells in a nematic solvent with finite elements on an adaptive moving mesh

Science.gov (United States)

DeBenedictis, Andrew; Atherton, Timothy J.; Rodarte, Andrea L.; Hirst, Linda S.

2018-03-01

A micrometer-scale elastic shell immersed in a nematic liquid crystal may be deformed by the host if the cost of deformation is comparable to the cost of elastic deformation of the nematic. Moreover, such inclusions interact and form chains due to quadrupolar distortions induced in the host. A continuum theory model using finite elements is developed for this system, using mesh regularization and dynamic refinement to ensure quality of the numerical representation even for large deformations. From this model, we determine the influence of the shell elasticity, nematic elasticity, and anchoring condition on the shape of the shell and hence extract parameter values from an experimental realization. Extending the model to multibody interactions, we predict the alignment angle of the chain with respect to the host nematic as a function of aspect ratio, which is found to be in excellent agreement with experiments.

Nonlinear Finite Element Analysis of Shells with Large Aspect Ratio

Science.gov (United States)

Chang, T. Y.; Sawamiphakdi, K.

1984-01-01

A higher order degenerated shell element with nine nodes was selected for large deformation and post-buckling analysis of thick or thin shells. Elastic-plastic material properties are also included. The post-buckling analysis algorithm is given. Using a square plate, it was demonstrated that the none-node element does not have shear locking effect even if its aspect ratio was increased to the order 10 to the 8th power. Two sample problems are given to illustrate the analysis capability of the shell element.

FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE) NONLINEAR CALCULATIONS OF PLATES AND SHELLS

OpenAIRE

Bazhenov V.A.; Sacharov A.S.; Guliar A. I.; Pyskunov S.O.; Maksymiuk Y.V.

2014-01-01

Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

Waves on fluid-loaded shells and their resonance frequency spectrum

DEFF Research Database (Denmark)

Bao, X.L.; Uberall, H.; Raju, P.K.

2005-01-01

, or axially propagating waves both in the shell material, and in the fluid loading. Previous results by Bao et al. (J. Acoust. Soc. Am. 105 (1999) 2704) were obtained for the circumferential-wave dispersion curves on doubly loaded aluminum shells; the present study extends this to fluid-filled shells in air......Technical requirements for elastic (metal) cylindrical shells include the knowledge of their natural frequency spectrum. These shells may be empty and fluid-immersed, or fluid-filled in an ambient medium of air, or doubly fluid-loaded inside and out. They may support circumferential waves....... For practical applications, steel shells are most important and we have here obtained corresponding results for these. To find the natural frequencies of cylindrical shells, one may invoke the principle of phase matching where resonating standing waves are formed around the circumference, or in the axial...

Surface energy effect on free vibration of nano-sized piezoelectric double-shell structures

Science.gov (United States)

Fang, Xue-Qian; Zhu, Chang-Song; Liu, Jin-Xi; Liu, Xiang-Lin

2018-01-01

Combining Goldenveizer-Novozhilov shell theory, thin plate theory and electro-elastic surface theory, the size-dependent vibration of nano-sized piezoelectric double-shell structures under simply supported boundary condition is presented, and the surface energy effect on the natural frequencies is discussed. The displacement components of the cylindrical nano-shells and annular nano-plates are expanded as the superposition of standard Fourier series based on Hamilton's principle. The total stresses with consideration of surface energy effect are derived, and the total energy function is obtained by using Rayleigh-Ritz energy method. The free vibration equation is solved, and the natural frequency is analyzed. In numerical examples, it is found that the surface elastic constant, piezoelectric constant and surface residual stress show different effects on the natural frequencies. The effect of surface piezoelectric constant is the maximum. The effect of dimensions of the double-shell under different surface material properties is also examined.

Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

Science.gov (United States)

Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

2017-07-01

Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

Consideration of shear deformation in the analysis of unsymmetrical bending of moderately thick shells of revolution

International Nuclear Information System (INIS)

Das, M.L.

1975-01-01

A shear deformation theory is derived using a variational technique similar to Reissner-Naghdi linear theory neglecting the transverse normal stress. This theory is used to analyze shells of revolution subjected to arbitrary load distribution. The shell material is assumed to have two-dimensional elastic isotropy in directions tangent to its surface. Young's modulus may vary through the thickness and in the meridional direction. Poisson's ratio is assumed to be constant. Arbitrary temperature can be applied to the shell. Change of Young's modulus in the circumferential direction due to high temperature variation is neglected in the theory. All pertinent variables are expanded in Fourier series in the circumferential direction to get 5 ordinary differential equations, decoupled in individual Fourier components of independent displacements. Finite difference numerical technique is used to solve these differential equations. For handling these numerical quantities in orderly fashion, matrix algebra is utilized. Budiansky and Radkowski have applied a similar technique to solve the equations based on the classical shell theory of Sanders. Two independent computer programs are developed, one based on the shear deformation theory derived here and the other on the work of Budiansky and Radkowski. Two different circular cylindrical shells are utilized to explore the subject of this paper. They have the same geometric dimensions but different boundary conditions and one is fixed at both ends while the other has one end free

Atomic inner-shell physics

International Nuclear Information System (INIS)

Crasemann, B.

1985-01-01

This book discusses: relativistic and quantum electrodynamic effects on atomic inner shells; relativistic calculation of atomic transition probabilities; many-body effects in energetic atomic transitions; Auger Electron spectrometry of core levels of atoms; experimental evaluation of inner-vacancy level energies for comparison with theory; mechanisms for energy shifts of atomic K-X rays; atomic physics research with synchrotron radiation; investigations of inner-shell states by the electron energy-loss technique at high resolution; coherence effects in electron emission by atoms; inelastic X-ray scattering including resonance phenomena; Rayleigh scattering: elastic photon scattering by bound electrons; electron-atom bremsstrahlung; X-ray and bremsstrahlung production in nuclear reactions; positron production in heavy-ion collisions, and X-ray processes in heavy-ion collisions

Phason elasticity and surface roughening

International Nuclear Information System (INIS)

Tang Leihan; Jaric, M.V.

1990-01-01

The phason elasticity of two-dimensional (2D) equilibrium quasicrystals is discussed in analogy with surface roughening phenomena. Taking a Penrose tiling model as an example, we show that the phason elastic energy is linear in the phason strain at zero temperature (T = 0), but becomes quadratic at any T > 0 and sufficiently small strain. Heuristic and real-space renormalization group arguments are given for the thermal roughening of the hyper-surface which represents quasicrystal tiling. Monte Carlo method is applied to illustrate the logarithmically diverging phason fluctuations and power-law diffraction intensities at T > 0. For three-dimensional systems, we present arguments which suggest a finite temperature transition between two quasicrystal phases, characterized by linear and quadratic phason elastic energy, respectively. (author). 17 refs, 12 figs

Sensitivity study of buckling strength for cylindrical shells

Energy Technology Data Exchange (ETDEWEB)

Kato, Hideo; Sasaki, Toru [Institute of Nuclear Safety System Inc., Mihama, Fukui (Japan)

2001-09-01

Aiming at making clear buckling behavior of cylindrical shells under earthquake loadings, we investigated procedure of recent elastic-plastic buckling analysis by finite element method (FEM). Thereby it is confirmed that the buckling strength becomes as well as that of a shell with a cross section of a perfect cylinder, if we apply the first buckling eigenvector to imperfection mode and assume the maximum imperfection amplitude to be 1% of the wall thickness. And then, by carrying out sensitivity study of buckling with geometrical parameters, such as length (L), radius (R), wall thickness (t), and load parameter, such as pressure, we obtained several characteristics about buckling strength and buckling mode for cylindrical shells. From the geometrical parameter analysis, it is seen that bending buckling occurs for small R/t (thick wall) and elastic buckling occurs for 2{<=}L/R{<=}4 and R/t{>=}400. And from the load parameter analysis, it is shown that hoop stress caused by the inner pressure increases shear buckling strength but decreases bending buckling strength, and hoop stress by hydrostatic pressure changes buckling mode and generates local deformation. (author)

Review of Acceleration Methods for Seismic Analysis of Through-Wall Cracked Piping from the Viewpoint of Linear Elastic Fracture Mechanics

Energy Technology Data Exchange (ETDEWEB)

Kim, Jong Sung; Kim, Yong Woo [Sunchon National University, Suncheon (Korea, Republic of)

2014-10-15

Two acceleration methods, an effective force method (or inertia method) and a large mass method, have been applied for performing time history seismic analysis. The acceleration methods for uncracked structures have been verified via previous studies. However, no study has identified the validity of these acceleration methods for cracked piping. In this study, the validity of the acceleration methods for through-wall cracked piping is assessed via time history implicit dynamic elastic seismic analysis from the viewpoint of linear elastic fracture mechanics. As a result, it is identified that both acceleration methods show the same results for cracked piping if a large mass magnitude and maximum time increment are adequately selected.

Review of Acceleration Methods for Seismic Analysis of Through-Wall Cracked Piping from the Viewpoint of Linear Elastic Fracture Mechanics

International Nuclear Information System (INIS)

Kim, Jong Sung; Kim, Yong Woo

2014-01-01

Two acceleration methods, an effective force method (or inertia method) and a large mass method, have been applied for performing time history seismic analysis. The acceleration methods for uncracked structures have been verified via previous studies. However, no study has identified the validity of these acceleration methods for cracked piping. In this study, the validity of the acceleration methods for through-wall cracked piping is assessed via time history implicit dynamic elastic seismic analysis from the viewpoint of linear elastic fracture mechanics. As a result, it is identified that both acceleration methods show the same results for cracked piping if a large mass magnitude and maximum time increment are adequately selected

Local effects in thin elastic shell due to thermal and mechanical loadings

International Nuclear Information System (INIS)

Taheri, S.

1987-01-01

For a thick cylinder (1/15)<(h/rm)<(1/3) the local effect is represented by the same field. When the local effect is negligible the Love-Kirchhoff solution is valid for a thick cylinder. A shear effect shell theory may give for a thin cylinder a large error compared to the exact 3D solution on a thermal shock. The Love-Kirchhoff solution is generally not valid in the vicinity of a clamped or simply supported edge. A finite element program of thin shell with shear effect or thick shell ist not really reliable. A combination of 3D local solution and Love-Kirchhoff global solution through a transition zone may replace a complete 3D solution for not very thick structures. (orig./GL)

Cylindrical shell under impact load including transverse shear and normal stress

International Nuclear Information System (INIS)

Shakeri, M.; Eslami, M.R.; Ghassaa, M.; Ohadi, A.R.

1993-01-01

The general governing equations of shell of revolution under shock loads are reduced to equations describing the elastic behavior of cylindrical shell under axisymmetric impact load. The effect of lateral normal stress, transverse shear, and rotary inertia are included, and the equations are solved by Galerkin finite element method. The results are compared with the previous works of authors. (author)

Collusion and the elasticity of demand

OpenAIRE

David Collie

2004-01-01

The analysis of collusion in infinitely repeated Cournot oligopoly games has generally assumed that demand is linear, but this note uses constant-elasticity demand functions to investigate how the elasticity of demand affects the sustainability of collusion.

Determination of elastic modulus for hollow spherical shells via resonant ultrasound spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Ma, Xiaojun [Institute of Modern Physics, Fudan University, Shanghai 200433 (China); Research Center of Laser Fusion, CAEP, Mianyang 621900 (China); Tang, Xing; Wang, Zongwei [Research Center of Laser Fusion, CAEP, Mianyang 621900 (China); Chen, Qian; Qian, Menglu [Institute of Acoustic, Tongji University, Shanghai 200092 (China); Meng, Jie [Research Center of Laser Fusion, CAEP, Mianyang 621900 (China); Tang, Yongjian [Institute of Modern Physics, Fudan University, Shanghai 200433 (China); Research Center of Laser Fusion, CAEP, Mianyang 621900 (China); Shen, Hao [Institute of Modern Physics, Fudan University, Shanghai 200433 (China); Gao, Dangzhong, E-mail: dgaocn@163.com [Research Center of Laser Fusion, CAEP, Mianyang 621900 (China)

2017-04-15

Highlights: • The axisymmetric frequency equation of an isotropic hollow two-layer sphere is deduced by three dimension elasticity theory and global matrix method. • The simulated results demonstrate that the natural frequencies of a hollow sphere are more strongly dependent on Young’s modulus than Poisson's ratio. • The Young’s moduli of polymer capsules with an sub-millimeter inner radius are measured accurately with an uncertainty of ∼10%. - Abstract: The elastic property of a capsule is one of the essential parameters both in engineering applications and scientific understanding of material nature in inertial confinement fusion (ICF) experiments. The axisymmetric frequency equation of an isotropic hollow two-layer sphere is deduced by three dimension elasticity theory and global matrix method, and a combined resonant ultrasound spectroscopy(RUS), which consists of a piezoelectric-based resonant ultrasound spectroscopy(PZT-RUS) and a laser-based resonant ultrasound spectroscopy(LRUS), is developed for determining the elastic modulus of capsule. To understand the behavior of natural frequencies varying with elastic properties, the dependence of natural frequencies on Young’s modulus and Poisson’s ratio are calculated numerically. Some representative polymer capsules are measured using PZT-RUS and LRUS. Based on the theoretical and experimental results, the Young’s moduli of these capsules are measured accurately with an uncertainty of ∼10%.

FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE NONLINEAR CALCULATIONS OF PLATES AND SHELLS

Directory of Open Access Journals (Sweden)

Bazhenov V.A.

2014-06-01

Full Text Available Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

Transient response of rotating laminated functionally graded cylindrical shells in thermal environment

International Nuclear Information System (INIS)

Malekzadeh, P.; Heydarpour, Y.; Haghighi, M.R. Golbahar; Vaghefi, M.

2012-01-01

Based on the elasticity theory, the transient analysis of dynamically pressurized rotating multi-layered functionally graded (FG) cylindrical shells in thermal environment is presented. The variations of the field variables across the shell thickness are accurately modeled by dividing the shell into a set of co-axial mathematical layers in the radial direction. The initial thermo-mechanical stresses are obtained by solving the thermoelastic equilibrium equations. The differential quadrature method and Newmark's time integration scheme are employed to discretize the obtained governing equations of each mathematical layer. After performing the convergence and comparison studies, parametric studies for two common types of FG sandwich shells, namely, the shell with homogeneous inner/outer layers and FG core and the shell with FG inner/outer layers and homogeneous core are carried out. The influences of the temperature dependence of material properties, material graded index, the convective heat transfer coefficient, the angular velocity, the boundary condition and the geometrical parameters (length and thickness to outer radius ratios) on the dynamic response of the FG shells are investigated. Highlights: ► As a first endeavor, transient analysis of rotating laminated functionally graded cylinders. ► Employing an elasticity based discrete layer-differential quadrature method. ► Evaluating and including the initial thermo-mechanical stresses accurately. ► Considering the temperature-dependence of the material properties. ► Presenting some new results, which can be used as benchmark solution for future works.

Elastic metamaterial beam with remotely tunable stiffness

Energy Technology Data Exchange (ETDEWEB)

Qian, Wei [University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240 (China); Yu, Zhengyue [School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China); Wang, Xiaole [School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China); Lai, Yun [College of Physics, Optoelectronics and Energy & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006 (China); Yellen, Benjamin B., E-mail: yellen@duke.edu [University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240 (China); Department of Mechanical Engineering and Materials Science, Duke University, P.O. Box 90300, Hudson Hall, Durham, North Carolina 27708 (United States)

2016-02-07

We demonstrate a dynamically tunable elastic metamaterial, which employs remote magnetic force to adjust its vibration absorption properties. The 1D metamaterial is constructed from a flat aluminum beam milled with a linear array of cylindrical holes. The beam is backed by a thin elastic membrane, on which thin disk-shaped permanent magnets are mounted. When excited by a shaker, the beam motion is tracked by a Laser Doppler Vibrometer, which conducts point by point scanning of the vibrating element. Elastic waves are unable to propagate through the beam when the driving frequency excites the first elastic bending mode in the unit cell. At these frequencies, the effective mass density of the unit cell becomes negative, which induces an exponentially decaying evanescent wave. Due to the non-linear elastic properties of the membrane, the effective stiffness of the unit cell can be tuned with an external magnetic force from nearby solenoids. Measurements of the linear and cubic static stiffness terms of the membrane are in excellent agreement with experimental measurements of the bandgap shift as a function of the applied force. In this implementation, bandgap shifts by as much as 40% can be achieved with ∼30 mN of applied magnetic force. This structure has potential for extension in 2D and 3D, providing a general approach for building dynamically tunable elastic metamaterials for applications in lensing and guiding elastic waves.

Elastic metamaterial beam with remotely tunable stiffness

Science.gov (United States)

Qian, Wei; Yu, Zhengyue; Wang, Xiaole; Lai, Yun; Yellen, Benjamin B.

2016-02-01

We demonstrate a dynamically tunable elastic metamaterial, which employs remote magnetic force to adjust its vibration absorption properties. The 1D metamaterial is constructed from a flat aluminum beam milled with a linear array of cylindrical holes. The beam is backed by a thin elastic membrane, on which thin disk-shaped permanent magnets are mounted. When excited by a shaker, the beam motion is tracked by a Laser Doppler Vibrometer, which conducts point by point scanning of the vibrating element. Elastic waves are unable to propagate through the beam when the driving frequency excites the first elastic bending mode in the unit cell. At these frequencies, the effective mass density of the unit cell becomes negative, which induces an exponentially decaying evanescent wave. Due to the non-linear elastic properties of the membrane, the effective stiffness of the unit cell can be tuned with an external magnetic force from nearby solenoids. Measurements of the linear and cubic static stiffness terms of the membrane are in excellent agreement with experimental measurements of the bandgap shift as a function of the applied force. In this implementation, bandgap shifts by as much as 40% can be achieved with ˜30 mN of applied magnetic force. This structure has potential for extension in 2D and 3D, providing a general approach for building dynamically tunable elastic metamaterials for applications in lensing and guiding elastic waves.

Calculations of concrete plates and shells under impact load

International Nuclear Information System (INIS)

Kappler, H.; Krings, W.

1982-01-01

The dynamic behaviour of concrete slabs and shells is determined for a given load time function using axisymmetric computational models with an exact formulation for the midpoint. On the basis of a finite difference method, rotational inertia, shear deformation, elasticity and cracking are taken into account. For shells the coupling of bending moment and normal force is considered. Comparisons with two-dimensional models show good agreement connected with a considerable reduction of computational time. (orig.) [de

Fabrication of CuO–Pt core–shell nanohooks by in situ reconstructing the Pt-shells

Science.gov (United States)

Cao, Fan; Zheng, He; Zhao, Ligong; Huang, Rui; Jia, Shuangfeng; Liu, Huihui; Li, Lei; Wang, Zhao; Hu, Yongming; Gu, Haoshuang; Wang, Jianbo

2018-05-01

The design of various nanostructures with specific compositions and shapes is highly demanded due to the widespread use of micro/nano electro-mechanical systems. In this work, one-dimensional CuO–Pt core–shell nanowires (NWs) are acquired by depositing Pt nanoparticles onto CuO NWs and then mechanically-shaped into nanohooks. Subsequently, the hook-like shape is maintained by the Pt-shell which is reconstructed via Joule heat and re-solidified after cooling down, during which the elastic strain energy is stored in the CuO-core. The results provide a simple strategy to design nanostructures with various compositions and shapes, implying the potential applications in mechanical energy storage and shape memory nanodevices.

Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

Science.gov (United States)

Pipkins, Daniel Scott

Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially. linear model are compared to those

Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

KAUST Repository

Angela Mihai, L.; Goriely, Alain

2013-01-01

Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects

Reversible patterning of spherical shells through constrained buckling

Science.gov (United States)

Marthelot, J.; Brun, P.-T.; Jiménez, F. López; Reis, P. M.

2017-07-01

Recent advances in active soft structures envision the large deformations resulting from mechanical instabilities as routes for functional shape morphing. Numerous such examples exist for filamentary and plate systems. However, examples with double-curved shells are rarer, with progress hampered by challenges in fabrication and the complexities involved in analyzing their underlying geometrical nonlinearities. We show that on-demand patterning of hemispherical shells can be achieved through constrained buckling. Their postbuckling response is stabilized by an inner rigid mandrel. Through a combination of experiments, simulations, and scaling analyses, our investigation focuses on the nucleation and evolution of the buckling patterns into a reticulated network of sharp ridges. The geometry of the system, namely, the shell radius and the gap between the shell and the mandrel, is found to be the primary ingredient to set the surface morphology. This prominence of geometry suggests a robust, scalable, and tunable mechanism for reversible shape morphing of elastic shells.

The second-order S-matrix element for the elastic scattering of photons by K-shell bound electrons: the nonrelativistic limit

Energy Technology Data Exchange (ETDEWEB)

Costescu, A [Department of Physics, University of Bucharest, MG11, Bucharest-Magurele 76900 (Romania); Spanulescu, S [Department of Physics, University of Bucharest, MG11, Bucharest-Magurele 76900 (Romania); Stoica, C [Department of Physics, University of Bucharest, MG11, Bucharest-Magurele 76900 (Romania)

2007-08-14

The right expressions of the nonrelativistic K-shell Rayleigh scattering amplitudes and cross-sections are obtained by using the Coulomb Green's function method. Our analytical result does not have the spurious poles that occur in the old nonrelativistic result with retardation (Gavrila and Costescu 1970 Phys. Rev. A 2 1752). Starting from the expression of the second-order S-matrix element for the case of the elastic scattering of photons by K-shell bound electrons, we obtain the correct nonrelativistic Rayleigh angular distribution (valid for photon energies {omega} up to {alpha}Zm) by removing the relativistic higher order terms in {alpha}Z and {omega}/m. The imaginary part of the Rayleigh amplitudes is obtained for any scattering angles in a closed form in terms of elementary functions. Thereby a simple formula for the exact nonrelativistic photoeffect total cross-section is obtained via the optical theorem, giving significantly better predictions than Fischer's nonrelativistic photoeffect formula. Comparing the predictions given by our formulae with the full relativistic numerical calculations of Kissel et al (Phys. Rev. 1980 A 22 1970), and with experimental results, a fairly good agreement within 10% is found for the angular distribution of Rayleigh scattering for photon energies up to 200 keV and both below and above the first resonance.

The threshold anomaly in the interaction of s-d shell nuclei

International Nuclear Information System (INIS)

Bilwes, B.

1990-01-01

The energy dependence of the potential near the Coulomb barrier is studied by precise measurements of elastic scattering and quasi elastic reactions between s-d shell nuclei. The analyses with semi-microscopic (M3Y-folding model) and microscopic (closure approximation model) potentials allow us to demonstrate the generality of the threshold anomaly and the ability of these models to well reproduce the experimental data

The visco-elastic multilayer program VEROAD

NARCIS (Netherlands)

Hopman, P.C.

1996-01-01

The mathematical principles and derivation of a linear visco-elastic multilayer computer program are described. The mathematical derivation is based on Fourier Transformation. The program is called VEROAD, which is an acronym for Visco-Elastic ROad Analysis Delft. The program allows calculation of

Nonlinear Subincremental Method for Determination of Elastic-Plastic-Creep Behaviour

DEFF Research Database (Denmark)

Ottosen, N. Saabye; Gunneskov, O.

1985-01-01

to general elastic-plastic-creep behaviour including problems with a highly nonlinear total strain path caused by the occurrence of creep hardening. This nonlinear method degenerates to the linear approach for elastic-plastic behaviour and when secondary creep is present. It is also linear during step......The frequently used subincremental method has so far been used on a linear interpolation of the total strain path within each main step. This method has proven successful when elastic-plastic behaviour and secondary creep is involved. The authors propose a nonlinear subincremental method applicable...

Elastic band prediction equations for combined free-weight and elastic band bench presses and squats.

Science.gov (United States)

Shoepe, Todd C; Ramirez, David A; Almstedt, Hawley C

2010-01-01

Elastic bands added to traditional free-weight techniques have become a part of suggested training routines in recent years. Because of the variable loading patterns of elastic bands (i.e., greater stretch produces greater resistance), it is necessary to quantify the exact loading patterns of bands to identify the volume and intensity of training. The purpose of this study was to determine the length vs. tension properties of multiple sizes of a set of commonly used elastic bands to quantify the resistance that would be applied to free-weight plus elastic bench presses (BP) and squats (SQ). Five elastic bands of varying thickness were affixed to an overhead support beam. Dumbbells of varying weights were progressively added to the free end while the linear deformation was recorded with each subsequent weight increment. The resistance was plotted as a factor of linear deformation, and best-fit nonlinear logarithmic regression equations were then matched to the data. For both the BP and SQ loading conditions and all band thicknesses tested, R values were greater than 0.9623. These data suggest that differences in load exist as a result of the thickness of the elastic band, attachment technique, and type of exercise being performed. Facilities should adopt their own form of loading quantification to match their unique set of circumstances when acquiring, researching, and implementing elastic band and free-weight exercises into the training programs.

Numerical investigation of heat transfer characteristic of fixed planar elastic tube bundles

International Nuclear Information System (INIS)

Duan, Derong; Ge, Peiqi; Bi, Wenbo

2015-01-01

Highlights: • Both tube-side and shell-side of planar elastic tube bundles were investigated. • Heat transfer and fluid flow were studied from the local analysis perspective. • Secondary flow varies depending on the fluid flow state and the geometry of tube. • Curvature plays a role on the external flow field. • The heat transfer of the two intermediate tube bundles is augmented. - Abstract: Planar elastic tube bundles are a novel approach to enhance heat transfer by using flow-induced vibration. This paper studied the heat transfer characteristic and fluid flow in both tube-side and shell-side using numerical simulation. Two temperature difference formulas were used to calculate convective heat transfer coefficient and the results were verified by theoretical analysis and experimental correlations. The effect of Reynolds number on overall convective heat transfer coefficient and pressure drop in tube-side and shell-side were studied. The comparison of the secondary flow in planar elastic tube bundles and conical spiral tube bundles were conducted. The external flow field and local convective heat transfer around the periphery of fixed planar elastic tube bundles subjected to the cross fluid flow were also analyzed. The results show that the energy consumption efficiency should be taken into account in the forced heat transfer process conducted by adjusting the fluid flow. The secondary flow varies depending on the fluid flow state and the geometry of tube. Hence, it is deduced that the heat transfer enhancement is obtained because the thermal boundary layer in the deformed planar elastic tube bundles caused by flow-induced vibration is damaged by the disordered secondary flow. In addition, the convective heat transfer capability of outside the two intermediate tube bundles is enhanced because of the effect of irregular and complex fluid flow affected by the role of curved tubes on both sides

Geometric Nonlinear Computation of Thin Rods and Shells

Science.gov (United States)

Grinspun, Eitan

2011-03-01

We develop simple, fast numerical codes for the dynamics of thin elastic rods and shells, by exploiting the connection between physics, geometry, and computation. By building a discrete mechanical picture from the ground up, mimicking the axioms, structures, and symmetries of the smooth setting, we produce numerical codes that not only are consistent in a classical sense, but also reproduce qualitative, characteristic behavior of a physical system----such as exact preservation of conservation laws----even for very coarse discretizations. As two recent examples, we present discrete computational models of elastic rods and shells, with straightforward extensions to the viscous setting. Even at coarse discretizations, the resulting simulations capture characteristic geometric instabilities. The numerical codes we describe are used in experimental mechanics, cinema, and consumer software products. This is joint work with Miklós Bergou, Basile Audoly, Max Wardetzky, and Etienne Vouga. This research is supported in part by the Sloan Foundation, the NSF, Adobe, Autodesk, Intel, the Walt Disney Company, and Weta Digital.

Cell wall elasticity: I. A critique of the bulk elastic modulus approach and an analysis using polymer elastic principles

Science.gov (United States)

Wu, H. I.; Spence, R. D.; Sharpe, P. J.; Goeschl, J. D.

1985-01-01

The traditional bulk elastic modulus approach to plant cell pressure-volume relations is inconsistent with its definition. The relationship between the bulk modulus and Young's modulus that forms the basis of their usual application to cell pressure-volume properties is demonstrated to be physically meaningless. The bulk modulus describes stress/strain relations of solid, homogeneous bodies undergoing small deformations, whereas the plant cell is best described as a thin-shelled, fluid-filled structure with a polymer base. Because cell walls possess a polymer structure, an alternative method of mechanical analysis is presented using polymer elasticity principles. This initial study presents the groundwork of polymer mechanics as would be applied to cell walls and discusses how the matrix and microfibrillar network induce nonlinear stress/strain relationships in the cell wall in response to turgor pressure. In subsequent studies, these concepts will be expanded to include anisotropic expansion as regulated by the microfibrillar network.

Off-shell sensitivity, repulsive correlations and the pion-nucleus optical potential

Energy Technology Data Exchange (ETDEWEB)

Keister, B D [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA). Dept. of Physics

1977-07-01

Repulsive nucleon-nucleon correlations tend to reduce the dependence of pion-nucleus elastic scattering upon the off-shell pion-nucleon dynamics. However, optical potential calculations can in practice be quite sensitive to the particular choice of off-shell model parameters. It is argued that this sensitivity results from the nature of the optical potential as a one-body operator which introduces extra off-shell dependence not found in physical many-body process itself. Thus, one must be very careful in any attempt to extract correlation or off-shell information, or to predict pion-nucleus phase shifts, by means of an optical potential theory. Results of model calculations are presented for purposes of illustration.

Influence of temperature on elastic properties of caesium cyanide

International Nuclear Information System (INIS)

Singh, Preeti; Gaur, N.K.; Singh, R.K.

2007-01-01

An extended three body force shell model (ETSM), which incorporates the effects of translational-rotational (TR) coupling, three body interactions (TBI) and anharmonicity, has been applied to investigate the temperature dependence of the second order elastic constants (c ij , i,j=1,2) of CsCN. The elastic constant c 44 obtained by us shows an anomalous behaviour with the variation of temperature. The variations of elastic constants (c 11 , c 12 , c 44 ) with temperature are almost in excellent agreement with Brillouin scattering measured data. We have also evaluated the temperature variations of the third order elastic constants (c ijk ) and the pressure derivatives of the c ij in the CsCN material. However, their values could not be compared due to lack of experimental data. (copyright 2007 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

Axisymmetric thermoviscoelastoplastic state of branched laminar shells, taking account of transverse-shear and torsional deformation

International Nuclear Information System (INIS)

Galishin, A.Z.

1995-01-01

The nonaxisymmetric thermoelastic stress-strain state (SSS) of branched laminar orthotropic shells was considered; the axisymmetric thermoviscoelastic SSS of branched laminar orthotropic shells was considered; and the axisymmetric thermoviscoelastoplastic SSS of branched laminar isotropic shells was considered, taking into account of the transverse-shear deformation. In the present work, in contrast, the axisymmetric thermoviscoelastoplastic SSS of branched laminar isotropic shells is considered, taking account of transverse-shear and torsional deformation. Layers that are made from orthotropic materials and deform in the elastic region may be present

A linear stability analysis of thermal convection in spherical shells with variable radial gravity based on the Tau-Chebyshev method

International Nuclear Information System (INIS)

Avila, Ruben; Cabello-González, Ares; Ramos, Eduardo

2013-01-01

Highlights: • The Tau-Chebyshev method solves the linear fluid flow equations in spherical shells. • The fluid motion is driven by a central force proportional to the radial position. • The full Navier–Stokes equations are solved by the spectral element method. • The linear results are verified with the solution of the Navier–Stokes equations. • The solution of the linear problems is used to initiate non-linear calculations. -- Abstract: The onset of thermal convection in a non-rotating spherical shell is investigated using linear theory. The Tau-Chebyshev spectral method is used to integrate the linearized equations. We investigate the onset of thermal convection by considering two cases of the radial gravitational field (i) a local acceleration, acting radially inward, that is proportional to the distance from the center r, and (ii) a radial gravitational central force that is proportional to r −n . The former case has been widely analyzed in the literature, because it constitutes a simplified model that is usually used, in astrophysics and geophysics, and is studied here to validate the numerical method. The latter case was analyzed since the case n = 5 has been experimentally realized (by means of the dielectrophoretic effect) under microgravity condition, in the experimental container called GeoFlow, inside the International Space Station. Our study is aimed to clarify the role of (i) a radially inward central force (either proportional to r or to r −n ), (ii) a base conductive temperature distribution provided by either a uniform heat source or an imposed temperature difference between outer and inner spheres, and (iii) the aspect ratio η (ratio of the radii of the inner and outer spheres), on the critical Rayleigh number. In all cases the surface of the spheres has been assumed to be rigid. The results obtained with the linear theory based on the Tau-Chebyshev spectral method are compared with those of the integration of the full non-linear

Analysis of thin composite structures using an efficient hex-shell finite element

Energy Technology Data Exchange (ETDEWEB)

Shiri, Seddik [Universite Bordeaux, Pessac (France); Naceur, Hakim [Universite de valenciennes, Valenciennes (France)

2013-12-15

In this paper a general methodology for the modeling of material composite multilayered shell structures is proposed using a Hex-shell finite element modeling. The first part of the paper is devoted to the general FE formulation of the present composite 8-node Hex-shell element called SCH8, based only on displacement degrees of freedom. A particular attention is given to alleviate shear, trapezoidal and thickness locking, without resorting to the classical plane-stress assumption. The anisotropic material behavior of layered shells is modeled using a fully three dimensional elastic orthotropic material law in each layer, including the thickness stress component. Applications to laminate thick shell structures are studied to validate the methodology, and good results have been obtained in comparison with ABAQUS commercial code.

Linear elastic obstacles: analysis of experimental results in the case of stress dependent pre-exponentials

International Nuclear Information System (INIS)

Surek, T.; Kuon, L.G.; Luton, M.J.; Jones, J.J.

1975-01-01

For the case of linear elastic obstacles, the analysis of experimental plastic flow data is shown to have a particularly simple form when the pre-exponential factor is a single-valued function of the modulus-reduced stress. The analysis permits the separation of the stress and temperature dependence of the strain rate into those of the pre-exponential factor and the activation free energy. As a consequence, the true values of the activation enthalpy, volume and entropy also are obtained. The approach is applied to four sets of experimental data, including Zr, and the results for the pre-exponential term are examined for self-consistency in view of the assumed functional dependence

On the hyperporous non-linear elasticity model for fusion-relevant pebble beds

International Nuclear Information System (INIS)

Di Maio, P.A.; Giammusso, R.; Vella, G.

2010-01-01

Packed pebble beds are particular granular systems composed of a large amount of small particles, arranged in irregular lattices and surrounded by a gas filling interstitial spaces. Due to their heterogeneous structure, pebble beds have non-linear and strongly coupled thermal and mechanical behaviours whose constitutive models seem limited, being not suitable for fusion-relevant design-oriented applications. Within the framework of the modelling activities promoted for the lithiated ceramics and beryllium pebble beds foreseen in the Helium-Cooled Pebble Bed breeding blanket concept of DEMO, at the Department of Nuclear Engineering of the University of Palermo (DIN) a thermo-mechanical constitutive model has been set-up assuming that pebble beds can be considered as continuous, homogeneous and isotropic media. The present paper deals with the DIN non-linear elasticity constitutive model, based on the assumption that during the reversible straining of a pebble bed its effective logarithmic bulk modulus depends on the equivalent pressure according to a modified power law and its effective Poisson modulus remains constant. In these hypotheses the functional dependence of the effective tangential and secant bed deformation moduli on either the equivalent pressure or the volumetric strain have been derived in a closed analytical form. A procedure has been, then, defined to assess the model parameters for a given pebble bed from its oedometric test results and it has been applied to both polydisperse lithium orthosilicate and single size beryllium pebble beds.

Elastic and plastic buckling of shells. The CEASEMT system. Available results. Comparison with tests

International Nuclear Information System (INIS)

Hoffmann, A.; Roche, R.; Jeanpierre, F.; Goldstein, S.

1977-01-01

Specific routines for the analysis of elastic and elastic-plastic buckling have been written in the CEASEMT system of analysis by the finite element method. The basis of formulation are reviewed with emphasis on important points like: the correct and comprehensive formulation of the second order terms, the nonconservative loads. Some computational results are given and a comparison is made with experimental results (Euler type buckling of a long tube, elastic-plastic buckling of torispherical ends) [fr

A second-order virtual node algorithm for nearly incompressible linear elasticity in irregular domains

Science.gov (United States)

Zhu, Yongning; Wang, Yuting; Hellrung, Jeffrey; Cantarero, Alejandro; Sifakis, Eftychios; Teran, Joseph M.

2012-08-01

We present a cut cell method in R2 for enforcing Dirichlet and Neumann boundary conditions with nearly incompressible linear elastic materials in irregular domains. Virtual nodes on cut uniform grid cells are used to provide geometric flexibility in the domain boundary shape without sacrificing accuracy. We use a mixed formulation utilizing a MAC-type staggered grid with piecewise bilinear displacements centered at cell faces and piecewise constant pressures at cell centers. These discretization choices provide the necessary stability in the incompressible limit and the necessary accuracy in cut cells. Numerical experiments suggest second order accuracy in L∞. We target high-resolution problems and present a class of geometric multigrid methods for solving the discrete equations for displacements and pressures that achieves nearly optimal convergence rates independent of grid resolution.

Statistical mechanics of microscopically thin thermalized shells

Science.gov (United States)

Kosmrlj, Andrej

Recent explosion in fabrication of microscopically thin free standing structures made from graphene and other two-dimensional materials has led to a renewed interest in the mechanics of such structures in presence of thermal fluctuations. Since late 1980s it has been known that for flat solid sheets thermal fluctuations effectively increase the bending rigidity and reduce the bulk and shear moduli in a scale-dependent fashion. However, much is still unknown about the mechanics of thermalized flat sheets of complex geometries and about the mechanics of thermalized shells with non-zero background curvature. In this talk I will present recent development in the mechanics of thermalized ribbons, spherical shells and cylindrical tubes. Long ribbons are found to behave like hybrids between flat sheets with renormalized elastic constants and semi-flexible polymers, and these results can be used to predict the mechanics of graphene kirigami structures. Contrary to the anticipated behavior for ribbons, the non-zero background curvature of shells leads to remarkable novel phenomena. In shells, thermal fluctuations effectively generate negative surface tension, which can significantly reduce the critical buckling pressure for spherical shells and the critical axial load for cylindrical tubes. For large shells this thermally generated load becomes big enough to spontaneously crush spherical shells and cylindrical tubes even in the absence of external loads. I will comment on the relevance for crushing of microscopic shells (viral capsids, bacteria, microcapsules) due to osmotic shocks and for crushing of nanotubes.

THE STRESS-STRAIN STATE OF ELASTIC HALF-SPACE FROM RUNNING LINEAR LOAD ACTING ON THE LIMITED AND UNLIMITED EXTENT OVER ITS SURFACE

Directory of Open Access Journals (Sweden)

I. K. Badalakha

2009-02-01

Full Text Available The article shows the result of solving the problem of stress-strain state of an elastic half-space because of the load action that uniformly distributed over the line, with the use of untraditional linear dependence of deformations on stressed state that is different from the generalized Hooke’s law.

Equivalent Young's Modulus of Perforated Shell with Square Penetration Pattern

Energy Technology Data Exchange (ETDEWEB)

Jhung, Myung Jo; Ryu, Yong Ho [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of)

2011-05-15

The analysis of a plate or shell perforated with a large number of holes, by finite element method for instance, was a very costly and time-consuming technique which solves only one particular problem. But it is possible to model the perforated plate or shell and to analyze it and it is no more time-consuming theses days due to the rapid development of the computer and software. However, if a perforated plate or shell is submerged in fluid it is almost impossible to model and analyze it as is and the fluid at the same time, which is needed to investigate the effect of the fluid structure interaction. The simplest way to avoid time consuming and costly analysis of perforated plate or shell submerged in fluid is to replace the perforated plate or shell by an equivalent solid one considering weakening effect of holes. Many authors have proposed experimental or theoretical method to solve this problem for the plate. Slot and O'Donnell determined the effective elastic constants for the thick perforated plates by equating strains in the equivalent solid material to the average strains in the perforated material. O'Donnell also presented those of thin perforated plates. These results are implemented in Article A-8000 of Appendix A to the ASME code Section III, which contains a method of analysis for flat perforated plates when subjected to directly applied loads or loadings resulting from structural interaction with adjacent members. Unfortunately the effective elastic constants for the perforated shell are not found in any references. Therefore in this study the modal characteristics of the perforated shell are investigated and the equivalent material properties of perforated shell are suggested by performing several finite element analyses with respect to the ligament efficiencies

Linearized stability analysis of thin-shell wormholes with a cosmological constant

International Nuclear Information System (INIS)

Lobo, Francisco S N; Crawford, Paulo

2004-01-01

Spherically symmetric thin-shell wormholes in the presence of a cosmological constant are constructed applying the cut-and-paste technique implemented by Visser. Using the Darmois-Israel formalism the surface stresses, which are concentrated at the wormhole throat, are determined. This construction allows us to apply a dynamical analysis to the throat, considering linearized radial perturbations around static solutions. For a large positive cosmological constant, i.e., for the Schwarzschild-de Sitter solution, the region of stability is significantly increased, relatively to the null cosmological constant case, analysed by Poisson and Visser. With a negative cosmological constant, i.e., the Schwarzschild-anti de Sitter solution, the region of stability is decreased. In particular, considering static solutions with a generic cosmological constant, the weak and dominant energy conditions are violated, while for a 0 ≤ 3M the null and strong energy conditions are satisfied. The surface pressure of the static solution is strictly positive for the Schwarzschild and Schwarzschild-anti de Sitter spacetimes, but takes negative values, assuming a surface tension in the Schwarzschild-de Sitter solution, for high values of the cosmological constant and the wormhole throat radius

Remarks on orthotropic elastic models applied to wood

Directory of Open Access Journals (Sweden)

Nilson Tadeu Mascia

2006-09-01

Full Text Available Wood is generally considered an anisotropic material. In terms of engineering elastic models, wood is usually treated as an orthotropic material. This paper presents an analysis of two principal anisotropic elastic models that are usually applied to wood. The first one, the linear orthotropic model, where the material axes L (Longitudinal, R( radial and T(tangential are coincident with the Cartesian axes (x, y, z, is more accepted as wood elastic model. The other one, the cylindrical orthotropic model is more adequate of the growth caracteristics of wood but more mathematically complex to be adopted in practical terms. Specifically due to its importance in wood elastic parameters, this paper deals with the fiber orientation influence in these models through adequate transformation of coordinates. As a final result, some examples of the linear model, which show the variation of elastic moduli, i.e., Young´s modulus and shear modulus, with fiber orientation are presented.

Multi-scale hierarchy of Chelydra serpentina: microstructure and mechanical properties of turtle shell.

Science.gov (United States)

Balani, Kantesh; Patel, Riken R; Keshri, Anup K; Lahiri, Debrupa; Agarwal, Arvind

2011-10-01

Carapace, the protective shell of a freshwater snapping turtle, Chelydra serpentina, shields them from ferocious attacks of their predators while maintaining light-weight and agility for a swim. The microstructure and mechanical properties of the turtle shell are very appealing to materials scientists and engineers for bio-mimicking, to obtain a multi-functional surface. In this study, we have elucidated the complex microstructure of a dry Chelydra serpentina's shell which is very similar to a multi-layered composite structure. The microstructure of a turtle shell's carapace elicits a sandwich structure of waxy top surface with a harder sub-surface layer serving as a shielding structure, followed by a lamellar carbonaceous layer serving as shock absorber, and the inner porous matrix serves as a load-bearing scaffold while acting as reservoir of retaining water and nutrients. The mechanical properties (elastic modulus and hardness) of various layers obtained via nanoindentation corroborate well with the functionality of each layer. Elastic modulus ranged between 0.47 and 22.15 GPa whereas hardness varied between 53.7 and 522.2 MPa depending on the microstructure of the carapace layer. Consequently, the modulus of each layer was represented into object oriented finite element (OOF2) modeling towards extracting the overall effective modulus of elasticity (~4.75 GPa) of a turtle's carapace. Stress distribution of complex layered structure was elicited with an applied strain of 1% in order to understand the load sharing of various composite layers in the turtle's carapace. Copyright © 2011 Elsevier Ltd. All rights reserved.

Pattern zoology in biaxially pre-stretched elastic bilayers: from wrinkles and creases to fracture-like ridges

Science.gov (United States)

Al-Rashed, Rashed; Lopez JiméNez, Francisco; Reis, Pedro

The wrinkling of elastic bilayers under compression has been explored as a method to produce reversible surface topography, with applications ranging from microfluidics to tunable optics. We introduce a new experimental system to study the effects of pre-stretching on the instability patterns that result from the biaxial compression of thin shells bound to an elastic substrate. A pre-stretched substrate is first prepared by pressurizing an initially flat elastomeric disk and bulging it into a nearly hemispherical thick shell. The substrate is then coated with a thin layer of a polymer suspension, which, upon curing, results in a thin shell of nearly constant thickness. Releasing the pre-stretch in the substrate by deflating the system places the outer film in a state of biaxial compression, resulting in a variety of buckling patterns. We explore the parameter space by systematically varying the pre-stretch, the substrate/film stiffness mismatch, and the thickness of the film. This results in a continuous transition between different buckling patterns, from the dimples and wrinkles that are traditionally associated with the buckling of elastic bilayers, to creases and high aspect ratio `fracture-like' ridges, where the pre-stretch plays an essential role.

Elastic least-squares reverse time migration

KAUST Repository

Feng, Zongcai

2017-03-08

We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTMsolves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional leastsquares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTMwill produce migration noise stronger than that seen in the RTM images.

Elastic least-squares reverse time migration

KAUST Repository

Feng, Zongcai; Schuster, Gerard T.

2017-01-01

We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTMsolves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional leastsquares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTMwill produce migration noise stronger than that seen in the RTM images.

Elastic thickness determination based on Vening Meinesz-Moritz and flexural theories of isostasy

Science.gov (United States)

Eshagh, Mehdi

2018-06-01

Elastic thickness (Te) is one of mechanical properties of the Earth's lithosphere. The lithosphere is assumed to be a thin elastic shell, which is bended under the topographic, bathymetric and sediment loads on. The flexure of this elastic shell depends on its thickness or Te. Those shells having larger Te flex less. In this paper, a forward computational method is presented based on the Vening Meinesz-Moritz (VMM) and flexural theories of isostasy. Two Moho flexure models are determined using these theories, considering effects of surface and subsurface loads. Different values are selected for Te in the flexural method to see by which one, the closest Moho flexure to that of the VMM is achieved. The effects of topographic/bathymetric, sediments and crustal crystalline masses, and laterally variable upper mantle density, Young's modulus and Poisson's ratio are considered in whole computational process. Our mathematical derivations are based on spherical harmonics, which can be used to estimate Te at any single point, meaning that there is no edge effect in the method. However, the Te map needs to be filtered to remove noise at some points. A median filter with a window size of 5° × 5° and overlap of 4° works well for this purpose. The method is applied to estimate Te over South America using the data of CRUST1.0 and a global gravity model.

Laser Heating of the Core-Shell Nanowires

Science.gov (United States)

Astefanoaei, Iordana; Dumitru, Ioan; Stancu, Alexandru

2016-12-01

The induced thermal stress in a heating process is an important parameter to be known and controlled in the magnetization process of core-shell nanowires. This paper analyses the stress produced by a laser heating source placed at one end of a core-shell type structure. The thermal field was computed with the non-Fourier heat transport equation using a finite element method (FEM) implemented in Comsol Multiphysics. The internal stresses are essentially due to thermal gradients and different expansion characteristics of core and shell materials. The stress values were computed using the thermo elastic formalism and are depending on the laser beam parameters (spot size, power etc.) and system characteristics (dimensions, thermal characteristics). Stresses in the GPa range were estimated and consequently we find that the magnetic state of the system can be influenced significantly. A shell material as the glass which is a good thermal insulator induces in the magnetic core, the smaller stresses and consequently the smaller magnetoelastic energy. These results lead to a better understanding of the switching process in the magnetic materials.

Elasto/visco-plastic analysis of orthotropic moderately thick shells of revolution under asymmetrical loading

International Nuclear Information System (INIS)

Tao, K.; Takezono, S.

1989-01-01

An analytical method for the elasto/visco-plastic problems of general, orthotropic moderately thick shells of revolution subjected to asymmetrical loads is developed in consideration of the effect of shear deformations. The Reissner-Naghdi theory for elastic moderately thick shells is extended in this analysis. As the constitutive equation, Hooke's law for orthotropic materials is used in the elastic region, and equations based on the orthotropic visco-plastic theory derived from the orthotropic plastic theory by Hill are employed in the plastic range. The visco-plastic strain rates are related to the stresses by Perzyna's equation. The fundamental equations for the increment are numerically solved by a finite difference method and the solutions are obtained by summation of the incremental values. In order to check the adequacy of the numerical analysis, experiments are performed on the elasto/visco-plastic deformation of a titanium cylindrical shell subjected to locally distributed loads. Good agreement is obtained between the experimental results and analytical solutions

Predicting the elastic properties of double-walled carbon nanotubes by molecular dynamics simulation

International Nuclear Information System (INIS)

Zhang Chenli; Shen Huishen

2008-01-01

Molecular dynamics simulation is performed on a double-walled carbon nanotube (DWCNT) to predict its elastic properties based on a double-walled shear deformable shell model. By direct buckling measurement, we present here a method for uniquely determining the effective wall thickness for the shell model. Accounting for two different kinds of DWCNTs by adding an inner or outer tube to a fiducial tube, the mechanical properties of DWCNTs are carefully investigated as compared with those of the fiducial tube. It is found that the predicted values of Young's and shear moduli depend strongly on the construction and helicity of DWCNTs, while the dependence on nanotube length is relatively small. The results also confirm that the temperature variation has a significant effect on the elastic properties of DWCNTs

Pulsed-laser time-resolved thermal mirror technique in low-absorbance homogeneous linear elastic materials.

Science.gov (United States)

Lukasievicz, Gustavo V B; Astrath, Nelson G C; Malacarne, Luis C; Herculano, Leandro S; Zanuto, Vitor S; Baesso, Mauro L; Bialkowski, Stephen E

2013-10-01

A theoretical model for a time-resolved photothermal mirror technique using pulsed-laser excitation was developed for low absorption samples. Analytical solutions to the temperature and thermoelastic deformation equations are found for three characteristic pulse profiles and are compared to finite element analysis methods results for finite samples. An analytical expression for the intensity of the center of a continuous probe laser at the detector plane is derived using the Fresnel diffraction theory, which allows modeling of experimental results. Experiments are performed in optical glasses, and the models are fitted to the data. The parameters of the fit are in good agreement with previous literature data for absorption, thermal diffusion, and thermal expansion of the materials tested. The combined modeling and experimental techniques are shown to be useful for quantitative determination of the physical properties of low absorption homogeneous linear elastic material samples.

The effectiveness of a standardized rose hip powder, containing seeds and shells of Rosa canina, on cell longevity, skin wrinkles, moisture, and elasticity

Directory of Open Access Journals (Sweden)

Phetcharat L

2015-11-01

Full Text Available L Phetcharat,1,2 K Wongsuphasawat,1,2 K Winther31School of Antiaging and Regenerative Medicine, Mae Fah University, Bangkok, Thailand; 2Department of Anti-aging and Regenerative Medicine, Mae Fah University, Bangkok, Thailand; 3Institute for Nutrition, Exercise and Sports, University of Copenhagen, Frederiksberg C, DenmarkObjective: To evaluate the effects of a rose hip powder (Hyben Vital® made from seeds and shells on cell senescence, skin wrinkling, and aging.Methods: A total of 34 healthy subjects, aged 35–65 years, with wrinkles on the face (crow’s-feet were subjected to a randomized and double-blinded clinical study of the effects of the rose hip powder, as compared to astaxanthin, a well-known remedy against wrinkles. During the 8-week study, half of the participants ingested the standardized rose hip product, while the other half ingested astaxanthin. Objective measurements of facial wrinkles, skin moisture, and elasticity were made by using Visioscan, Corneometer, and Cutometer at the beginning of the study, after 4 weeks, and after 8 weeks. Evaluation of participant satisfaction of both supplements was assessed using questionnaires. In addition, the effect of the rose hip preparation on cell longevity was measured in terms of leakage of hemoglobin through red cell membranes (hemolytic index in blood samples kept in a blood bank for 5 weeks. Significance of all values was attained with P≤0.05.Results: In the double-blinded study, the rose hip group showed statistically significant improvements in crow’s-feet wrinkles (P<0.05, skin moisture (P<0.05, and elasticity (P<0.05 after 8 weeks of treatment. A similar improvement was observed for astaxanthin, with P-values 0.05, 0.001, and 0.05. Likewise, both groups expressed equal satisfaction with the results obtained in their self-assessment. The rose hip powder further resulted in increased cell longevity of erythrocyte cells during storage for 5 weeks in a blood bank

Two-photon exchange corrections in elastic lepton-proton scattering

Energy Technology Data Exchange (ETDEWEB)

Tomalak, Oleksandr; Vanderhaeghen, Marc [Johannes Gutenberg Universitaet Mainz (Germany)

2015-07-01

The measured value of the proton charge radius from the Lamb shift of energy levels in muonic hydrogen is in strong contradiction, by 7-8 standard deviations, with the value obtained from electronic hydrogen spectroscopy and the value extracted from unpolarized electron-proton scattering data. The dominant unaccounted higher order contribution in scattering experiments corresponds to the two photon exchange (TPE) diagram. The elastic contribution to the TPE correction was studied with the fixed momentum transfer dispersion relations and compared to the hadronic model with off-shell photon-nucleon vertices. A dispersion relation formalism with one subtraction was proposed. Theoretical predictions of the TPE elastic contribution to the unpolarized elastic electron-proton scattering and polarization transfer observables in the low momentum transfer region were made. The TPE formalism was generalized to the case of massive leptons and the elastic contribution was evaluated for the kinematics of upcoming muon-proton scattering experiment (MUSE).

A finite-element for the analysis of shell intersections

International Nuclear Information System (INIS)

Koves, W.J.; Nair, S.

1994-01-01

The analysis of discontinuity stresses at shell intersections is a problem of great importance in several major industries. Some of the major areas of interest are pressure-containing equipment, such as reactors and piping, in the nuclear and fossil power industry; pressure vessels and heat exchangers in the petrochemical industry; bracing in offshore oil platforms; and aerospace structures. A specialized shell-intersection finite element, which is compatible with adjoining shell elements, has been developed that has the capability of physically representing the complex three-dimensional geometry and stress state at shell intersections. The element geometry is a contoured shape that matches a wide variety of practical nozzle configurations used in ASME Code pressure vessel construction, and allows computational rigor. A closed-form theory of elasticity solution was used to compute the stress state and strain energy in the element. The concept of an energy-equivalent nodal displacement and force vector set was then developed to allow complete compatibility with adjoining shell elements and retain the analytical rigor within the element. This methodology provides a powerful and robust computation scheme that maintains the computational efficiency of shell element solutions. The shell-intersection element was then applied to the cylinder-sphere and cylinder-cylinder intersection problems

Shell morphology and Raman spectra of epitaxial Ge-SixGe1-x and Si-SixGe1-x core-shell nanowires

Science.gov (United States)

Wen, Feng; Dillen, David C.; Kim, Kyounghwan; Tutuc, Emanuel

2017-06-01

We investigate the shell morphology and Raman spectra of epitaxial Ge-SixGe1-x and Si-SixGe1-x core-shell nanowire heterostructures grown using a combination of a vapor-liquid-solid (VLS) growth mechanism for the core, followed by in-situ epitaxial shell growth using ultra-high vacuum chemical vapor deposition. Cross-sectional transmission electron microscopy reveals that the VLS growth yields cylindrical Ge, and Si nanowire cores grown along the ⟨111⟩, and ⟨110⟩ or ⟨112⟩ directions, respectively. A hexagonal cross-sectional morphology is observed for Ge-SixGe1-x core-shell nanowires terminated by six {112} facets. Two distinct morphologies are observed for Si-SixGe1-x core-shell nanowires that are either terminated by four {111} and two {100} planes associated with the ⟨110⟩ growth direction or four {113} and two {111} planes associated with the ⟨112⟩ growth direction. We show that the Raman spectra of Si- SixGe1-x are correlated with the shell morphology thanks to epitaxial growth-induced strain, with the core Si-Si mode showing a larger red shift in ⟨112⟩ core-shell nanowires compared to their ⟨110⟩ counterparts. We compare the Si-Si Raman mode value with calculations based on a continuum elasticity model coupled with the lattice dynamic theory.

Pion elastic and inelastic scattering from 15N

International Nuclear Information System (INIS)

Saunders, D.P.

1991-12-01

Data were obtained on the Clinton P. Anderson Los Alamos Meson Physics Facility Energetic Pion Channel and Spectrometer for elastic and inelastic pion scattering from ground state 15 N nuclei. States observed here included those of 0.0, 5.27, 6.32, 7.16, 7.30, 7.57, 8.31, 8.57, 9.15, 9.76, 9.9, 10.7, 11.3, 11.9, 12.5, 12.9, 13.1, 14.1, 14.4, 14.6, 15.0, 16.5, 16.9, 17.2, 17.6, 18.3, 18.7, and 18.9 MeV excitation energies. Angular distributions were obtained for scattering at angles from 25 degree to 90 degree in 5 degree increments with an incident pion energy of 164 MeV. Optical model analyses of the elastic (0 MeV) angular distributions with equal point proton and neutron densities in both momentum and coordinate space formulations accurately predict the data, although the two formulations require different energy shifts to do so. This difference is thought to be a result of the more accurate nonlocal representation of the nuclear potential in the momentum space code. Additional spectra were obtained for scattering at constant momentum transfers of .94 and 1.57 fm -1 in order to generate constant momentum transfer excitation functions. Use of these excitation functions, σ(π + )/σ(π - ) ratios, and shell model DWIA calculations allowed identification of several excited states having shell-model-like, single particle-hole, pure spin-flip excitations. Shell model and collective model DWIA calculations, as well as the q = .94 and 1.57 fm -1 excitation functions and the σ(π + )/σ(π - ) ratios indicate that the other states are generally well represented by a shell model description with collective enhancements

Simulation of thermal stress and buckling instability in Si/Ge and Ge/Si core/shell nanowires.

Science.gov (United States)

Das, Suvankar; Moitra, Amitava; Bhattacharya, Mishreyee; Dutta, Amlan

2015-01-01

The present study employs the method of atomistic simulation to estimate the thermal stress experienced by Si/Ge and Ge/Si, ultrathin, core/shell nanowires with fixed ends. The underlying technique involves the computation of Young's modulus and the linear coefficient of thermal expansion through separate simulations. These two material parameters are combined to obtain the thermal stress on the nanowires. In addition, the thermally induced stress is perceived in the context of buckling instability. The analysis provides a trade-off between the geometrical and operational parameters of the nanostructures. The proposed methodology can be extended to other materials and structures and helps with the prediction of the conditions under which a nanowire-based device might possibly fail due to elastic instability.

Elasto/visco-plastic analysis of moderately thick shells of revolution under asymmetrical loading

International Nuclear Information System (INIS)

Tao, K.; Takezono, S.

1987-01-01

In the present paper the analytical formulation for the elasto/visco-plastic problems of general, moderately thick shells of revolution subjected to asymmetrical loads is developed in consideration of the effect of shear deformation. The equations of equilibrium and the relations between the strains and displacements are derived by extending the Reissner-Naghdi theory (1941, 1957) for elastic shells with given consideration to the effect of shear deformation. As the constitutive relation, Hooke's law is used in the liner elastic range, and the elasto/visco-plastic equations by Perzyna (1966) are employed in the plastic range. The fundamental equations on the elasto/visco-plastic problems derived for incremental values are numerically solved by a finite difference method and the solutions are obtained by summation of the incremental values. (orig./GL)

The creep of multi-layered moderately thick shells of revolution under asymmetrical loading

International Nuclear Information System (INIS)

Takezono, S.; Migita, K.

1987-01-01

In the present paper the authors study the creep deformation of the multi-layered thick shells of revolution under asymmetrical loads. The equations of equilibrium and the strain-displacement relations are derived from the Reissner-Naghdi theory (1941, 1957) for elastic shells where a consideration on the effect of shear deformation is given. In the theory of creep it is assumed that in a given increment of time the total strain increments are composed of an elastic part and a part due to creep. The elastic strains are proportional to the stresses by Hooke's law. For the constitutive equations in the creep range, McVetty's equation modified by Arrhenius' equation for thermal effect is employed. The basic differential equations on the creep problems derived for the incremental values with respect to time are numerically solved by a finite difference method and the solutions at any time are obtained by summation of the incremental values. Resultant forces and resultant moments are given from numerical integration of the stresses by Simpson's 1/3 rules. (orig./GL)

Estimating the price elasticity of expenditure for prescription drugs in the presence of non-linear price schedules: an illustration from Quebec, Canada.

Science.gov (United States)

Contoyannis, Paul; Hurley, Jeremiah; Grootendorst, Paul; Jeon, Sung-Hee; Tamblyn, Robyn

2005-09-01

The price elasticity of demand for prescription drugs is a crucial parameter of interest in designing pharmaceutical benefit plans. Estimating the elasticity using micro-data, however, is challenging because insurance coverage that includes deductibles, co-insurance provisions and maximum expenditure limits create a non-linear price schedule, making price endogenous (a function of drug consumption). In this paper we exploit an exogenous change in cost-sharing within the Quebec (Canada) public Pharmacare program to estimate the price elasticity of expenditure for drugs using IV methods. This approach corrects for the endogeneity of price and incorporates the concept of a 'rational' consumer who factors into consumption decisions the price they expect to face at the margin given their expected needs. The IV method is adapted from an approach developed in the public finance literature used to estimate income responses to changes in tax schedules. The instrument is based on the price an individual would face under the new cost-sharing policy if their consumption remained at the pre-policy level. Our preferred specification leads to expenditure elasticities that are in the low range of previous estimates (between -0.12 and -0.16). Naïve OLS estimates are between 1 and 4 times these magnitudes. (c) 2005 John Wiley & Sons, Ltd.

Isogeometric shell formulation based on a classical shell model

KAUST Repository

Niemi, Antti

2012-09-04

This paper constitutes the first steps in our work concerning isogeometric shell analysis. An isogeometric shell model of the Reissner-Mindlin type is introduced and a study of its accuracy in the classical pinched cylinder benchmark problem presented. In contrast to earlier works [1,2,3,4], the formulation is based on a shell model where the displacement, strain and stress fields are defined in terms of a curvilinear coordinate system arising from the NURBS description of the shell middle surface. The isogeometric shell formulation is implemented using the PetIGA and igakit software packages developed by the authors. The igakit package is a Python package used to generate NURBS representations of geometries that can be utilised by the PetIGA finite element framework. The latter utilises data structures and routines of the portable, extensible toolkit for scientific computation (PETSc), [5,6]. The current shell implementation is valid for static, linear problems only, but the software package is well suited for future extensions to geometrically and materially nonlinear regime as well as to dynamic problems. The accuracy of the approach in the pinched cylinder benchmark problem and present comparisons against the h-version of the finite element method with bilinear elements. Quadratic, cubic and quartic NURBS discretizations are compared against the isoparametric bilinear discretization introduced in [7]. The results show that the quadratic and cubic NURBS approximations exhibit notably slower convergence under uniform mesh refinement as the thickness decreases but the quartic approximation converges relatively quickly within the standard variational framework. The authors future work is concerned with building an isogeometric finite element method for modelling nonlinear structural response of thin-walled shells undergoing large rigid-body motions. The aim is to use the model in a aeroelastic framework for the simulation of flapping wings.

Elastic silicone encapsulation of n-hexadecyl bromide by microfluidic approach as novel microencapsulated phase change materials

International Nuclear Information System (INIS)

Fu, Zhenjin; Su, Lin; Li, Jing; Yang, Ruizhuang; Zhang, Zhanwen; Liu, Meifang; Li, Jie; Li, Bo

2014-01-01

Highlights: • n-Hexadecyl bromide was encapsuled in elastic silicone shell. • The surfaces of microcapsules were smooth and the cross sections were compact. • Latent heat of microcapsules was 76.35 J g −1 . • The microencapsulation ratio was 49 wt.%. • The microcapsules had good thermal stability. - Abstract: The elastic silicone/n-hexadecyl bromide microcapsules were prepared as novel microencapsulated phase change materials by microfluidic approach with the co-flowing channels, where the double oil1-in-oil2-in-water (O1/O2/W) droplets with a core–shell geometry were fabricated. The thermal characterizations of the microcapsules were investigated using differential scanning calorimetry (DSC) and thermogravimetry analysis (TGA). The DSC results showed that the microcapsules had good energy storage capacity with melting and freezing enthalpies 76.35 J g −1 and 78.67 J g −1 , respectively. The TGA investigation showed that the microcapsules had good thermal stability. The surfaces of microcapsules were smooth and the cross sections were compact from the results of optical microscope and scanning electron microscopy (SEM). Optical microscope showed that the silicone shell can provide expansion place due to its elastic property. Therefore, the silicone/n-hexadecyl bromide microcapsules showed good potential as thermal regulating textile and thermal insulation materials

First-order system least squares for the pure traction problem in planar linear elasticity

Energy Technology Data Exchange (ETDEWEB)

Cai, Z.; Manteuffel, T.; McCormick, S.; Parter, S.

1996-12-31

This talk will develop two first-order system least squares (FOSLS) approaches for the solution of the pure traction problem in planar linear elasticity. Both are two-stage algorithms that first solve for the gradients of displacement, then for the displacement itself. One approach, which uses L{sup 2} norms to define the FOSLS functional, is shown under certain H{sup 2} regularity assumptions to admit optimal H{sup 1}-like performance for standard finite element discretization and standard multigrid solution methods that is uniform in the Poisson ratio for all variables. The second approach, which is based on H{sup -1} norms, is shown under general assumptions to admit optimal uniform performance for displacement flux in an L{sup 2} norm and for displacement in an H{sup 1} norm. These methods do not degrade as other methods generally do when the material properties approach the incompressible limit.

Non-linear waves in heterogeneous elastic rods via homogenization

KAUST Repository

Quezada de Luna, Manuel

2012-03-01

We consider the propagation of a planar loop on a heterogeneous elastic rod with a periodic microstructure consisting of two alternating homogeneous regions with different material properties. The analysis is carried out using a second-order homogenization theory based on a multiple scale asymptotic expansion. © 2011 Elsevier Ltd. All rights reserved.

Elastic plastic fracture mechanics

International Nuclear Information System (INIS)

Simpson, L.A.

1978-07-01

The application of linear elastic fracture mechanics (LEFM) to crack stability in brittle structures is now well understood and widely applied. However, in many structural materials, crack propagation is accompanied by considerable crack-tip plasticity which invalidates the use of LEFM. Thus, present day research in fracture mechanics is aimed at developing parameters for predicting crack propagation under elastic-plastic conditions. These include critical crack-opening-displacement methods, the J integral and R-curve techniques. This report provides an introduction to these concepts and gives some examples of their applications. (author)

Wave motion in elastic solids

CERN Document Server

Graff, Karl F

1991-01-01

This highly useful textbook presents comprehensive intermediate-level coverage of nearly all major topics of elastic wave propagation in solids. The subjects range from the elementary theory of waves and vibrations in strings to the three-dimensional theory of waves in thick plates. The book is designed not only for a wide audience of engineering students, but also as a general reference for workers in vibrations and acoustics. Chapters 1-4 cover wave motion in the simple structural shapes, namely strings, longitudinal rod motion, beams and membranes, plates and (cylindrical) shells. Chapter

About two new efficient nonlinear shell elements

International Nuclear Information System (INIS)

Yin, J.; Suo, X.Z.; Combescure, A.

1989-01-01

The aim of the paper is to present the development of two shell elements for non linear analysis. The first one is an axisymetric curved shell element and it is developed for buckling analysis. The formulation is given, as well as some typical applications. The second one is an extension of the classical DKT element to large strains taking into account all aspects of non linearities. This element is used for the simulation of four point bending of cracked pipes. The whole experiment is simulated by the calculation taking into account very large strains at the crack tip and propagation of the crack

A refined element-based Lagrangian shell element for geometrically nonlinear analysis of shell structures

Directory of Open Access Journals (Sweden)

Woo-Young Jung

2015-04-01

Full Text Available For the solution of geometrically nonlinear analysis of plates and shells, the formulation of a nonlinear nine-node refined first-order shear deformable element-based Lagrangian shell element is presented. Natural co-ordinate-based higher order transverse shear strains are used in present shell element. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, a refined first-order shear deformation theory for thin and thick shells, which results in parabolic through-thickness distribution of the transverse shear strains from the formulation based on the third-order shear deformation theory, is proposed. This formulation eliminates the need for shear correction factors in the first-order theory. To avoid difficulties resulting from large increments of the rotations, a scheme of attached reference system is used for the expression of rotations of shell normal. Numerical examples demonstrate that the present element behaves reasonably satisfactorily either for the linear or for geometrically nonlinear analysis of thin and thick plates and shells with large displacement but small strain. Especially, the nonlinear results of slit annular plates with various loads provided the benchmark to test the accuracy of related numerical solutions.

Forced Vibrations of a Two-Layer Orthotropic Shell with an Incomplete Contact Between Layers

Science.gov (United States)

Ghulghazaryan, L. G.; Khachatryan, L. V.

2018-01-01

Forced vibrations of a two-layer orthotropic shell, with incomplete contact conditions between layers, when the upper face of the shell is free and the lower one is subjected to a dynamic action are considered. By an asymptotic method, the solution of the corresponding dynamic equations and correlations of a 3D problem of elasticity theory is obtained. The amplitudes of forced vibrations are determined, and resonance conditions are established.

A non-linear elastic constitutive framework for replicating plastic deformation in solids.

Energy Technology Data Exchange (ETDEWEB)

Roberts, Scott Alan; Schunk, Peter Randall

2014-02-01

Ductile metals and other materials typically deform plastically under large applied loads; a behavior most often modeled using plastic deformation constitutive models. However, it is possible to capture some of the key behaviors of plastic deformation using only the framework for nonlinear elastic mechanics. In this paper, we develop a phenomenological, hysteretic, nonlinear elastic constitutive model that captures many of the features expected of a plastic deformation model. This model is based on calculating a secant modulus directly from a materials stress-strain curve. Scalar stress and strain values are obtained in three dimensions by using the von Mises invariants. Hysteresis is incorporated by tracking an additional history variable and assuming an elastic unloading response. This model is demonstrated in both single- and multi-element simulations under varying strain conditions.

Coherently Strained Si-SixGe1-x Core-Shell Nanowire Heterostructures.

Science.gov (United States)

Dillen, David C; Wen, Feng; Kim, Kyounghwan; Tutuc, Emanuel

2016-01-13

Coherently strained Si-SixGe1-x core-shell nanowire heterostructures are expected to possess a positive shell-to-core conduction band offset, allowing for quantum confinement of electrons in the Si core. We report the growth of epitaxial, coherently strained Si-SixGe1-x core-shell heterostructures through the vapor-liquid-solid mechanism for the Si core, followed in situ by the epitaxial SixGe1-x shell growth using ultrahigh vacuum chemical vapor deposition. The Raman spectra of individual nanowires reveal peaks associated with the Si-Si optical phonon mode in the Si core and the Si-Si, Si-Ge, and Ge-Ge vibrational modes of the SixGe1-x shell. The core Si-Si mode displays a clear red-shift compared to unstrained, bare Si nanowires thanks to the lattice mismatch-induced tensile strain, in agreement with calculated values using a finite-element continuum elasticity model combined with lattice dynamic theory. N-type field-effect transistors using Si-SixGe1-x core-shell nanowires as channel are demonstrated.

Stressed-deformed state of mountain rocks in elastic stage and between elasticity

Directory of Open Access Journals (Sweden)

Samedov A.M.

2017-12-01

destroy as a plastic material. In the elastic stage, the link between stress and strain is linear.

Isostructural solid-solid phase transition in monolayers of soft core-shell particles at fluid interfaces: structure and mechanics.

Science.gov (United States)

Rey, Marcel; Fernández-Rodríguez, Miguel Ángel; Steinacher, Mathias; Scheidegger, Laura; Geisel, Karen; Richtering, Walter; Squires, Todd M; Isa, Lucio

2016-04-21

We have studied the complete two-dimensional phase diagram of a core-shell microgel-laden fluid interface by synchronizing its compression with the deposition of the interfacial monolayer. Applying a new protocol, different positions on the substrate correspond to different values of the monolayer surface pressure and specific area. Analyzing the microstructure of the deposited monolayers, we discovered an isostructural solid-solid phase transition between two crystalline phases with the same hexagonal symmetry, but with two different lattice constants. The two phases corresponded to shell-shell and core-core inter-particle contacts, respectively; with increasing surface pressure the former mechanically failed enabling the particle cores to come into contact. In the phase-transition region, clusters of particles in core-core contacts nucleate, melting the surrounding shell-shell crystal, until the whole monolayer moves into the second phase. We furthermore measured the interfacial rheology of the monolayers as a function of the surface pressure using an interfacial microdisk rheometer. The interfaces always showed a strong elastic response, with a dip in the shear elastic modulus in correspondence with the melting of the shell-shell phase, followed by a steep increase upon the formation of a percolating network of the core-core contacts. These results demonstrate that the core-shell nature of the particles leads to a rich mechanical and structural behavior that can be externally tuned by compressing the interface, indicating new routes for applications, e.g. in surface patterning or emulsion stabilization.

Core-Shell Double Gyroid Structure Formed by Linear ABC Terpolymer Thin Films.

Science.gov (United States)

Antoine, Ségolène; Aissou, Karim; Mumtaz, Muhammad; Telitel, Siham; Pécastaings, Gilles; Wirotius, Anne-Laure; Brochon, Cyril; Cloutet, Eric; Fleury, Guillaume; Hadziioannou, Georges

2018-05-01

The synthesis and self-assembly in thin-film configuration of linear ABC triblock terpolymer chains consisting of polystyrene (PS), poly(2-vinylpyridine) (P2VP), and polyisoprene (PI) are described. For that purpose, a hydroxyl-terminated PS-b-P2VP (45 kg mol -1 ) building block and a carboxyl-terminated PI (9 kg mol -1 ) are first separately prepared by anionic polymerization, and then are coupled via a Steglich esterification reaction. This quantitative and metal-free catalyst synthesis route reveals to be very interesting since functionalization and purification steps are straightforward, and well-defined terpolymers are produced. A solvent vapor annealing (SVA) process is used to promote the self-assembly of frustrated PS-b-P2VP-b-PI chains into a thin-film core-shell double gyroid (Q 230 , space group: Ia3¯d) structure. As terraces are formed within PS-b-P2VP-b-PI thin films during the SVA process under a CHCl 3 vapor, different plane orientations of the Q 230 structure ((211), (110), (111), and (100)) are observed at the polymer-air interface depending on the film thickness. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

On elastic moduli and elastic anisotropy in polycrystalline martensitic NiTi

International Nuclear Information System (INIS)

Qiu, S.; Clausen, B.; Padula, S.A.; Noebe, R.D.; Vaidyanathan, R.

2011-01-01

A combined experimental and computational effort was undertaken to provide insight into the elastic response of B19' martensitic NiTi variants as they exist in bulk, polycrystalline aggregate form during monotonic tensile and compressive loading. The experimental effort centered on using in situ neutron diffraction during loading to measure elastic moduli in several directions along with an average Young's modulus and a Poisson's ratio. The measurements were compared with predictions from a 30,000 variant, self-consistent polycrystalline deformation model that accounted for the elastic intergranular constraint, and also with predictions of single crystal behavior from previously published ab initio studies. Variant conversion and detwinning processes that influenced the intergranular constraint occurred even at stresses where the macroscopic stress-strain response appeared linear. Direct evidence of these processes was revealed in changes in texture, which were captured in inverse pole figures constructed from the neutron diffraction measurements.

Continuum mechanics elasticity, plasticity, viscoelasticity

CERN Document Server

Dill, Ellis H

2006-01-01

FUNDAMENTALS OF CONTINUUM MECHANICSMaterial ModelsClassical Space-TimeMaterial BodiesStrainRate of StrainCurvilinear Coordinate SystemsConservation of MassBalance of MomentumBalance of EnergyConstitutive EquationsThermodynamic DissipationObjectivity: Invariance for Rigid MotionsColeman-Mizel ModelFluid MechanicsProblems for Chapter 1BibliographyNONLINEAR ELASTICITYThermoelasticityMaterial SymmetriesIsotropic MaterialsIncompressible MaterialsConjugate Measures of Stress and StrainSome Symmetry GroupsRate Formulations for Elastic MaterialsEnergy PrinciplesGeometry of Small DeformationsLinear ElasticitySpecial Constitutive Models for Isotropic MaterialsMechanical Restrictions on the Constitutive RelationsProblems for Chapter 2BibliographyLINEAR ELASTICITYBasic EquationsPlane StrainPlane StressProperties of SolutionsPotential EnergySpecial Matrix NotationThe Finite Element Method of SolutionGeneral Equations for an Assembly of ElementsFinite Element Analysis for Large DeformationsProblems for Chapter 3Bibliograph...

Reconstruction of constitutive parameters in isotropic linear elasticity from noisy full-field measurements

International Nuclear Information System (INIS)

Bal, Guillaume; Bellis, Cédric; Imperiale, Sébastien; Monard, François

2014-01-01

Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated moduli. A simple gradient system for the sought constitutive parameters is derived algebraically from the momentum equation, whose coefficients are expressed in terms of the measured displacement fields and their spatial derivatives. Direct integration of this system is discussed to finally demonstrate the inexpediency of such an approach when dealing with noisy data. Upon using polluted measurements, an alternative variational formulation is deployed to invert for the physical parameters. Analysis of this latter inversion procedure provides existence and uniqueness results while the reconstruction stability with respect to the measurements is investigated. As the inversion procedure requires differentiating the measurements twice, a numerical differentiation scheme based on an ad hoc regularization then allows an optimally stable reconstruction of the sought moduli. Numerical results are included to illustrate and assess the performance of the overall approach. (paper)

Elastoplastic buckling of quasi axisymmetric shells of revolution

International Nuclear Information System (INIS)

Combescure, A.

1987-01-01

This paper gives the formulation of a finite element which allows the computation of quasi axisymmetric shells of revolution. This element has two nodes and the displacement field is developped in Fourier series. In this paper, an emphasis is put on the elastic and plastic buckling formulation. Two examples are developped in details showing the applicability and the interest of such a finite element. (orig.)

The chocolate-egg problem: Fabrication of thin elastic shells through coating

Science.gov (United States)

Lee, Anna; Marthelot, Joel; Brun, Pierre-Thomas; Reis, Pedro M.

2015-03-01

We study the fabrication of thin polymeric shells based on the coating of a curved surface by a viscous fluid. Upon polymerization of the resulting thin film, a slender solid structure is delivered after demolding. This technique is extensively used, empirically, in manufacturing, where it is known as rotational molding, as well as in the food industry, e.g. for chocolate-eggs. This problem is analogous to the Landau-Levich-Derjaguin coating of plates and fibers and Bretherton's problem of film deposition in cylindrical channels, albeit now on a double-curved geometry. Here, the balance between gravity, viscosity, surface tension and polymerization rate can yield a constant thickness film. We seek to identify the physical ingredients that govern the final film thickness and its profile. In our experiments using organosilicon, we systematically vary the properties of the fluid, as well as the curvature of the substrate onto which the film is coated, and characterize the final thickness profile of the shells. A reduced model is developed to rationalize the process.

Stability analysis of thin-shell wormholes from charged black string

Energy Technology Data Exchange (ETDEWEB)

Sharif, M.; Azam, M., E-mail: msharif.math@pu.edu.pk, E-mail: azammath@gmail.com [Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore-54590 (Pakistan)

2013-04-01

In this paper, we construct thin-shell wormholes from charged black string through cut and paste procedure and investigate its stability. We assume modified generalized Chaplygin gas as a dark energy fluid (exotic matter) present in the thin layer of matter-shell. The stability of these constructed thin-shell wormholes is investigated in the scenario of linear perturbations. We conclude that static stable as well as unstable configurations are possible for cylindrical thin-shell wormholes.

Non-linear general instability of ring-stiffened conical shells under external hydrostatic pressure

International Nuclear Information System (INIS)

Ross, C T F; Kubelt, C; McLaughlin, I; Etheridge, A; Turner, K; Paraskevaides, D; Little, A P F

2011-01-01

The paper presents the experimental results for 15 ring-stiffened circular steel conical shells, which failed by non-linear general instability. The results of these investigations were compared with various theoretical analyses, including an ANSYS eigen buckling analysis and another ANSYS analysis; which involved a step-by-step method until collapse; where both material and geometrical nonlinearity were considered. The investigation also involved an analysis using BS5500 (PD 5500), together with the method of Ross of the University of Portsmouth. The ANSYS eigen buckling analysis tended to overestimate the predicted buckling pressures; whereas the ANSYS nonlinear results compared favourably with the experimental results. The PD5500 analysis was very time consuming and tended to grossly underestimate the experimental buckling pressures and in some cases, overestimate them. In contrast to PD5500 and ANSYS, the design charts of Ross of the University of Portsmouth were the easiest of all these methods to use and generally only slightly underestimated the experimental collapse pressures. The ANSYS analyses gave some excellent graphical displays.

Standard test method for linear-elastic plane-strain fracture toughness KIc of metallic materials

CERN Document Server

American Society for Testing and Materials. Philadelphia

2009-01-01

1.1 This test method covers the determination of fracture toughness (KIc) of metallic materials under predominantly linear-elastic, plane-strain conditions using fatigue precracked specimens having a thickness of 1.6 mm (0.063 in.) or greater subjected to slowly, or in special (elective) cases rapidly, increasing crack-displacement force. Details of test apparatus, specimen configuration, and experimental procedure are given in the Annexes. Note 1—Plane-strain fracture toughness tests of thinner materials that are sufficiently brittle (see 7.1) can be made using other types of specimens (1). There is no standard test method for such thin materials. 1.2 This test method is divided into two parts. The first part gives general recommendations and requirements for KIc testing. The second part consists of Annexes that give specific information on displacement gage and loading fixture design, special requirements for individual specimen configurations, and detailed procedures for fatigue precracking. Additional a...

Gene expression correlated with delay in shell formation in larval Pacific oysters (Crassostrea gigas) exposed to experimental ocean acidification provides insights into shell formation mechanisms.

Science.gov (United States)

De Wit, Pierre; Durland, Evan; Ventura, Alexander; Langdon, Chris J

2018-02-22

Despite recent work to characterize gene expression changes associated with larval development in oysters, the mechanism by which the larval shell is first formed is still largely unknown. In Crassostrea gigas, this shell forms within the first 24 h post fertilization, and it has been demonstrated that changes in water chemistry can cause delays in shell formation, shell deformations and higher mortality rates. In this study, we use the delay in shell formation associated with exposure to CO 2 -acidified seawater to identify genes correlated with initial shell deposition. By fitting linear models to gene expression data in ambient and low aragonite saturation treatments, we are able to isolate 37 annotated genes correlated with initial larval shell formation, which can be categorized into 1) ion transporters, 2) shell matrix proteins and 3) protease inhibitors. Clustering of the gene expression data into co-expression networks further supports the result of the linear models, and also implies an important role of dynein motor proteins as transporters of cellular components during the initial shell formation process. Using an RNA-Seq approach with high temporal resolution allows us to identify a conceptual model for how oyster larval calcification is initiated. This work provides a foundation for further studies on how genetic variation in these identified genes could affect fitness of oyster populations subjected to future environmental changes, such as ocean acidification.

A hyper elasticity method for interactive virtual design of hearing aids

DEFF Research Database (Denmark)

Darkner, Sune; Erleben, Kenny

2011-01-01

We present a computational efficient method for isotropic hyper elasticity based on functional analysis. By selecting a class of shape functions, we arrive at a computational scheme which yields very sparse tensors. This enables fast computations of the hyper elastic energy potential and its...... derivatives. We achieve efficiency and performance through the use of shape functions that are linear in their parameters and through rotation into the eigenspace of the right Cauchy–Green strain tensor. This makes near real time evaluation of hyper elasticity of complex meshes on CPU relatively easy...... to implement. The approach does not rely on a specific shape function or material model but offers a general framework for isotropic hyper elasticity. The method is aimed at interactive and accurate non-linear hyper elastic modeling for a wide range of industrial virtual design applications, which we exemplify...

Morphology and linear-elastic moduli of random network solids.

Science.gov (United States)

Nachtrab, Susan; Kapfer, Sebastian C; Arns, Christoph H; Madadi, Mahyar; Mecke, Klaus; Schröder-Turk, Gerd E

2011-06-17

The effective linear-elastic moduli of disordered network solids are analyzed by voxel-based finite element calculations. We analyze network solids given by Poisson-Voronoi processes and by the structure of collagen fiber networks imaged by confocal microscopy. The solid volume fraction ϕ is varied by adjusting the fiber radius, while keeping the structural mesh or pore size of the underlying network fixed. For intermediate ϕ, the bulk and shear modulus are approximated by empirical power-laws K(phi)proptophin and G(phi)proptophim with n≈1.4 and m≈1.7. The exponents for the collagen and the Poisson-Voronoi network solids are similar, and are close to the values n=1.22 and m=2.11 found in a previous voxel-based finite element study of Poisson-Voronoi systems with different boundary conditions. However, the exponents of these empirical power-laws are at odds with the analytic values of n=1 and m=2, valid for low-density cellular structures in the limit of thin beams. We propose a functional form for K(ϕ) that models the cross-over from a power-law at low densities to a porous solid at high densities; a fit of the data to this functional form yields the asymptotic exponent n≈1.00, as expected. Further, both the intensity of the Poisson-Voronoi process and the collagen concentration in the samples, both of which alter the typical pore or mesh size, affect the effective moduli only by the resulting change of the solid volume fraction. These findings suggest that a network solid with the structure of the collagen networks can be modeled in quantitative agreement by a Poisson-Voronoi process. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The pion-deuteron forward elastic amplitude in the non-overlapping potentials model

International Nuclear Information System (INIS)

Butterworth, D.S.

1978-01-01

The pion-deuteron forward elastic amplitude has been calculated in the non-overlapping potentials model, which enables a description of off-shell propagation effects in terms of on-shell amplitudes. Calculations include spin, isospin and deuteron D-state probability effects. Two energy regions are considered. First the pion-nucleon P 33 resonance region, where, using a formalism developed by Agassi and Gal (Ann. Phys.; 75:56 (1973) and 94:184 (1975)), the full multiple-scattering series is summed in an approximation of P 33 wave dominance of the higher-order scatterings. Second, for the subsequent highest-energy region, the double-scattering term only is calculated. Fermi smearing effects are included in both cases. Predictions for the total cross section, its dependence on the deuteron alignment and the real part of the forward elastic amplitude are compared with those of Glauber theory, and data where available. Convergence of the multiple-scattering series is also discussed. (author)

On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

Science.gov (United States)

BOERTJENS, G. J.; VAN HORSSEN, W. T.

2000-08-01

In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.

Efficient education policy: A second-order elasticity rule

OpenAIRE

Richter, Wolfram F.

2010-01-01

Assuming a two-period model with endogenous choices of labour, education, and saving, efficient education policy is characterized for a Ramsey-like scenario in which the government is constrained to use linear instruments. It is shown that education should be effectively subsidized if, and only if, the elasticity of the earnings function is increasing in education. The strength of second-best subsidization increases in the elasticity of the elasticity of the earnings function. This second-ord...

On elastic moduli and elastic anisotropy in polycrystalline martensitic NiTi

Energy Technology Data Exchange (ETDEWEB)

Qiu, S. [Advanced Materials Processing and Analysis Center (AMPAC), Mechanical, Materials and Aerospace Engineering Department, University of Central Florida, Orlando, FL 32816 (United States); Clausen, B. [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Padula, S.A.; Noebe, R.D. [NASA Glenn Research Center, Cleveland, OH 44135 (United States); Vaidyanathan, R., E-mail: raj@mail.ucf.edu [Advanced Materials Processing and Analysis Center (AMPAC), Mechanical, Materials and Aerospace Engineering Department, University of Central Florida, Orlando, FL 32816 (United States)

2011-08-15

A combined experimental and computational effort was undertaken to provide insight into the elastic response of B19' martensitic NiTi variants as they exist in bulk, polycrystalline aggregate form during monotonic tensile and compressive loading. The experimental effort centered on using in situ neutron diffraction during loading to measure elastic moduli in several directions along with an average Young's modulus and a Poisson's ratio. The measurements were compared with predictions from a 30,000 variant, self-consistent polycrystalline deformation model that accounted for the elastic intergranular constraint, and also with predictions of single crystal behavior from previously published ab initio studies. Variant conversion and detwinning processes that influenced the intergranular constraint occurred even at stresses where the macroscopic stress-strain response appeared linear. Direct evidence of these processes was revealed in changes in texture, which were captured in inverse pole figures constructed from the neutron diffraction measurements.

Support minimized inversion of acoustic and elastic wave scattering

International Nuclear Information System (INIS)

Safaeinili, A.

1994-01-01

This report discusses the following topics on support minimized inversion of acoustic and elastic wave scattering: Minimum support inversion; forward modelling of elastodynamic wave scattering; minimum support linearized acoustic inversion; support minimized nonlinear acoustic inversion without absolute phase; and support minimized nonlinear elastic inversion

Buckling of steel containment shells. Task 4. Use of the PANDA program for simple buckling analyses of stiffened cylindrical shells. Final report, 25 August 1980-30 September 1982

International Nuclear Information System (INIS)

Bushnell, D.

1982-12-01

Under Task 4 the PANDA computer program was modified to permit calculation of critical load interaction curves for buckling of stiffened cylindrical shells with stiffeners running axially or circumferentially or both. Knockdown factors for geometric imperfections and plasticity reduction factors were introduced so that interaction curves can now be calculated for imperfect elastic-plastic shells. The knockdown factors and plasticity reduction factors are computed from a modified form of ASME Code Case N-284. The new version of PANDA was checked by making numerous comparisons with tests on fabricated stiffened cylinders

Modeling elastic anisotropy in strained heteroepitaxy.

Science.gov (United States)

Dixit, Gopal Krishna; Ranganathan, Madhav

2017-09-20

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the [Formula: see text] [Formula: see text] on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to [Formula: see text] facets on the surface.

Modeling elastic anisotropy in strained heteroepitaxy

Science.gov (United States)

Krishna Dixit, Gopal; Ranganathan, Madhav

2017-09-01

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the Ge0.25 Si0.75 on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to facets on the surface.

Elastic silicone encapsulation of n-hexadecyl bromide by microfluidic approach as novel microencapsulated phase change materials

Energy Technology Data Exchange (ETDEWEB)

Fu, Zhenjin [Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang 621900 (China); School of Materials Science and Engineering, Southwest University of Science and Technology, Mianyang 621010 (China); Su, Lin; Li, Jing; Yang, Ruizhuang; Zhang, Zhanwen; Liu, Meifang; Li, Jie [Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang 621900 (China); Li, Bo, E-mail: LB6711@126.com [Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang 621900 (China)

2014-08-20

Highlights: • n-Hexadecyl bromide was encapsuled in elastic silicone shell. • The surfaces of microcapsules were smooth and the cross sections were compact. • Latent heat of microcapsules was 76.35 J g{sup −1}. • The microencapsulation ratio was 49 wt.%. • The microcapsules had good thermal stability. - Abstract: The elastic silicone/n-hexadecyl bromide microcapsules were prepared as novel microencapsulated phase change materials by microfluidic approach with the co-flowing channels, where the double oil1-in-oil2-in-water (O1/O2/W) droplets with a core–shell geometry were fabricated. The thermal characterizations of the microcapsules were investigated using differential scanning calorimetry (DSC) and thermogravimetry analysis (TGA). The DSC results showed that the microcapsules had good energy storage capacity with melting and freezing enthalpies 76.35 J g{sup −1} and 78.67 J g{sup −1}, respectively. The TGA investigation showed that the microcapsules had good thermal stability. The surfaces of microcapsules were smooth and the cross sections were compact from the results of optical microscope and scanning electron microscopy (SEM). Optical microscope showed that the silicone shell can provide expansion place due to its elastic property. Therefore, the silicone/n-hexadecyl bromide microcapsules showed good potential as thermal regulating textile and thermal insulation materials.

Nonlinear dynamic response of electro-thermo-mechanically loaded piezoelectric cylindrical shell reinforced with BNNTs

International Nuclear Information System (INIS)

Yang, J H; Yang, J; Kitipornchai, S

2012-01-01

This paper presents an investigation on the nonlinear dynamic response of piezoelectric cylindrical shells reinforced with boron nitride nanotubes (BNNTs) under a combined axisymmetric electro-thermo-mechanical loading. By employing the classical Donnell shell theory, the von Kármán–Donnell kinematic relationship, and a piezo-elastic constitutive law including thermal effects, the nonlinear governing equations of motion of the shell are derived through the Reissner variational principle. The finite difference method and a time-integration scheme are used to obtain the nonlinear dynamic response of the BNNT-reinforced piezoelectric shell. A parametric study is conducted, showing the effects of geometrically nonlinear deformation, applied voltage, temperature change, mechanical load, BNNT volume fraction and boundary conditions on the nonlinear dynamic response. (paper)

Extreme non-linear elasticity and transformation optics

DEFF Research Database (Denmark)

Gersborg, Allan Roulund; Sigmund, Ole

2010-01-01

realizations correspond to minimizers of elastic energy potentials for extreme values of the mechanical Poisson's ratio ν . For TE (Hz) polarized light an incompressible transformation ν = 1/2 is ideal and for TM (E z) polarized light one should use a compressible transformation with negative Poissons's ratio......Transformation optics is a powerful concept for designing novel optical components such as high transmission waveguides and cloaking devices. The selection of specific transformations is a non-unique problem. Here we reveal that transformations which allow for all dielectric and broadband optical...... ν = -1. For the TM polarization the mechanical analogy corresponds to a modified Liao functional known from the transformation optics literature. Finally, the analogy between ideal transformations and solid mechanical material models automates and broadens the concept of transformation optics...

Extremal Overall Elastic Response of Polycrystalline Materials

DEFF Research Database (Denmark)

Bendsøe, Martin P; Lipton, Robert

1996-01-01

Polycrystalline materials comprised of grains obtained froma single anisotropic material are considered in the frameworkof linear elasticity. No assumptions on the symmetry of thepolycrystal are made. We subject the material to independentexternal strain and stress fields with prescribed mean...... values.We show that the extremal overall elastic response is alwaysachieved by a configuration consisting of a single properlyoriented crystal. This result is compared to results for isotropicpolycrystals....

Improved Properties of Coconut Shell Regenerated Cellulose Biocomposite Films using Butyl Methacrylate

Directory of Open Access Journals (Sweden)

Farah Norain Hahary

2015-11-01

Full Text Available Butyl methacrylate acid (BMA was used to enhance the properties of coconut shell (CS and regenerated cellulose (RC biocomposite films. The effects of coconut shell content and BMA on the tensile properties, crystallinity index (CrI, thermal properties, and morphology of biocomposite films were investigated. An increase in CS content, up to 3 wt.%, increased the tensile strength and modulus of elasticity, but decreased the elongation at break. The CS-RC biocomposite films treated with BMA exhibited higher tensile strength and modulus of elasticity but lower elongation at break. The crystallinity index (CrI and thermal stability of CS-RC biocomposite films increased with increasing CS up to 3 wt.%. Treated CS biocomposite films had better thermal stability than untreated CS biocomposite films. The presence of BMA increased the crystallinity of CS regenerated cellulose biocomposite films. Enhancement of the interfacial interaction of CS-RC biocomposite films was revealed by morphological study.

DFT calculation for elastic constants of orthorhombic structure within WIEN2K code: A new package (ortho-elastic)

International Nuclear Information System (INIS)

Reshak, Ali H.; Jamal, Morteza

2012-01-01

Highlights: ► A new package for calculating elastic constants of orthorhombic structure is released. ► The package called ortho-elastic. ► It is compatible with [FP-(L)APW+lo] method implemented in WIEN2k code. ► Several orthorhombic structure compounds were used to test the new package. ► Elastic constants calculated using this package show good agreement with experiment. - Abstract: A new package for calculating the elastic constants of orthorhombic structure is released. The package called ortho-elastic. The formalism of calculating the ortho-elastic constants is described in details. The package is compatible with the highly accurate all-electron full-potential (linearized) augmented plane-wave plus local orbital [FP-(L)APW+lo] method implemented in WIEN2k code. Several orthorhombic structure compounds were used to test the new package. We found that the calculated elastic constants using the new package show better agreement with the available experimental data than the previous theoretical results used different methods. In this package the second-order derivative E ″ (ε) of polynomial fit E=E(ε) of energy vs strains at zero strain (ε=0), used to calculate the orthorhombic elastic constants.

Off-shell effects in Higgs decays to heavy gauge bosons and signal-background interference in Higgs decays to photons at a linear collider

International Nuclear Information System (INIS)

Liebler, Stefan

2015-03-01

We discuss off-shell contributions in Higgs decays to heavy gauge bosons H→VV (*) with V element of {Z,W} for a standard model (SM) Higgs boson for both dominant production processes e + e - →ZH→ZVV (*) and e + e - ν anti νH→ν anti νVV (*) at a (linear) e + e - collider. Dependent on the centre-of-mass energy off-shell effects are sizable and important for the understanding of the electroweak symmetry breaking mechanism. Moreover we shortly investigate the effects of the signal-background interference in H→γγ decays for the Higgsstrahlung initiated process e + e - →Zγγ, where we report a similar shift in the invariant mass peak of the two photons as found for the LHC. For both effects we discuss the sensitivity to the total Higgs width.

Practical solution of plastic deformation problems in elastic-plastic range

Science.gov (United States)

Mendelson, A; Manson, S

1957-01-01

A practical method for solving plastic deformation problems in the elastic-plastic range is presented. The method is one of successive approximations and is illustrated by four examples which include a flat plate with temperature distribution across the width, a thin shell with axial temperature distribution, a solid cylinder with radial temperature distribution, and a rotating disk with radial temperature distribution.

Two Propositions on the Application of Point Elasticities to Finite Price Changes.

Science.gov (United States)

Daskin, Alan J.

1992-01-01

Considers counterintuitive propositions about using point elasticities to estimate quantity changes in response to price changes. Suggests that elasticity increases with price along a linear demand curve, but falling quantity demand offsets it. Argues that point elasticity with finite percentage change in price only approximates percentage change…

Dynamic reponse of a cylindrical shell immersed in a potential fluid

International Nuclear Information System (INIS)

Cummings, G.E.

1978-01-01

A numerical solution technique is presented for determining the dynamic response of a thin, elastic, circular, cylindrical shell of constant wall thickness and density, immersed in a potential fluid. The shell may be excited by an arbitrary radial forcing function with a specified time history and spatial distribution. In addition, a pressure history may be specified over a segment of the fluid outer boundary. Any of the natural shell end conditions may be prescribed. A numerical instability prevented direct solutions where the ratio of the hydrodynamic forces to shell inertial forces is greater than two. This instability is believed to be the result of the weak coupling between the equations describing the fluid to those describing the shell. To circumvent this instability, an effective mass was calculated and added to the shell. Comparison of numerical to experimental results are made using a 1 / 12 scale model of a nuclear reactor core support barrel. Natural frequencies and modes are determined for this model in air, water, and oil. The computed frequencies compare to experimental results to within 15%. The use of this numerical technique is illustrated by comparing it to an analytical solution for shell beam modes and an uncertainty in the analytical technique concerning the proper effective mass to use, is resolved

Dynamic reponse of a cylindrical shell immersed in a potential fluid

Energy Technology Data Exchange (ETDEWEB)

Cummings, G.E.

1978-04-18

A numerical solution technique is presented for determining the dynamic response of a thin, elastic, circular, cylindrical shell of constant wall thickness and density, immersed in a potential fluid. The shell may be excited by an arbitrary radial forcing function with a specified time history and spatial distribution. In addition, a pressure history may be specified over a segment of the fluid outer boundary. Any of the natural shell end conditions may be prescribed. A numerical instability prevented direct solutions where the ratio of the hydrodynamic forces to shell inertial forces is greater than two. This instability is believed to be the result of the weak coupling between the equations describing the fluid to those describing the shell. To circumvent this instability, an effective mass was calculated and added to the shell. Comparison of numerical to experimental results are made using a /sup 1///sub 12/ scale model of a nuclear reactor core support barrel. Natural frequencies and modes are determined for this model in air, water, and oil. The computed frequencies compare to experimental results to within 15%. The use of this numerical technique is illustrated by comparing it to an analytical solution for shell beam modes and an uncertainty in the analytical technique concerning the proper effective mass to use, is resolved.

Elasto/visco-plastic analysis of moderately thick shells of revolution

International Nuclear Information System (INIS)

Takezono, S.; Tanoue, M.

1981-01-01

The analytical formulation on the elasto-visco-plastic problems of general, moderately thick shells of revolution subjected to axisymmetrical load is developed by extension of the Reissner theory in elastic shells where a consideration on the effect of shear deformations is given. The authors employ as constitutive relation of the shell materials Perzyna's equation where in the plastic range the viscosity of the material is considered. The criterion for yielding used in this analysis is the von Mises yield theory. The basic differential equations derived for elasto-visco-plastic problems are numerically solved by a finite difference method, and the solutions are obtained by integration of the incremental values. As a numerical example, the elasto/visco-plastic deformation of pressure vessels is analyzed, and the results are compared with those from the classical theory which neglects the effect of shear deformations. (orig.)

Elastic and inelastic form factors of the Ne20 in the Hartree-Fock approximation

International Nuclear Information System (INIS)

Oliveira, S.A.C. de.

1977-01-01

Properties of Ne 20 fundamental band are studied such as particle densities and elastic and inelastic form factors. A two body interaction is used and its matrix elements involve only the independent particle states of the 1s-0d shell [pt

Comparison of elastic and inelastic seismic response of high temperature piping systems

International Nuclear Information System (INIS)

Thomas, F.M.; McCabe, S.L.; Liu, Y.

1994-01-01

A study of high temperature power piping systems is presented. The response of the piping systems is determined when subjected to seismic disturbances. Two piping systems are presented, a main steam line, and a cold reheat line. Each of the piping systems are modeled using the ANSYS computer program and two analyses are performed on each piping system. First, each piping system is subjected to a seismic disturbance and the pipe material is assumed to remain linear and elastic. Next the analysis is repeated for each piping system when the pipe material is modeled as having elastic-plastic behavior. The results of the linear elastic analysis and elastic-plastic analysis are compared for each of the two pipe models. The pipe stresses, strains, and displacements, are compared. These comparisons are made so that the effect of the material yielding can be determined and to access what error is made when a linear analysis is performed on a system that yields

Buckling of long liquid-filled cylindrical shells

International Nuclear Information System (INIS)

Saal, H.

1982-01-01

The experimental investigation confirms the stresses and displacements which result from a nonlinear analysis of the shell. The linear analysis gives a good approximation for the stresses and deformations which significantly deviate from those according to beam theory. This approximation is to the safe side - (remarkably only for the displacements and circumferential stresses). The application of an equivalent cylinder model to the determination of the buckling load gives rather good agreement with the experimental results. There is only little imperfection sensitivity in this load case as the experiments show. Again the theoretical buckling load which is based on the stresses and displacements from linear shell theory is on the safe side. (orig./RW)

Superstring elastic scattering at √s≥1019 GeV. The covariant loop calculus approach

International Nuclear Information System (INIS)

Bellini, A.; Cristofano, G.; Fabbrichesi, M.; Roland, K.; Texas Univ., Austin, TX

1990-01-01

We study quantum gravity by considering the elastic scattering of two on-shell string ground states in the large s, fixed t asymptotic limit. The amplitude is computed by means of the covariant loop calculus which turns out to be a powerful method in the study of such a Regge regime. The leading contribution in powers of s is shown to factorize at any g-loop order in a product of g+1 tree amplitudes times the expectation value of a factorized operator. The cumulative effect of these contributions - once it has been resummed - restores unitarity in the theory and gives a deflection angle in agreement with the linear approximation to general relativity. In the process, it is possible to determine the normalization dictated by unitarity of all terms in the topological expansion. Next, the first sub-leading contribution is calculated at the two-loop order, the so-called H-diagram. A resummation of such terms gives rise to the first non-linear correction in the deflection angle. Our results are in agreement with previous work by Amati, Ciafaloni and Veneziano in the framework of Regge-Gribov techniques. The correspondence between the two approaches is discussed. (orig.)

Finite rotation shells basic equations and finite elements for Reissner kinematics

CERN Document Server

Wisniewski, K

2010-01-01

This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements - not included in standard textbooks on finite elements - are addressed, and the book includes an extensive bibliography.

Existence of equilibrium states of hollow elastic cylinders submerged in a fluid

Directory of Open Access Journals (Sweden)

M. B. M. Elgindi

1992-01-01

Full Text Available This paper is concerned with the existence of equilibrium states of thin-walled elastic, cylindrical shell fully or partially submerged in a fluid. This problem obviously serves as a model for many problems with engineering importance. Previous studies on the deformation of the shell have assumed that the pressure due to the fluid is uniform. This paper takes into consideration the non-uniformity of the pressure by taking into account the effect of gravity. The presence of a pressure gradient brings additional parameters to the problem which in turn lead to the consideration of several boundary value problems.

Vibrations of Elastic Systems With Applications to MEMS and NEMS

CERN Document Server

Magrab, Edward B

2012-01-01

This work presents a unified approach to the vibrations of elastic systems as applied to MEMS devices, mechanical components, and civil structures. Applications include atomic force microscopes, energy harvesters, and carbon nanotubes and consider such complicating effects as squeeze film damping, viscous fluid loading, in-plane forces, and proof mass interactions with their elastic supports. These effects are analyzed as single degree-of-freedom models and as more realistic elastic structures. The governing equations and boundary conditions for beams, plates, and shells with interior and boundary attachments are derived by applying variational calculus to an expression describing the energy of the system. The advantages of this approach regarding the generation of orthogonal functions and the Rayleigh-Ritz method are demonstrated. A large number of graphs and tables are given to show the impact of various factors on the systems’ natural frequencies, mode shapes, and responses.

Laser-based linear and nonlinear guided elastic waves at surfaces (2D) and wedges (1D).

Science.gov (United States)

Hess, Peter; Lomonosov, Alexey M; Mayer, Andreas P

2014-01-01

The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump-probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented. Copyright © 2013 Elsevier B.V. All rights reserved.

Contact-resonance atomic force microscopy for nanoscale elastic property measurements: Spectroscopy and imaging

International Nuclear Information System (INIS)

Stan, G.; Krylyuk, S.; Davydov, A.V.; Vaudin, M.D.; Bendersky, L.A.; Cook, R.F.

2009-01-01

Quantitative measurements of the elastic modulus of nanosize systems and nanostructured materials are provided with great accuracy and precision by contact-resonance atomic force microscopy (CR-AFM). As an example of measuring the elastic modulus of nanosize entities, we used the CR-AFM technique to measure the out-of-plane indentation modulus of tellurium nanowires. A size-dependence of the indentation modulus was observed for the investigated tellurium nanowires with diameters in the range 20-150 nm. Over this diameter range, the elastic modulus of the outer layers of the tellurium nanowires experienced significant enhancement due to a pronounced surface stiffening effect. Quantitative estimations for the elastic moduli of the outer and inner parts of tellurium nanowires of reduced diameter are made with a core-shell structure model. Besides localized elastic modulus measurements, we have also developed a unique CR-AFM imaging capability to map the elastic modulus over a micrometer-scale area. We used this CR-AFM capability to construct indentation modulus maps at the junction between two adjacent facets of a tellurium microcrystal. The clear contrast observed in the elastic moduli of the two facets indicates the different surface crystallography of these facets.

Zirconium elasticity modules

International Nuclear Information System (INIS)

Vavra, G.

1978-01-01

Considered are the limit and the intermediate values of the Young modulus E, modulus of shear G and of linear modulus of compression K obtainable at various temperatures (4.2 to 1133 K) for single crystals of α-zirconium. Determined and presented are the corrected isotropic elasticity characteristics of E, G, K over the above range of temperatures of textured and non-textured α-Zr

Elastic Property Simulation of Nano-particle Reinforced Composites

Directory of Open Access Journals (Sweden)

He Jiawei

2016-01-01

Full Text Available A series of numerical micro-mechanical models for two kinds of particle (cylindrical and discal particle reinforced composites are developed to investigate the effect of microstructural parameters on the elastic properties of composites. The effects of both the degree of particle clustering and particle’s shape on the elastic mechanical properties of composites are investigated. In addition, single particle unit cell approximation is good enough for the analysis of the effect of averaged parameters when only linear elastic response is considered without considering the particle clustering in particle-reinforced composites.

DESTRUCTION CRITERION IN MODEL OF NON-LINEAR ELASTIC PLASTIC MEDIUM

Directory of Open Access Journals (Sweden)

O. L. Shved

2014-01-01

Full Text Available The paper considers a destruction criterion in a specific phenomenological model of elastic plastic medium which significantly differs from the known criteria. In case of vector interpretation of rank-2 symmetric tensors yield surface in the Cauchy stress space is formed by closed piecewise concave surfaces of its deviator sections with due account of experimental data. Section surface is determined by normal vector which is selected from two private vectors of criterial “deviator” operator. Such selection is not always possible in the case of anisotropy growth. It is expected that destruction can only start when a process point in the stress space is located in the current deviator section of the yield surface. It occurs when a critical point appears in the section, and a private value of an operator becomes N-fold in the point that determines the private vector corresponding to the normal vector. Unique and reasonable selection of the normal vector becomes impossible in the critical point and an yield criteria loses its significance in the point.When the destruction initiation is determined there is a possibility of a special case due to the proposed conic form of the yield surface. The deviator section degenerates into the point at the yield surface peak. Criterion formulation at the surface peak lies in the fact that there is no physically correct solution while using a state equation in regard to elastic distortion measures with a fixed tensor of elastic turn. Such usage of the equation is always possible for the rest points of the yield surface and it is considered as an obligatory condition for determination of the deviator section. A critical point is generally absent at any deviator section of the yield surface for isotropic material. A limiting value of the mean stress has been calculated at uniform tension.

Homogenized Elastic Properties of Graphene for Small Deformations

Directory of Open Access Journals (Sweden)

Jurica Sorić

2013-09-01

Full Text Available In this paper, we provide the quantification of the linear and non-linear elastic mechanical properties of graphene based upon the judicious combination of molecular mechanics simulation results and homogenization methods. We clarify the influence on computed results by the main model features, such as specimen size, chirality of microstructure, the effect of chosen boundary conditions (imposed displacement versus force and the corresponding plane stress transformation. The proposed approach is capable of explaining the scatter of the results for computed stresses, energy and stiffness and provides the bounds on graphene elastic properties, which are quite important in modeling and simulation of the virtual experiments on graphene-based devices.

Microscopic cluster model analysis of 14O+p elastic scattering

International Nuclear Information System (INIS)

Baye, D.; Descouvemont, P.; Leo, F.

2005-01-01

The 14 O+p elastic scattering is discussed in detail in a fully microscopic cluster model. The 14 O cluster is described by a closed p shell for protons and a closed p3/2 subshell for neutrons in the translation-invariant harmonic-oscillator model. The exchange and spin-orbit parameters of the effective forces are tuned on the energy levels of the 15 C mirror system. With the generator-coordinate and microscopic R-matrix methods, phase shifts and cross sections are calculated for the 14 O+p elastic scattering. An excellent agreement is found with recent experimental data. A comparison is performed with phenomenological R-matrix fits. Resonances properties in 15 F are discussed

Elastic representation surfaces of unidirectional graphite/epoxy composites

International Nuclear Information System (INIS)

Kriz, R.D.; Ledbetter, H.M.

1985-01-01

Unidirectional graphite/epoxy composites exhibit high elastic anisotropy and unusual geometrical features in their elastic-property polar diagrams. From the five-component transverse-isotropic elastic-stiffness tensor we compute and display representation surfaces for Young's modulus, torsional modulus, linear compressibility, and Poisson's ratios. Based on Christoffel-equation solutions, we describe some unusual elastic-wave-surface topological features. Musgrave considered in detail the differences between phase-velocity and group-velocity surfaces arising from high elastic anisotropy. For these composites, we find effects similar to, but more dramatic than, Musgrave's. Some new, unexpected results for graphite/epoxy include: a shear-wave velocity that exceeds a longitudinal velocity in the plane transverse to the fiber; a wave that changes polarization character from longitudinal to transverse as the propagation direction sweeps from the fiber axis to the perpendicular axis

Analysis of thermal-plastic response of shells of revolution by numerical integration

International Nuclear Information System (INIS)

Leonard, J.W.

1975-01-01

An economic technique for the numerical analysis of the elasto-plastic behaviour of shells of revolution would be of considerable value in the nuclear reactor industry. A numerical method based on the numerical integration of the governing shell equations has been shown, for elastic cases, to be more efficient than the finite element method when applied to shells of revolution. In the numerical integration method, the governing differential equations of motion are converted into a set of initial-value problems. Each initial-value problem is integrated numerically between meridional boundary points and recombined so as to satisfy boundary conditions. For large-deflection elasto-plastic behaviour, the equations are nonlinear and, hence, are recombined in an iterative manner using the Newton-Raphson procedure. Suppression techniques are incorporated in order to eliminate extraneous solutions within the numerical integration procedure. The Reissner-Meissner shell theory for shells of revolution is adopted to account for large deflection and higher-order rotation effects. The computer modelling of the equations is quite general in that specific shell segment geometries, e.g. cylindrical, spherical, toroidal, conical segments, and any combinations thereof can be handled easily. (Auth.)

Ultrafast Dynamics of Metallo-Dielectric Core-Shell Particles

NARCIS (Netherlands)

Shan, X.

2008-01-01

Optical properties of metallic nano-structures have attracted a lot of attention in the past decades. In this thesis, we focus on nano-sized silica-core gold-shell particles, study the linear, nonlinear and acoustic vibrations of the particles. The linear optical properties in the visible range of

Elastic wave excitation in centrosymmetric strontium titanate crystals

International Nuclear Information System (INIS)

Yushin, N.K.; Sotnikov, A.V.

1980-01-01

The main experimental dependencies are measured and the excitation mechanism of elastic waves in centrosymmetric crystals is established. The surface generation of three-dimensional elastic waves of the 30 MHz frequency in strontium titanate crystals is observed and studied. Elastic wave excitation is observed in the 4 350 K temperature range. The efficiency of hysteresis excitation depends on the external electric field. The effect of light irradiation on the amplitude of excited elastic waves is observed. It is shown that escitation is connected with linearization of electrostriction by the constant electric field appearing in a near-surface crystal layer due to phenomena in the Schottky barrier and appearance of electretic near-electrode layers

Modeling Pseudo-elastic Behavior of Springback

International Nuclear Information System (INIS)

Xia, Z. Cedric

2005-01-01

One of the principal foundations of mathematical theory of conventional plasticity for rate-independent metals is that there exists a well-defined yield surface in stress space for any material point under deformation. A material point can undergo further plastic deformation if the applied stresses are beyond current yield surface which is generally referred as 'plastic loading'. On the other hand, if the applied stress state falls within or on the yield surface, the metal will deform elastically only and is said to be undergoing 'elastic unloading'. Although it has been always recognized throughout the history of development of plasticity theory that there is indeed inelastic deformation accompanying elastic unloading, which leads to metal's hysteresis behavior, its effects were thought to be negligible and were largely ignored in the mathematical treatment.Recently there have been renewed interests in the study of unloading behavior of sheet metals upon large plastic deformation and its implications on springback prediction. Springback is essentially an elastic recovery process of a formed sheet metal blank when it is released from the forming dies. Its magnitude depends on the stress states and compliances of the deformed sheet metal if no further plastic loading occurs during the relaxation process. Therefore the accurate determination of material compliances during springback and its effective incorporation into simulation software are important aspects for springback calculation. Some of the studies suggest that the unloading curve might deviate from linearity, and suggestions were made that a reduced elastic modulus be used for springback simulation.The aim of this study is NOT to take a position on the debate of whether elastic moduli are changed during sheet metal forming process. Instead we propose an approach of modeling observed psuedoelastic behavior within the context of mathematical theory of plasticity, where elastic moduli are treated to be

The elastic response of composite materials

International Nuclear Information System (INIS)

Laws, N.

1980-01-01

The theory of linear elasticity is used to study the elastic response of composite materials. The main concern is the prediction of overall moduli. Some attention is paid to the problem of deciding upon when the idea of an overall modulus is meaningful. In addition it is shown how to calculate some rigorous bounds on the overall moduli, and some predictions of the self-consistent method are discussed. The paper mainly concentrates on isotropic dispersions of spheres, unidirectional fibre-reinforced materials and laminates. (author)

Vascular elastic photoacoustic tomography in humans

Science.gov (United States)

Hai, Pengfei; Zhou, Yong; Liang, Jinyang; Li, Chiye; Wang, Lihong V.

2016-03-01

Quantification of vascular elasticity can help detect thrombosis and prevent life-threatening conditions such as acute myocardial infarction or stroke. Here, we propose vascular elastic photoacoustic tomography (VE-PAT) to measure vascular elasticity in humans. VE-PAT was developed by incorporating a linear-array-based photoacoustic computed tomography system with a customized compression stage. By measuring the deformation of blood vessels under uniaxial loading, VE-PAT was able to quantify the vascular compliance. We first demonstrated the feasibility of VE-PAT in blood vessel phantoms. In large vessel phantoms, VE-PAT detected a decrease in vascular compliance due to simulated thrombosis, which was validated by a standard compression test. In small blood vessel phantoms embedded 3 mm deep in gelatin, VE-PAT detected elasticity changes at depths that are difficult to image using other elasticity imaging techniques. We then applied VE-PAT to assess vascular compliance in a human subject and detected a decrease in vascular compliance when an occlusion occurred downstream from the measurement point, demonstrating the potential of VE-PAT in clinical applications such as detection of deep venous thrombosis.

Mechanically, the shoot apical meristem of Arabidopsis behaves like a shell inflated by a pressure of about 1 MPa

Directory of Open Access Journals (Sweden)

Léna eBeauzamy

2015-11-01

Full Text Available In plants, the shoot apical meristem contains the stem cells and is responsible for the generation of all aerial organs. Mechanistically, organogenesis is associated with an auxin-dependent local softening of the epidermis. This has been proposed to be sufficient to trigger outgrowth, because the epidermis is thought to be under tension and stiffer than internal tissues in all the aerial part of the plant. However, this has not been directly demonstrated in the shoot apical meristem. Here we tested this hypothesis in Arabidopsis using indentation methods and modeling. We considered two possible scenarios: either the epidermis does not have unique properties and the meristem behaves as a homogeneous linearly-elastic tissue, or the epidermis is under tension and the meristem exhibits the response of a shell under pressure. Large indentation depths measurements with a large tip (~size of the meristem were consistent with a shell-like behavior. This also allowed us to deduce a value of turgor pressure, estimated at 0.82 ± 0.16 MPa. Indentation with atomic force microscopy provided local measurements of pressure in the epidermis, further confirming the values obtained from large deformations. Altogether, our data demonstrate that the Arabidopsis shoot apical meristem behaves like a shell under a MPa range pressure and support a key role for the epidermis in shaping the shoot apex.

Multislice theory of fast electron scattering incorporating atomic inner-shell ionization

International Nuclear Information System (INIS)

Dwyer, C.

2005-01-01

It is demonstrated how atomic inner-shell ionization can be incorporated into a multislice theory of fast electron scattering. The resulting theory therefore accounts for both inelastic scattering due to inner-shell ionization and dynamical elastic scattering. The theory uses a description of the ionization process based on the angular momentum representation for both the initial and final states of the atomic electron. For energy losses near threshold, only a small number of independent states of the ejected atomic electron need to be considered, reducing demands on computing time, and eliminating the need for tabulated inelastic scattering factors. The theory is used to investigate the influence of the collection aperture size on the spatial origin of the silicon K-shell EELS signal generated by a STEM probe. The validity of a so-called local approximation is also considered

Acoustic radiation force on cylindrical shells in a plane standing wave

International Nuclear Information System (INIS)

Mitri, F G

2005-01-01

In this paper, the radiation force per length resulting from a plane standing wave incident on an infinitely long cylindrical shell is computed. The cases of elastic and viscoelastic shells immersed in ideal (non-viscous) fluids are considered with particular emphasis on their thickness and the content of their interior hollow spaces. Numerical calculations of the radiation force function Y st are performed. The fluid-loading effect on the radiation force function curves is analysed as well. The results show several features quite different when the interior hollow space is changed from air to water. Moreover, the theory developed here is more general since it includes the results on cylinders

Nonlinear viscoelastic behaviour of shells of revolution under arbitrary loading

International Nuclear Information System (INIS)

Leonard, J.W.; Arbabi-Kanjoori, F.

1975-01-01

A formulation and solution technique are presented for the creep analysis of shells of revolution subjected to arbitrary loads and temperature changes. Arbitrary creep laws are admitted in the formulation with specific attention given to the two common laws, i.e. strain hardening and time hardening. The governing equations for creep of shells of revolution are derived. The solution method requires the quasi-static linearization of the equations: linear incremental behaviour is assumed during each time step. The incremental equations are expanded in Fourier series and solved by a numerical integration technique. (Auth.)

An Aeroelastic Evaluation of the Flexible Thermal Protection System for an Inatable Aerodynamic Decelerator

Science.gov (United States)

Goldman, Benjamin D.

The purpose of this dissertation is to study the aeroelastic stability of a proposed flexible thermal protection system (FTPS) for the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). A flat, square FTPS coupon exhibits violent oscillations during experimental aerothermal testing in NASA's 8 Foot High Temperature Tunnel, leading to catastrophic failure. The behavior of the structural response suggested that aeroelastic flutter may be the primary instability mechanism, prompting further experimental investigation and theoretical model development. Using Von Karman's plate theory for the panel-like structure and piston theory aerodynamics, a set of aeroelastic models were developed and limit cycle oscillations (LCOs) were calculated at the tunnel flow conditions. Similarities in frequency content of the theoretical and experimental responses indicated that the observed FTPS oscillations were likely aeroelastic in nature, specifically LCO/flutter. While the coupon models can be used for comparison with tunnel tests, they cannot predict accurately the aeroelastic behavior of the FTPS in atmospheric flight. This is because the geometry of the flight vehicle is no longer a flat plate, but rather (approximately) a conical shell. In the second phase of this work, linearized Donnell conical shell theory and piston theory aerodynamics are used to calculate natural modes of vibration and flutter dynamic pressures for various structural models composed of one or more conical shells resting on several circumferential elastic supports. When the flight vehicle is approximated as a single conical shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case, as "hump-mode" flutter is possible. Aeroelastic models that consider the individual FTPS layers as separate shells exhibit

On Perturbation Solutions for Axisymmetric Bending Boundary Values of a Deep Thin Spherical Shell

Directory of Open Access Journals (Sweden)

Rong Xiao

2014-01-01

Full Text Available On the basis of the general theory of elastic thin shells and the Kirchhoff-Love hypothesis, a fundamental equation for a thin shell under the moment theory is established. In this study, the author derives Reissner’s equation with a transverse shear force Q1 and the displacement component w. These basic unknown quantities are derived considering the axisymmetry of the deep, thin spherical shell and manage to constitute a boundary value question of axisymmetric bending of the deep thin spherical shell under boundary conditions. The asymptotic solution is obtained by the composite expansion method. At the end of this paper, to prove the correctness and accuracy of the derivation, an example is given to compare the numerical solution by ANSYS and the perturbation solution. Meanwhile, the effects of material and geometric parameters on the nonlinear response of axisymmetric deep thin spherical shell under uniform external pressure are also analyzed in this paper.

Non-linear seismic analysis of structures coupled with fluid

International Nuclear Information System (INIS)

Descleve, P.; Derom, P.; Dubois, J.

1983-01-01

This paper presents a method to calculate non-linear structure behaviour under horizontal and vertical seismic excitation, making possible the full non-linear seismic analysis of a reactor vessel. A pseudo forces method is used to introduce non linear effects and the problem is solved by superposition. Two steps are used in the method: - Linear calculation of the complete model. - Non linear analysis of thin shell elements and calculation of seismic induced pressure originating from linear and non linear effects, including permanent loads and thermal stresses. Basic aspects of the mathematical formulation are developed. It has been applied to axi-symmetric shell element using a Fourier series solution. For the fluid interaction effect, a comparison is made with a dynamic test. In an example of application, the displacement and pressure time history are given. (orig./GL)

Creeping gaseous flows through elastic tube and annulus micro-configurations

Science.gov (United States)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2016-11-01

Gaseous flows in elastic micro-configurations is relevant to biological systems (e.g. alveolar ducts in the lungs) as well as to applications such as gas actuated soft micro-robots. We here examine the effect of low-Mach-number compressibility on creeping gaseous axial flows through linearly elastic tube and annulus micro-configurations. For steady flows, the leading-order effects of elasticity on the pressure distribution and mass-flux are obtained. For transient flow in a tube with small deformations, elastic effects are shown to be negligible in leading order due to compressibility. We then examine transient flows in annular configurations where the deformation is significant compared with the gap between the inner and outer cylinders defining the annulus. Both compressibility and elasticity are obtained as dominant terms interacting with viscosity. For a sudden flux impulse, the governing non-linear leading order diffusion equation is initially approximated by a porous-medium-equation of order 2.5 for the pressure square. However, as the fluid expand and the pressure decreases, the governing equation degenerates to a porous-medium-equation of order 2 for the pressure.

Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis.

Science.gov (United States)

Jiang, Yi; Li, Guoyang; Qian, Lin-Xue; Liang, Si; Destrade, Michel; Cao, Yanping

2015-10-01

We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.

Uniqueness in inverse elastic scattering with finitely many incident waves

International Nuclear Information System (INIS)

Elschner, Johannes; Yamamoto, Masahiro

2009-01-01

We consider the third and fourth exterior boundary value problems of linear isotropic elasticity and present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves. Our approach is based on a reflection principle for the Navier equation. (orig.)

A Reevaluation of Price Elasticities for Irrigation Water

Science.gov (United States)

Howitt, Richard E.; Watson, William D.; Adams, Richard M.

1980-08-01

The effectiveness of pricing systems in the allocation of irrigation water is linked with the price elasticity of demand of farmers for water. Using microeconomic theory, it is shown that omission of the elasticity of demand for the crop produced leads to an inelastic bias in the demand for irrigated water. Linear programing approaches omit the product elasticity of demand and are consequently biased, whereas quadratic programing approaches to estimating derived demands for irrigation water include product demand functions. The difference between the resulting estimates are empirically demonstrated for regional derived demand functions estimated from a model of California's agricultural industry.

Negative stiffness honeycombs as tunable elastic metamaterials

Science.gov (United States)

Goldsberry, Benjamin M.; Haberman, Michael R.

2018-03-01

Acoustic and elastic metamaterials are media with a subwavelength structure that behave as effective materials displaying atypical effective dynamic properties. These material systems are of interest because the design of their sub-wavelength structure allows for direct control of macroscopic wave dispersion. One major design limitation of most metamaterial structures is that the dynamic response cannot be altered once the microstructure is manufactured. However, the ability to modify wave propagation in the metamaterial with an external stimulus is highly desirable for numerous applications and therefore remains a significant challenge in elastic metamaterials research. In this work, a honeycomb structure composed of a doubly periodic array of curved beams, known as a negative stiffness honeycomb (NSH), is analyzed as a tunable elastic metamaterial. The nonlinear static elastic response that results from large deformations of the NSH unit cell leads to a large variation in linear elastic wave dispersion associated with infinitesimal motion superposed on the externally imposed pre-strain. A finite element model is utilized to model the static deformation and subsequent linear wave motion at the pre-strained state. Analysis of the slowness surface and group velocity demonstrates that the NSH exhibits significant tunability and a high degree of anisotropy which can be used to guide wave energy depending on static pre-strain levels. In addition, it is shown that partial band gaps exist where only longitudinal waves propagate. The NSH therefore behaves as a meta-fluid, or pentamode metamaterial, which may be of use for applications of transformation elastodynamics such as cloaking and gradient index lens devices.

Density functional calculations of elastic properties of portlandite, Ca(OH)(2)

DEFF Research Database (Denmark)

Laugesen, Jakob Lund

2005-01-01

The elastic constants of portlandite, Ca(OH)(2), are calculated by use of density functional theory. A lattice optimization of an infinite (periodic boundary conditions) lattice is performed on which strains are applied. The elastic constants are extracted by minimizing Hooke's law of linear...

Advanced non-linear flow-induced vibration and fretting-wear analysis capabilities

Energy Technology Data Exchange (ETDEWEB)

Toorani, M.; Pan, L.; Li, R.; Idvorian, N. [Babcock and Wilcox Canada Ltd., Cambridge, Ontario (Canada); Vincent, B.

2009-07-01

Fretting wear is a potentially significant degradation mechanism in nuclear steam generators and other shell and tube heat transfer equipment as well. This paper presents an overview of the recently developed code FIVDYNA which is used for the non-linear flow-induced vibration and fretting wear analysis for operating steam generators (OTSG and RSG) and shell-and-tube heat exchangers. FIVDYNA is a non-linear time-history Flow-Induced Vibration (FIV) analysis computer program that has been developed by Babcock and Wilcox Canada to advance the understanding of tube vibration and tube to tube-support interaction. In addition to the dynamic fluid induced forces the program takes into account other tube static forces due to axial and lateral tube preload and thermal interaction loads. The program is capable of predicting the location where the fretting wear is most likely to occur and its magnitude taking into account the support geometry including gaps. FIVDYNA uses the general purpose finite element computer code ABAQUS as its solver. Using ABAQUS gives the user the flexibility to add additional forces to the tube ranging from tube preloads and the support offsets to thermal loads. The forces currently being modeled in FIVDYNA are the random turbulence, steady drag force, fluid-elastic forces, support offset and pre-strain force (axial loads). This program models the vibration of tubes and calculates the structural dynamic characteristics, and interaction forces between the tube and the tube supports. These interaction forces are then used to calculate the work rate at the support and eventually the predicted depth of wear scar on the tube. A very good agreement is found with experiments and also other computer codes. (author)

Size-dependent elastic moduli and vibrational properties of fivefold twinned copper nanowires

Science.gov (United States)

Zheng, Y. G.; Zhao, Y. T.; Ye, H. F.; Zhang, H. W.

2014-08-01

Based on atomistic simulations, the elastic moduli and vibration behaviors of fivefold twinned copper nanowires are investigated in this paper. Simulation results show that the elastic (i.e., Young’s and shear) moduli exhibit size dependence due to the surface effect. The effective Young’s modulus is found to decrease slightly whereas the effective shear modulus increases slightly with the increase in the wire radius. Both moduli tend to approach certain values at a larger radius and can be suitably described by core-shell composite structure models. Furthermore, we show by comparing simulation results and continuum predictions that, provided the effective Young’s and shear moduli are used, classic elastic theory can be applied to describe the small-amplitude vibration of fivefold twinned copper nanowires. Moreover, for the transverse vibration, the Timoshenko beam model is more suitable because shear deformation becomes apparent.

Size-dependent elastic moduli and vibrational properties of fivefold twinned copper nanowires

International Nuclear Information System (INIS)

Zheng, Y G; Zhao, Y T; Ye, H F; Zhang, H W

2014-01-01

Based on atomistic simulations, the elastic moduli and vibration behaviors of fivefold twinned copper nanowires are investigated in this paper. Simulation results show that the elastic (i.e., Young’s and shear) moduli exhibit size dependence due to the surface effect. The effective Young’s modulus is found to decrease slightly whereas the effective shear modulus increases slightly with the increase in the wire radius. Both moduli tend to approach certain values at a larger radius and can be suitably described by core-shell composite structure models. Furthermore, we show by comparing simulation results and continuum predictions that, provided the effective Young’s and shear moduli are used, classic elastic theory can be applied to describe the small-amplitude vibration of fivefold twinned copper nanowires. Moreover, for the transverse vibration, the Timoshenko beam model is more suitable because shear deformation becomes apparent. (paper)

An orthogonality condition model treatment of elastic and inelastic (α, 12C) scattering

International Nuclear Information System (INIS)

Suzuki, Y.; Imanishi, B.

1981-02-01

Elastic and inelastic scattering of α-particles on the deformed nucleus 12 C are investigated in the range of incident α-particle energies of 9 to 11 MeV by using the coupled-channel method with orthogonality condition. A doubly folded potential generated by the shell model wave functions of the α-particle and the deformed nucleus 12 C is employed for the relative motion between the α-particle and 12 C. Good agreement between theory and experiment is obtained for the elastic and inelastic angular distributions and the resonance structures. It is found, from the Born series expansion of the T-matrix, that the orthogonality constraint stresses the effects of the channel-coupling between the elastic and inelastic processes, and it indicates that the DWBA does not work well in this system. (author)

Nonlinear viscoelastic behavior of shells of revolution under arbitrary loading

International Nuclear Information System (INIS)

Leonard, J.W.; Arbaki-Kanjoori, F.

1975-01-01

The requirement of some structural components such as propulsion systems and gas turbines to operate at high temperatures and pressures make the accurate evaluation of the creep phenomenon exigent (in fast breeder reactor for example). For the expected increases in operating temperatures and pressures, it becomes necessary to perform a thorough analysis of integral structural components of nuclear power plants throughout their life span. Since a large class of structures operating at elevated temperatures are composed of rotationally symmetric shells, a solution technique can be developed which involves the numerical integration of the governing shell equations. This method has been successfully applied to the static and dynamic analysis of thin elastic shells of revolution and for some cases of inelastic material behavior. It has been shown to render solutions efficiently and accurately, usually with only a fraction of computer time and storage requirements and data manipulation that is required for other numerical schemes such as the finite element method. Furthermore, the numerical integration method allows more flexibility for varying the integration step lengths than does the finite difference method and can provide uniform accuracy throughout the analysis. For nonlinear viscoelastic behavior the numerical integration technique is expected to provide similar efficiency to that obtained for the elastic problems. The computer program developed can accept time variation of material properties. Since a single form for the material constitutive law cannot encompass all materials, provisions are made so that the analysis of a very large class of material behavior can be accomplished

An anisotropic linear thermo-viscoelastic constitutive law - Elastic relaxation and thermal expansion creep in the time domain

Science.gov (United States)

Pettermann, Heinz E.; DeSimone, Antonio

2017-09-01

A constitutive material law for linear thermo-viscoelasticity in the time domain is presented. The time-dependent relaxation formulation is given for full anisotropy, i.e., both the elastic and the viscous properties are anisotropic. Thereby, each element of the relaxation tensor is described by its own and independent Prony series expansion. Exceeding common viscoelasticity, time-dependent thermal expansion relaxation/creep is treated as inherent material behavior. The pertinent equations are derived and an incremental, implicit time integration scheme is presented. The developments are implemented into an implicit FEM software for orthotropic material symmetry under plane stress assumption. Even if this is a reduced problem, all essential features are present and allow for the entire verification and validation of the approach. Various simulations on isotropic and orthotropic problems are carried out to demonstrate the material behavior under investigation.

Sound transmission through double cylindrical shells lined with porous material under turbulent boundary layer excitation

Science.gov (United States)

Zhou, Jie; Bhaskar, Atul; Zhang, Xin

2015-11-01

This paper investigates sound transmission through double-walled cylindrical shell lined with poroelastic material in the core, excited by pressure fluctuations due to the exterior turbulent boundary layer (TBL). Biot's model is used to describe the sound wave propagating in the porous material. Three types of constructions, bonded-bonded, bonded-unbonded and unbonded-unbonded, are considered in this study. The power spectral density (PSD) of the inner shell kinetic energy is predicted for two turbulent boundary layer models, different air gap depths and three types of polyimide foams, respectively. The peaks of the inner shell kinetic energy due to shell resonance, hydrodynamic coincidence and acoustic coincidence are discussed. The results show that if the frequency band over the ring frequency is of interest, an air gap, even if very thin, should exist between the two elastic shells for better sound insulation. And if small density foam has a high flow resistance, a superior sound insulation can still be maintained.

Dynamic strength of cylindrical fiber-glass shells and basalt plastic shells under multiple explosive loading

Science.gov (United States)

Syrunin, M. A.; Fedorenko, A. G.

2006-08-01

We have shown experimentally that, for cylindrical shells made of oriented fiberglass platic and basalt plastic there exists a critical level of deformations, at which a structure sustains a given number of explosions from the inside. The magnitude of critical deformation for cylindrical fiberglass shells depends linearly on the logarithm of the number of loads that cause failure. For a given type of fiberglass, there is a limiting level of explosive action, at which the number of loads that do not lead to failure can be sufficiently large (more than ˜ 102). This level is attained under loads, which are an order of magnitude lower than the limiting loads under a single explosive action. Basalt plastic shells can be repeatedly used even at the loads, which cause deformation by ˜ 30-50% lower than the safe value ˜ 3.3.5% at single loading.

Buckling Analysis for Stiffened Anisotropic Circular Cylinders Based on Sanders Nonlinear Shell Theory

Science.gov (United States)

Nemeth, Michael P.

2014-01-01

Nonlinear and bifurcation buckling equations for elastic, stiffened, geometrically perfect, right-circular cylindrical, anisotropic shells subjected to combined loads are presented that are based on Sanders' shell theory. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated-composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discrepancies between the results obtained by using Donnell's equations and variants of Sanders' equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.

Effect of the Pauli principle in elastic scattering

International Nuclear Information System (INIS)

Picklesimer, A.; Thaler, R.M.

1981-01-01

The effect of imposition of the Pauli principle for two-fragment elastic nuclear scattering is examined. It is shown that the antisymmetrized problem can be cast into the Lippmann-Schwinger form with an effective interaction in which the effect of the Pauli principle is entirely absorbed into the effective interaction potential operator. This result enables the formalism to be developed in analogy with the unsymmetrized formulation. Central to the approach is the choice of the off-shell extension of the transition operator. Comparison is made with a previously proposed treatment based on a different off-shell extension. It is shown that both the antisymmetrized transition operator and the associated optical potential proposed herein are readily expressed as spectator expansions in which the effect of the Pauli principle among the active fermions is incorporated in a physically appealing fashion at each stage of the expansion

Shaping through buckling in elastic gridshells: from camping tents to architectural roofs

Science.gov (United States)

Reis, Pedro

Elastic gridshells comprise an initially planar network of elastic rods that is actuated into a 3D shell-like structure by loading its extremities. This shaping results from elastic buckling and the subsequent geometrically nonlinear deformation of the grid structure. Architectural elastic gridshells first appeared in the 1970's. However, to date, only a limited number of examples have been constructed around the world, primarily due to the challenges involved in their structural design. Yet, elastic gridshells are highly appealing: they can cover wide spans with low self-weight, they allow for aesthetically pleasing shapes and their construction is typically simple and rapid. We study the mechanics of elastic gridshells by combining precision model experiments that explore their scale invariance, together with computer simulations that employ the Discrete Elastic Rods method. Excellent agreement is found between the two. Upon validation, the numerics are then used to systematically explore parameter space and identify general design principles for specific target final shapes. Our findings are rationalized using the theory of discrete Chebyshev nets, together with the group theory for crystals. Higher buckling modes occur for some configurations due to geometric incompatibility at the boundary and result in symmetry breaking. Along with the systematic classification of the various possible modes of deformation, we provide a reduced model that rationalizes form-finding in elastic gridshells. This work was done in collaboration with Changyeob Baek, Khalid Jawed and Andrew Sageman-Furnas. We are grateful to the NSF for funding (CAREER, CMMI-1351449).

The use of COD and plastic instability in crack propagation and arrest in shells

Science.gov (United States)

Erdogan, F.; Ratwani, M.

1974-01-01

The initiation, growth, and possible arrest of fracture in cylindrical shells containing initial defects are dealt with. For those defects which may be approximated by a part-through semi-elliptic surface crack which is sufficiently shallow so that part of the net ligament in the plane of the crack is still elastic, the existing flat plate solution is modified to take into account the shell curvature effect as well as the effect of the thickness and the small scale plastic deformations. The problem of large defects is then considered under the assumptions that the defect may be approximated by a relatively deep meridional part-through surface crack and the net ligament through the shell wall is fully yielded. The results given are based on an 8th order bending theory of shallow shells using a conventional plastic strip model to account for the plastic deformations around the crack border.

Two-Sided Estimates of Thermo-elastic Characteristics of Dispersed Inclusion Composites

Directory of Open Access Journals (Sweden)

V. S. Zarubin

2015-01-01

Full Text Available The composites, dispersion-reinforced with inclusions from high-strength and high-modulus materials are widely used in technology. Nanostructure elements can perform the role of such inclusions as well. Possible applications of such composites in heat-stressed structures under heavy mechanical and thermal influences significantly depend on a complex of thermo-mechanical characteristics including the values of the moduli of elasticity and coefficient of linear thermal expansion. There are different approaches to construction of mathematical models that allow calculating dependences to estimate elastic characteristics of composites. Relation between thermoelastic properties of matrix and inclusions of the composite with its temperature coefficient of linear expansion is studied in less detail. Thus, attention has been insufficient in estimating a degree of reliability and a possible error of derived dependencies.A dual variation formulation of the problem of thermo-elasticity in a non-uniform solids simulating the properties and structure of the composite with dispersed inclusions, makes it possible to define two-sided limits of possible values of the volume elasticity modulus, shear modulus, and coefficient of linear thermal expansion of such composite. These limits allow us to estimate the maximum possible error, if to take a half-sum of the limit values of these parameters as the thermoelastic characteristics of the composite. Implementing this approach to find possible errors, arising when using one or another calculating dependency, improves reliability of predicted thermo-elastic characteristics as applied to existing and promising composites.

Analysis of elastic-plastic dynamic response of reinforced concrete frame structure

International Nuclear Information System (INIS)

Li Zhongcheng

2009-01-01

Based on a set of data from seismic response test on an R/C frame, a force-based R/C beam fibre model with non-linear material properties and bond-slip effects are presented firstly in this paper, and then the applications to the tested R/C frame are presented to illustrate the model characteristics and to show the accuracy of seismic analysis including consideration of non-linear factors. It can be concluded that the elastic-plastic analysis is a potential step toward the accurate modelling for the dynamic analyses of R/C structures. Especially for the seismic safety re-evaluation of the existing NPPs, the elastic-plastic methodology with consideration of different non-linearities should be involved. (author)

Fully coupled heat conduction and deformation analyses of visco-elastic solids

KAUST Repository

Khan, Kamran

2012-04-21

Visco-elastic materials are known for their capability of dissipating energy. This energy is converted into heat and thus changes the temperature of the materials. In addition to the dissipation effect, an external thermal stimulus can also alter the temperature in a viscoelastic body. The rate of stress relaxation (or the rate of creep) and the mechanical and physical properties of visco-elastic materials, such as polymers, vary with temperature. This study aims at understanding the effect of coupling between the thermal and mechanical response that is attributed to the dissipation of energy, heat conduction, and temperature-dependent material parameters on the overall response of visco-elastic solids. The non-linearly viscoelastic constitutive model proposed by Schapery (Further development of a thermodynamic constitutive theory: stress formulation, 1969,Mech. Time-Depend. Mater. 1:209-240, 1997) is used and modified to incorporate temperature- and stress-dependent material properties. This study also formulates a non-linear energy equation along with a dissipation function based on the Gibbs potential of Schapery (Mech. Time-Depend. Mater. 1:209-240, 1997). A numerical algorithm is formulated for analyzing a fully coupled thermo-visco-elastic response and implemented it in a general finite-element (FE) code. The non-linear stress- and temperature-dependent material parameters are found to have significant effects on the coupled thermo-visco-elastic response of polymers considered in this study. In order to obtain a realistic temperature field within the polymer visco-elastic bodies undergoing a non-uniform heat generation, the role of heat conduction cannot be ignored. © Springer Science+Business Media, B. V. 2012.

Enceladus's crust as a non-uniform thin shell: I tidal deformations

Science.gov (United States)

Beuthe, Mikael

2018-03-01

The geologic activity at Enceladus's south pole remains unexplained, though tidal deformations are probably the ultimate cause. Recent gravity and libration data indicate that Enceladus's icy crust floats on a global ocean, is rather thin, and has a strongly non-uniform thickness. Tidal effects are enhanced by crustal thinning at the south pole, so that realistic models of tidal tectonics and dissipation should take into account the lateral variations of shell structure. I construct here the theory of non-uniform viscoelastic thin shells, allowing for depth-dependent rheology and large lateral variations of shell thickness and rheology. Coupling to tides yields two 2D linear partial differential equations of the fourth order on the sphere which take into account self-gravity, density stratification below the shell, and core viscoelasticity. If the shell is laterally uniform, the solution agrees with analytical formulas for tidal Love numbers; errors on displacements and stresses are less than 5% and 15%, respectively, if the thickness is less than 10% of the radius. If the shell is non-uniform, the tidal thin shell equations are solved as a system of coupled linear equations in a spherical harmonic basis. Compared to finite element models, thin shell predictions are similar for the deformations due to Enceladus's pressurized ocean, but differ for the tides of Ganymede. If Enceladus's shell is conductive with isostatic thickness variations, surface stresses are approximately inversely proportional to the local shell thickness. The radial tide is only moderately enhanced at the south pole. The combination of crustal thinning and convection below the poles can amplify south polar stresses by a factor of 10, but it cannot explain the apparent time lag between the maximum plume brightness and the opening of tiger stripes. In a second paper, I will study the impact of a non-uniform crust on tidal dissipation.

NIF-Scale Hohlraum Asymmetry Studies Using Point-Projection Radiograph of Thin Shells

International Nuclear Information System (INIS)

Pollaine, S.; Bradley, D.; Landen, O.; Wallace, R.; Jones, O.

2000-01-01

Our current OMEGA experimental campaign is developing the thin shell diagnostic for use on NIF with the needed accuracy. The thin shell diagnostic has the advantage of linearity over alternative measurement techniques, so that low-order modes will not corrupt the measurement of high-order modes. Although our random measurement errors are adequate, we need to monitor beam balance and ensure that the thin shells have a uniform thickness

Stability of generic thin shells in conformally flat spacetimes

Energy Technology Data Exchange (ETDEWEB)

Amirabi, Z. [Eastern Mediterranean Univ., Gazimagusa (Turkey). Dept. of Physics

2017-07-15

Some important spacetimes are conformally flat; examples are the Robertson-Walker cosmological metric, the Einstein-de Sitter spacetime, and the Levi-Civita-Bertotti-Robinson and Mannheim metrics. In this paper we construct generic thin shells in conformally flat spacetime supported by a perfect fluid with a linear equation of state, i.e., p = ωσ. It is shown that, for the physical domain of ω, i.e., 0 < ω ≤ 1, such thin shells are not dynamically stable. The stability of the timelike thin shells with the Mannheim spacetime as the outer region is also investigated. (orig.)

Semi-Coercive Variational Inequalities with Uncertain Input Data. Applications to Shaloow Shells

Czech Academy of Sciences Publication Activity Database

Hlaváček, Ivan; Lovíšek, J.

2005-01-01

Roč. 15, č. 2 (2005), s. 273-299 ISSN 0218-2025 R&D Projects: GA ČR(CZ) GA201/01/1200; GA ČR(CZ) GA201/02/1058 Institutional research plan: CEZ:AV0Z10190503 Keywords : control of variational inequalities * uncertain input data * shallow elastic shells Subject RIV: BA - General Mathematics Impact factor: 1.248, year: 2005

Buckling strength of spherical shells under combined loads

International Nuclear Information System (INIS)

Nagashima, H.; Kokubo, K.; Takayanagi, M.; Hayasaka, Y.; Kume, T.; Nagata, T.

1995-01-01

Many studies on buckling of cylindrical shells have been conducted, and many buckling evaluation equations have been proposed for actual plant designs; however, buckling of spherical shells under combined horizontal and vertical loads cannot be evaluated due to insufficient data. There is a particular lack of buckling data for spherical shells under lateral loads. To establish a method for estimating the buckling strength of spherical shells, we investigate the interactions between horizontal and vertical (compressive tensile) loads by conducting buckling tests. Applying several combinations of these loads in tests and using computer linear analysis, we obtain interaction curves. This study reports on the buckling tests conducted using spherical shell 1120 mm in dia., 0.7 mm thick and 696 mm high, which are shaped individually by press-forming and finally joined together by four meridional welds, using a specially made jig. Initial imperfections before testing and local deformations after each loading increment during testing are measured with special measuring equipment, and the interaction curve of horizontal and vertical loads and effect of imperfection on the buckling strength of spherical shells are obtained. Nonlinear FEM programs are developed using an 8-node isoparametric shell element and a four-node quadrilateral element of C 0 type with reduced integration based upon a Mindlin-Reissner theory which includes transverse shear. Actual initial imperfections are generally in irregular patterns. Thus, there may be several definitions of the equivalent magnitudes of initial imperfections related to buckling loads. Equivalent magnitudes have no practical meaning unless they can be obtained easily not only for small structures such as test shells but also for large actual structures. In the present study, we define the equivalent magnitude of initial imperfections as the maximum local ruggedness measured radially from a circular temperature having a radius equal

QUANTITATIVE NON-DESTRUCTIVE EVALUATION (QNDE) OF THE ELASTIC MODULI OF POROUS TIAL ALLOYS

International Nuclear Information System (INIS)

Yeheskel, O.

2008-01-01

The elastic moduli of γ-TiA1 were studied in porous samples consolidated by various techniques e.g. cold isostatic pressing (CIP), pressure-less sintering, or hot isostatic pressing (HIP). Porosity linearly affects the dynamic elastic moduli of samples. The results indicate that the sound wave velocities and the elastic moduli affected by the processing route and depend not only on the attained density but also on the consolidation temperature. In this paper we show that there is linear correlation between the shear and the longitudinal sound velocities in porous TiA1. This opens the way to use a single sound velocity as a tool for quantitative non-destructive evaluation (QNDE) of porous TiA1 alloys. Here we demonstrate the applicability of an equation derived from the elastic theory and used previously for porous cubic metals

Elastic properties of gamma-Pu by resonant ultrasound spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Migliori, Albert [Los Alamos National Laboratory; Betts, J [Los Alamos National Laboratory; Trugman, A [Los Alamos National Laboratory; Mielke, C H [Los Alamos National Laboratory; Mitchell, J N [Los Alamos National Laboratory; Ramos, M [Los Alamos National Laboratory; Stroe, I [WORXESTER, MA

2009-01-01

Despite intense experimental and theoretical work on Pu, there is still little understanding of the strange properties of this metal. We used resonant ultrasound spectroscopy method to investigate the elastic properties of pure polycrystalline Pu at high temperatures. Shear and longitudinal elastic moduli of the {gamma}-phase of Pu were determined simultaneously and the bulk modulus was computed from them. A smooth linear and large decrease of all elastic moduli with increasing temperature was observed. We calculated the Poisson ratio and found that it increases from 0.242 at 519K to 0.252 at 571K.

Some Comments on the Status of Shell Theory at the End of the 20th Century: Complaints and Correctives

Science.gov (United States)

Simmonds, James G.

1998-01-01

This review is divided into complaints and correctives. Complaints are directed at: sloppy refereeing and editing; authors who fail to read or acknowledge what others have done; the mis-naming or mis-crediting of results; the misunderstanding and misuse of the Kirchhoff hypothesis; inflated claims of accuracy based on overly-simplified benchmark problems; the failure to appreciate the inherent errors in various shell models; the failure to appreciate that the physical response and mathematical structure of shell theory are fundamentally different from 3-dimensional elasticity; and the irrelevance of Cosserat-type theories. Correctives include a simple, straight-forward derivation of a general nonlinear dynamic shell theory with the following features: (1) the equations of motion and kinematics (and those of thermodynamics, if desired) are exact consequences of their 3-dimensional counterparts; (2) there are no asymptotic or series expansions through the thickness; (3) all approximations (including the Kirchhoff Hypothesis) occur in the constitutive relations; (4) in static problems, there is a mixed form of the governing equations involving a mixed-energy density and exhibiting remnants of the well-known static-geometric duality of linear theory which is numerically robust because the limiting cases of nonlinear membrane theory and inextensional bending theory fall out naturally. (These latter two special cases are known to produce numerical nightmares unless treated with great care); and (5) all equations may be expressed in coordinate-free form (although, sometimes, a hybrid form is shown to be superior).

On the hyperbolicity condition in linear elasticity

Directory of Open Access Journals (Sweden)

Remigio Russo

1991-05-01

Full Text Available This talk, which is mainly expository and based on [2-5], discusses the hyperbolicity conditions in linear elastodynamics. Particular emphasis is devoted to the key role it plays in the uniqueness questions associated with the mixed boundary-initial value problem in unbounded domains.

The role of fullerene shell upon stuffed atom polarization potential

OpenAIRE

Amusia, M. Ya.; Chernysheva, L. V.

2015-01-01

We have demonstrated that the polarization of the fullerene shell considerably alters the polarization potential of an atom, stuffed inside a fullerene. This essentially affects the electron elastic scattering phases as well as corresponding cross-sections. We illustrate the general trend by concrete examples of electron scattering by endohedrals of Neon and Argon. To obtain the presented results, we have suggested a simplified approach that permits to incorporate the effect of fullerenes pol...

Charged thin-shell gravastars in noncommutative geometry

Energy Technology Data Exchange (ETDEWEB)

Oevguen, Ali [Pontificia Universidad Catolica de Valparaiso, Instituto de Fisica, Valparaiso (Chile); Eastern Mediterranean University, Physics Department, Famagusta, Northern Cyprus (Turkey); Banerjee, Ayan [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Jusufi, Kimet [State University of Tetovo, Physics Department, Tetovo (Macedonia, The Former Yugoslav Republic of); Institute of Physics, Ss. Cyril and Methodius University, Faculty of Natural Sciences and Mathematics, Skopje (Macedonia, The Former Yugoslav Republic of)

2017-08-15

In this paper we construct a charged thin-shell gravastar model within the context of noncommutative geometry. To do so, we choose the interior of the nonsingular de Sitter spacetime with an exterior charged noncommutative solution by cut-and-paste technique and apply the generalized junction conditions. We then investigate the stability of a charged thin-shell gravastar under linear perturbations around the static equilibrium solutions as well as the thermodynamical stability of the charged gravastar. We find the stability regions, by choosing appropriate parameter values, located sufficiently close to the event horizon. (orig.)

A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

Science.gov (United States)

Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

2017-12-01

Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.

Non-linear dynamic response of reactor containment

International Nuclear Information System (INIS)

Takemori, T.; Sotomura, K.; Yamada, M.

1975-01-01

A computer program was developed to investigate the elasto-plastic behavior of structures. This program is outlined and the problems of non-linear response of structures are discussed. Since the mode superposition method is only valid in an elastic analysis, the direct integration method was adopted here. As the sample model, an actual reactor containment (reactor building) of PWR plant was adopted. This building consists of three components, that is, a concrete internal structure, a steel containment vessel and a concrete outer shield wall. These components are resting on a rigid foundation mat. Therefore they were modeled with a lumped mass model respectively and coupled on the foundation. The following assumptions were employed to establish the properties of dynamic model: rocking and swaying springs of soil can be obtained from an elastic half-space solution, and the hysteretic characteristic of springs is bi-linear; springs connecting each mass are dealt with shear beams so that both bending and shear deflections can be included (Hysteretic characteristics of springs are linear, bi-linear and tri-linear for the internal structure, the containment vessel and the outer shield wall, respectively); generally, each damping coefficient is given for each mode in modal superposition (However, a damping matrix must be made directly in a non-linear response). Therefore the damping matrix of the model was made by combining the damping matrices [C] of each component obtained by Caughy's method and a damping value of the rocking and swaying by the half-space solution. On the basis of above conditions, the non-linear response of the structure was obtained and the difference between elastic and elasto-plastic analysis is presented

Nonlinear nonlocal vibration of embedded DWCNT conveying fluid using shell model

Energy Technology Data Exchange (ETDEWEB)

Ghorbanpour Arani, A., E-mail: aghorban@kashanu.ac.ir [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of); Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan (Iran, Islamic Republic of); Zarei, M.Sh.; Amir, S.; Khoddami Maraghi, Z. [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of)

2013-02-01

In this work nonlinear vibration of double-walled carbon nanotube (DWCNT) embedded in an elastic medium and subjected to an axial fluid flow (incompressible and non-viscose) is investigated. The elastic medium is simulated using Pasternak foundation in which adjacent layer interactions are assumed to have been coupled by van der Waals (VdW) force. The higher-order equation of motion is derived using Hamilton's principle and nonlocal-nonlinear shell theory. Galerkin and averaging methods are adopted to solve the higher-order governing equations. Elastic medium, small scale parameter, velocity and fluid density are taken into account to calculate the effects of axial and circumferential wave numbers in this study. Results reveal that increasing circumferential wave number, leads to enhanced nonlinearity. Critical flow velocities of DWCNT are inversely related to the non-local parameter (e{sub 0}a), so that increase in the later lead to reduced critical flow velocities.

Summary compilation of shell element performance versus formulation.

Energy Technology Data Exchange (ETDEWEB)

Heinstein, Martin Wilhelm; Hales, Jason Dean (Idaho National Laboratory, Idaho Falls, ID); Breivik, Nicole L.; Key, Samuel W. (FMA Development, LLC, Great Falls, MT)

2011-07-01

This document compares the finite element shell formulations in the Sierra Solid Mechanics code. These are finite elements either currently in the Sierra simulation codes Presto and Adagio, or expected to be added to them in time. The list of elements are divided into traditional two-dimensional, plane stress shell finite elements, and three-dimensional solid finite elements that contain either modifications or additional terms designed to represent the bending stiffness expected to be found in shell formulations. These particular finite elements are formulated for finite deformation and inelastic material response, and, as such, are not based on some of the elegant formulations that can be found in an elastic, infinitesimal finite element setting. Each shell element is subjected to a series of 12 verification and validation test problems. The underlying purpose of the tests here is to identify the quality of both the spatially discrete finite element gradient operator and the spatially discrete finite element divergence operator. If the derivation of the finite element is proper, the discrete divergence operator is the transpose of the discrete gradient operator. An overall summary is provided from which one can rank, at least in an average sense, how well the individual formulations can be expected to perform in applications encountered year in and year out. A letter grade has been assigned albeit sometimes subjectively for each shell element and each test problem result. The number of A's, B's, C's, et cetera assigned have been totaled, and a grade point average (GPA) has been computed, based on a 4.0-system. These grades, combined with a comparison between the test problems and the application problem, can be used to guide an analyst to select the element with the best shell formulation.

Numerical Simulation of the Layer-Bylayer Destruction of Cylindrical Shells Under Explosive Loading

Science.gov (United States)

Abrosimov, N. A.; Novoseltseva, N. A.

2015-09-01

A technique of numerical analysis of the influence of reinforcement structure on the nature of the dynamic response and the process of layer-by-layer destruction of layered fiberglass cylindrical shells under an axisymmetric internal explosive loading is elaborated. The kinematic model of deformation of the laminate package is based on a nonclassical theory of shells. The geometric dependences are based on simple quadratic relations of the nonlinear theory of elasticity. The relationship between the stress and strain tensors are established by using Hooke's law for orthotropic bodies with account of degradation of stiffness characteristics of the multilayer composite due to the local destruction of some its elementary layers. An energetically consistent system of dynamic equations for composite cylindrical shells is obtained by minimizing the functional of total energy of the shell as a three-dimensional body. The numerical method for solving the formulated initial boundary-value problem is based on an explicit variational-difference scheme. Results confirming the reliability of the method used to analyze the influence of reinforcement structure on the character of destruction and the bearing capacity of pulse-loaded cylindrical shells are presented.

Elasticity in Elastics-An in-vitro study.

Science.gov (United States)

Kamisetty, Supradeep Kumar; Nimagadda, Chakrapani; Begam, Madhoom Ponnachi; Nalamotu, Raghuveer; Srivastav, Trilok; Gs, Shwetha

2014-04-01

Orthodontic tooth movement results from application of forces to teeth. Elastics in orthodontics have been used both intra-orally and extra- orally to a great effect. Their use, combined with good patient co-operation provides the clinician with the ability to correct both anteroposterior and vertical discrepancies. Force decay over a period of time is a major problem in the clinical usage of latex elastics and synthetic elastomers. This loss of force makes it difficult for the clinician to determine the actual force transmitted to the dentition. It's the intent of the clinician to maintain optimal force values over desired period of time. The majority of the orthodontic elastics on the market are latex elastics. Since the early 1990s, synthetic products have been offered in the market for latex-sensitive patients and are sold as nonlatex elastics. There is limited information on the risk that latex elastics may pose to patients. Some have estimated that 0.12-6% of the general population and 6.2% of dental professionals have hypersensitivity to latex protein. There are some reported cases of adverse reactions to latex in the orthodontic population but these are very limited to date. Although the risk is not yet clear, it would still be inadvisable to prescribe latex elastics to a patient with a known latex allergy. To compare the in-vitro performance of latex and non latex elastics. Samples of 0.25 inch, latex and non latex elastics (light, medium, heavy elastics) were obtained from three manufacturers (Forestadent, GAC, Glenroe) and a sample size of ten elastics per group was tested. The properties tested included cross sectional area, internal diameter, initial force generated by the elastics, breaking force and the force relaxation for the different types of elastics. Force relaxation testing involved stretching the elastics to three times marketed internal diameter (19.05 mm) and measuring force level at intervals over a period of 48 hours. The data were

Extremal Overall Elastic Response of Polycrystalline Materials

DEFF Research Database (Denmark)

Bendsøe, Martin P; Lipton, Robert

1997-01-01

Polycrystalline materials comprised of grains obtained from a single anisotropic material are considered in the framework of linear elasticity. No assumptions on the symmetry of the polycrystal are made. We subject the material to independent external strain and stress fields with prescribed mean...

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

Science.gov (United States)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Application of elasticity theory at Sandia Labortories

International Nuclear Information System (INIS)

Davison, L.

1975-01-01

Examples are given of the application of linear elasticity theory to the solution of practical problems encountered at Sandia Laboratories. It is being applied to a very broad range of problems: those in one, two, and three spatial dimensions, some involving static and some dynamic response, to materials having isotropic and anisotropic symmetry, to homogeneous and inhomogeneous bodies, etc. Various extensions of the theory to include electric, magnetic and thermal effects, to account for material microstructure, for radiation and spall damage, chemical reactions, and other phenomena have been developed and/or applied. In some applications linear elasticity represents the physics of a problem well and is the theory of choice. In others the theory was used because it lent insight into a larger problem that was also attacked by means of other theories and/or experiment, and in some cases it serves as a part of a more encompassing theory

Influence of initial imperfections on ultimate strength of spherical shells

Directory of Open Access Journals (Sweden)

Chang-Li Yu

2017-09-01

Full Text Available Comprehensive consideration regarding influence mechanisms of initial imperfections on ultimate strength of spherical shells is taken to satisfy requirement of deep-sea structural design. The feasibility of innovative numerical procedure that combines welding simulation and non-linear buckling analysis is verified by a good agreement to experimental and theoretical results. Spherical shells with a series of wall thicknesses to radius ratios are studied. Residual stress and deformations from welding process are investigated separately. Variant influence mechanisms are discovered. Residual stress is demonstrated to be influential to stress field and buckling behavior but not to the ultimate strength. Deformations are proved to have a significant impact on ultimate strength. When central angles are less than critical value, concave magnitudes reduce ultimate strengths linearly. However, deformations with central angles above critical value are of much greater harm. Less imperfection susceptibility is found in spherical shells with larger wall thicknesses to radius ratios.

Design of the RC containment shell of a nuclear reactor for aircraft impact

International Nuclear Information System (INIS)

Filho, F.V.; Coombs, R.F.; Barreto, L.C.

1981-01-01

This paper deals with the following points: i) Characterization of a particular region of the shell which is modeled as a one-degree-of freedom system for the non-linear dynamic analysis. This is achieved through a proper interpretation of the results of the global analysis. ii) Development of a method of non-linear dynamic analysis for the considered one-degree-of freedom model. iii) Comparative analysis of the design for flexural strength, and punching shear, according to American and German standards. Interaction diagrams for bending and normal force are developed according to the two standards. The concepts of the foregoing items are exemplified with the verification of the shell reinforcement of a PWR reactor. A simplified method of non-linear dynamic analysis for airplane crash is presented. This method takes into account all the important influences of the problem. The results of this analysis are used in the design of the shell reinforcement according to American and German Standards. (orig./HP)

Free vibration analysis of elastically supported Timoshenko columns ...

Indian Academy of Sciences (India)

, concen- trated mass ... linear equations of motion for transverse vibrations of a simply supported beam carrying con- centrated ... a cantilever Timoshenko beam with a rigid tip mass. Ferreira .... Figure 3. Free body diagram of elastic support.

Nonlinear Vibration and Mode Shapes of FG Cylindrical Shells

Directory of Open Access Journals (Sweden)

Saeed Mahmoudkhani

Full Text Available Abstract The nonlinear vibration and normal mode shapes of FG cylindrical shells are investigated using an efficient analytical method. The equations of motion of the shell are based on the Donnell’s non-linear shallow-shell, and the material is assumed to be gradually changed across the thickness according to the simple power law. The solution is provided by first discretizing the equations of motion using the multi-mode Galerkin’s method. The nonlinear normal mode of the system is then extracted using the invariant manifold approach and employed to decouple the discretized equations. The homotopy analysis method is finally used to determine the nonlinear frequency. Numerical results are presented for the backbone curves of FG cylindrical shells, nonlinear mode shapes and also the nonlinear invariant modal surfaces. The volume fraction index and the geometric properties of the shell are found to be effective on the type of nonlinear behavior and also the nonlinear mode shapes of the shell. The circumferential half-wave numbers of the nonlinear mode shapes are found to change with time especially in a thinner cylinder.

Thermodynamics and elastic properties of Ir from first-principle calculations

International Nuclear Information System (INIS)

Li Qiang; Huang Duohui; Cao Qilong; Wang Fanhou

2013-01-01

Within the framework of the quasiharmonic approximation, the thermodynamics and elastic properties, including phonon dispersion curves, equation of state, linear thermal expansion coefficient and temperature-dependent entropy, enthalpy, heat capacity, elastic constants, bulk modulus, shear modulus, Young's modulus of Ir have been studied using first-principles projector-augmented wave method. The results revealed that the predicted phonon dispersion curves of Ir are in agreement with the experimental measurements by neutron diffractions. Considering the thermal electronic contribution to Helmholtz free energy, the calculated entropy, enthalpy, heat capacity and linear thermal expansion co- efficient from the first-principle are consistent well with the experimental data. At 2600 K, the electronic heat capacity accounts for 17% of the total heat capacity at constant pressure, thus the thermal electronic contribution to Helmholtz free energy is very important. The predicted elastic constants, bulk modulus, shear modulus and Young's modulus at room temperature are also in agreement with the available measurements and increase with the increasing temperature. (authors)

Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

KAUST Repository

Angela Mihai, L.

2013-03-01

Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects manifested by specific models. As the finite element method computes uniform deformations exactly, for simple shear deformation and pure shear stress, the Poynting effect is represented exactly, while for the generalised shear and simple torsion, where the deformation is non-uniform, the solution is approximated efficiently and guaranteed computational bounds on the magnitude of the Poynting effect are obtained. The numerical results further indicate that, for a given elastic material, the same sign effect occurs under different shearing mechanisms, showing the genericity of the Poynting effect under a variety of shearing loads. In order to derive numerical models that exhibit either the positive or the negative Poynting effect, the so-called generalised empirical inequalities, which are less restrictive than the usual empirical inequalities involving material parameters, are assumed. © 2012 Elsevier Ltd.

Charge carrier dynamics investigation of CuInS{sub 2} quantum dots films using injected charge extraction by linearly increasing voltage (i-CELIV): the role of ZnS Shell

Energy Technology Data Exchange (ETDEWEB)

Bi, Ke; Sui, Ning; Zhang, Liquan; Wang, Yinghui, E-mail: yinghui-wang@outlook.com; Liu, Qinghui, E-mail: liuqinghui@jlu.edu.cn; Tan, Mingrui [Jilin University, Femtosecond Laser Laboratory, Key Laboratory of Physics and Technology for Advanced Batteries (Ministry of Education), College of Physics (China); Zhou, Qiang [Jilin University, Key Laboratory of Superhard Materials, College of Physics (China); Zhang, Hanzhuang, E-mail: zhanghz@jlu.edu.cn [Jilin University, Femtosecond Laser Laboratory, Key Laboratory of Physics and Technology for Advanced Batteries (Ministry of Education), College of Physics (China)

2016-12-15

The role of ZnS shell on the photo-physical properties within CuInS{sub 2}/ZnS quantum dots (QDs) is carefully studied in optoelectronic devices. Linearly increasing voltage technique has been employed to investigate the charge carrier dynamics of both CuInS{sub 2} and CuInS{sub 2}/ZnS QDs films. This study shows that charge carriers follow a similar behavior of monomolecular recombination in this film, with their charge transfer rate correlates to the increase of applied voltage. It turns out that the ZnS shell could affect the carrier diffusion process through depressing the trapping states and would build up a potential barrier.

Thin-shell wormholes from the regular Hayward black hole

Energy Technology Data Exchange (ETDEWEB)

Halilsoy, M.; Ovgun, A.; Mazharimousavi, S.H. [Eastern Mediterranean University, Department of Physics, Mersin 10 (Turkey)

2014-03-15

We revisit the regular black hole found by Hayward in 4-dimensional static, spherically symmetric spacetime. To find a possible source for such a spacetime we resort to the nonlinear electrodynamics in general relativity. It is found that a magnetic field within this context gives rise to the regular Hayward black hole. By employing such a regular black hole we construct a thin-shell wormhole for the case of various equations of state on the shell. We abbreviate a general equation of state by p = ψ(σ) where p is the surface pressure which is a function of the mass density (σ). In particular, linear, logarithmic, Chaplygin, etc. forms of equations of state are considered. In each case we study the stability of the thin shell against linear perturbations.We plot the stability regions by tuning the parameters of the theory. It is observed that the role of the Hayward parameter is to make the TSW more stable. Perturbations of the throat with small velocity condition are also studied. The matter of our TSWs, however, remains exotic. (orig.)

Analysis of thermal-plastic response of shells of revolution by numerical integration

International Nuclear Information System (INIS)

Leonard, J.W.

1975-01-01

A numerical method based instead on the numerical integration of the governing shell equations has been shown, for elastic cases, to be more efficient than the finite element method when applied to shells of revolution. In the numerical integration method, the governing differential equations of motions are converted into a set of initial-value problems. Each initial-value problem is integrated numerically between meridional boundary points and recombined so as to satisfy boundary conditions. For large-deflection elasto-plastic behavior, the equations are nonlinear and, hence, are recombined in an iterative manner using the Newton-Raphson procedure. Suppression techniques are incorporated in order to eliminate extraneous solutions within the numerical integration procedure. The Reissner-Meissner shell theory for shells of revolution is adopted to account for large deflection and higher-order rotation effects. The computer modelling of the equations is quite general in that specific shell segment geometries, e.g. cylindrical, spherical, toroidal, conical segments, and any combinations thereof can be handled easily. The elasto-plastic constitutive relations adopted are in accordance with currently recommended constitutive equations for inelastic design analysis of FFTF Components. The Von Mises yield criteria and associated flow rule is used and the kinematic hardening law is followed. Examples are considered in which stainless steels common to LMFBR application are used

Homogenization of Winkler-Steklov spectral conditions in three-dimensional linear elasticity

Science.gov (United States)

Gómez, D.; Nazarov, S. A.; Pérez, M. E.

2018-04-01

We consider a homogenization Winkler-Steklov spectral problem that consists of the elasticity equations for a three-dimensional homogeneous anisotropic elastic body which has a plane part of the surface subject to alternating boundary conditions on small regions periodically placed along the plane. These conditions are of the Dirichlet type and of the Winkler-Steklov type, the latter containing the spectral parameter. The rest of the boundary of the body is fixed, and the period and size of the regions, where the spectral parameter arises, are of order ɛ . For fixed ɛ , the problem has a discrete spectrum, and we address the asymptotic behavior of the eigenvalues {β _k^ɛ }_{k=1}^{∞} as ɛ → 0. We show that β _k^ɛ =O(ɛ ^{-1}) for each fixed k, and we observe a common limit point for all the rescaled eigenvalues ɛ β _k^ɛ while we make it evident that, although the periodicity of the structure only affects the boundary conditions, a band-gap structure of the spectrum is inherited asymptotically. Also, we provide the asymptotic behavior for certain "groups" of eigenmodes.

Extrinsic contribution to the non-linearity in a PZT disc

Energy Technology Data Exchange (ETDEWEB)

Perez, Rafel [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Albareda, Alfons [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Garcia, Jose E [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Tiana, Jordi [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Ringgaard, Erling [Ferroperm Piezoceramics A/S, Hejreskovvej 18, DK-3490 Kvistgaard (Denmark); Wolny, Wanda W [Ferroperm Piezoceramics A/S, Hejreskovvej 18, DK-3490 Kvistgaard (Denmark)

2004-10-07

Non-linear increases in elastic, piezoelectric (direct and reverse) and dielectric coefficients have been measured under a high electrical field or under high mechanical stress. The permittivity and reverse piezoelectric coefficient can be measured by applying a high voltage at a low frequency, while the elastic compliance and direct piezoelectric coefficient can be measured at the first radial resonance frequency in order to apply a high stress. The non-linear behaviour has been analysed at the radial resonance of a disc. In all the materials tested, the results show that there is a close relation between the non-linear increments of the different coefficients. An empirical model has been proposed in order to describe and understand these relations. It is assumed that either the strain or the electrical displacement is produced by intrinsic and extrinsic processes, but only the latter, which consist mainly in the motion of domain walls, contribute to the non-linearity. The model enables us to find the domain wall contribution to elastic, piezoelectric and dielectric non-linearities, and allows us to compare the amplitudes of the fields and stresses that produce the same displacement of domain walls.

Contact instabilities of anisotropic and inhomogeneous soft elastic films

Science.gov (United States)

Tomar, Gaurav; Sharma, Ashutosh

2012-02-01

Anisotropy plays important roles in various biological phenomena such as adhesion of geckos and grasshoppers enabled by the attachment pods having hierarchical structures like thin longitudinal setae connected with threads mimicked by anisotropic films. We study the contact instability of a transversely isotropic thin elastic film when it comes in contact proximity of another surface. In the present study we investigate the contact stability of a thin incompressible transversely isotropic film by performing linear stability analysis. Based on the linear stability analysis, we show that an approaching contactor renders the film unstable. The critical wavelength of the instability is a function of the total film thickness and the ratio of the Young's modulus in the longitudinal direction and the shear modulus in the plane containing the longitudinal axis. We also analyze the stability of a thin gradient film that is elastically inhomogeneous across its thickness. Compared to a homogeneous elastic film, it becomes unstable with a longer wavelength when the film becomes softer in going from the surface to the substrate.

Analytic Solution to Shell Boundary – Value Problems

Directory of Open Access Journals (Sweden)

Yu. I. Vinogradov

2015-01-01

Full Text Available Object of research is to find analytical solution to the shell boundary – value problems, i.e. to consider the solution for a class of problems concerning the mechanics of hoop closed shells strain.The objective of work is to create an analytical method to define a stress – strain state of shells under non-axisymmetric loading. Thus, a main goal is to derive the formulas – solutions of the linear ordinary differential equations with variable continuous coefficients.The partial derivative differential equations of mechanics of shells strain by Fourier's method of variables division are reduced to the system of the differential equations with ordinary derivatives. The paper presents the obtained formulas to define solutions of the uniform differential equations and received on their basis formulas to define a particular solution depending on a type of the right parts of the differential equations.The analytical algorithm of the solution of a boundary task uses an approach to transfer the boundary conditions to the randomly chosen point of an interval of changing independent variable through the solution of the canonical matrix ordinary differential equation with the subsequent solution of system of algebraic equations for compatibility of boundary conditions at this point. Efficiency of algorithm is based on the fact that the solution of the ordinary differential equations is defined as the values of Cauchy – Krylova functions, which meet initial arbitrary conditions.The results of researches presented in work are useful to experts in the field of calculus mathematics, dealing with solution of systems of linear ordinary differential equations and creation of effective analytical computing methods to solve shell boundary – value problems.

The price elasticity of electricity demand in South Australia

International Nuclear Information System (INIS)

Fan Shu; Hyndman, Rob J.

2011-01-01

In this paper, the price elasticity of electricity demand, representing the sensitivity of customer demand to the price of electricity, has been estimated for South Australia. We first undertake a review of the scholarly literature regarding electricity price elasticity for different regions and systems. Then we perform an empirical evaluation of the historic South Australian price elasticity, focussing on the relationship between price and demand quantiles at each half-hour of the day. This work attempts to determine whether there is any variation in price sensitivity with the time of day or quantile, and to estimate the form of any relationships that might exist in South Australia. - Highlights: → We review the scholarly literature on electricity own-price elasticity for different regions and systems. → We use annual log-linear econometric models of the electricity demand to estimate the historic South Australian price elasticity. → We focus on the relationship between price and demand quantiles at each half-hour of the day. → The overall price elasticity in South Australia ranges from -0.363 to -0.428.

Effects of ocean acidification on the shells of four Mediterranean gastropod species near a CO2 seep.

Science.gov (United States)

Duquette, Ashley; McClintock, James B; Amsler, Charles D; Pérez-Huerta, Alberto; Milazzo, Marco; Hall-Spencer, Jason M

2017-11-30

Marine CO 2 seeps allow the study of the long-term effects of elevated pCO 2 (ocean acidification) on marine invertebrate biomineralization. We investigated the effects of ocean acidification on shell composition and structure in four ecologically important species of Mediterranean gastropods (two limpets, a top-shell snail, and a whelk). Individuals were sampled from three sites near a volcanic CO 2 seep off Vulcano Island, Italy. The three sites represented ambient (8.15pH), moderate (8.03pH) and low (7.73pH) seawater mean pH. Shell mineralogy, microstructure, and mechanical strength were examined in all four species. We found that the calcite/aragonite ratio could vary and increased significantly with reduced pH in shells of one of the two limpet species. Moreover, each of the four gastropods displayed reductions in either inner shell toughness or elasticity at the Low pH site. These results suggest that near-future ocean acidification could alter shell biomineralization and structure in these common gastropods. Copyright © 2017 Elsevier Ltd. All rights reserved.

Dynamic elasticity measurement for prosthetic socket design.

Science.gov (United States)

Kim, Yujin; Kim, Junghoon; Son, Hyeryon; Choi, Youngjin

2017-07-01

The paper proposes a novel apparatus to measure the dynamic elasticity of human limb in order to help the design and fabrication of the personalized prosthetic socket. To take measurements of the dynamic elasticity, the desired force generated as an exponential chirp signal in which the frequency increases and amplitude is maintained according to time progress is applied to human limb and then the skin deformation is recorded, ultimately, to obtain the frequency response of its elasticity. It is referred to as a Dynamic Elasticity Measurement Apparatus (DEMA) in the paper. It has three core components such as linear motor to provide the desired force, loadcell to implement the force feedback control, and potentiometer to record the skin deformation. After measuring the force/deformation and calculating the dynamic elasticity of the limb, it is visualized as 3D color map model of the limb so that the entire dynamic elasticity can be shown at a glance according to the locations and frequencies. For the visualization, the dynamic elasticities measured at specific locations and frequencies are embodied using the color map into 3D limb model acquired by using 3D scanner. To demonstrate the effectiveness, the visualized dynamic elasticities are suggested as outcome of the proposed system, although we do not have any opportunity to apply the proposed system to the amputees. Ultimately, it is expected that the proposed system can be utilized to design and fabricate the personalized prosthetic socket in order for releasing the wearing pain caused by the conventional prosthetic socket.

Semidefinite linear complementarity problems

International Nuclear Information System (INIS)

Eckhardt, U.

1978-04-01

Semidefinite linear complementarity problems arise by discretization of variational inequalities describing e.g. elastic contact problems, free boundary value problems etc. In the present paper linear complementarity problems are introduced and the theory as well as the numerical treatment of them are described. In the special case of semidefinite linear complementarity problems a numerical method is presented which combines the advantages of elimination and iteration methods without suffering from their drawbacks. This new method has very attractive properties since it has a high degree of invariance with respect to the representation of the set of all feasible solutions of a linear complementarity problem by linear inequalities. By means of some practical applications the properties of the new method are demonstrated. (orig.) [de

Density functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi2

International Nuclear Information System (INIS)

Ravindran, P.; Fast, L.; Korzhavyi, P.A.; Johansson, B.; Wills, J.; Eriksson, O.

1998-01-01

A theoretical formalism to calculate the single crystal elastic constants for orthorhombic crystals from first principle calculations is described. This is applied for TiSi 2 and we calculate the elastic constants using a full potential linear muffin-tin orbital method using the local density approximation (LDA) and generalized gradient approximation (GGA). The calculated values compare favorably with recent experimental results. An expression to calculate the bulk modulus along crystallographic axes of single crystals, using elastic constants, has been derived. From this the calculated linear bulk moduli are found to be in good agreement with the experiments. The shear modulus, Young's modulus, and Poisson's ratio for ideal polycrystalline TiSi 2 are also calculated and compared with corresponding experimental values. The directional bulk modulus and the Young's modulus for single crystal TiSi 2 are estimated from the elastic constants obtained from LDA as well as GGA calculations and are compared with the experimental results. The shear anisotropic factors and anisotropy in the linear bulk modulus are obtained from the single crystal elastic constants. From the site and angular momentum decomposed density of states combined with a charge density analysis and the elastic anisotropies, the chemical bonding nature between the constituents in TiSi 2 is analyzed. The Debye temperature is calculated from the average elastic wave velocity obtained from shear and bulk modulus as well as the integration of elastic wave velocities in different directions of the single crystal. The calculated elastic properties are found to be in good agreement with experimental values when the generalized gradient approximation is used for the exchange and correlation potential. copyright 1998 American Institute of Physics

Effects of a high mean stress on the high cycle fatigue life of PWA 1480 and correlation of data by linear elastic fracture mechanics

Science.gov (United States)

Majumdar, S.; Kwasny, R.

1985-01-01

High-cycle fatigue tests using 5-mm-diameter smooth specimens were performed on the single crystal alloy PWA 1480 (001 axis) at 70F (room temperature) in air and at 100F (538C) in vacuum (10 to the -6 power torr). Tests were conducted at zero mean stress as well as at high tensile mean stress. The results indicate that, although a tensile mean stress, in general, reduces life, the reduction in fatigue strength, for a given mean stress at a life of one million cycles, is much less than what is predicted by the usual linear Goodman plot. Further, the material appears to be significantly more resistant to mean stress effects at 1000F than at 70F. Metallographic examinations of failed specimens indicate that failures in all cases are initiated from micropores of sizes of the order of 30 to 40 microns. Since the macroscopic stress-strain response in all cases was observed to be linear elastic, linear elastic fracture mechanics (LEFM) analyses were carried out to determine the crack growth curves of the material assuming that crack initiation from a micropore (a sub o = 40 microns) occurs very early in life. The results indicate that the calculated crack growth rates at an R (defined as the ratio between minimum stress to maximum stress) value of zero are approximately the same at 70F as at 1000F. However, the calculated crack growth rates at other R ratios, both positive and negative, tend to be higher at 70F than at 1000F. Calculated threshold effects at large R values tend to be independent of temperature in the temperature regime studied. They are relatively constant with increasing R ratio up to a value of about 0.6, beyond which the calculated threshold stress intensity factor range decreases rapidly with increasing R ratios.

A meta-analysis of the price elasticity of gasoline demand. A SUR approach

NARCIS (Netherlands)

Brons, M.R.E.; Nijkamp, P.; Pels, E.; Rietveld, P.

2008-01-01

Automobile gasoline demand can be expressed as a multiplicative function of fuel efficiency, mileage per car and car ownership. This implies a linear relationship between the price elasticity of total fuel demand and the price elasticities of fuel efficiency, mileage per car and car ownership. In

Explicit Dynamic Finite Element Method for Predicting Implosion/Explosion Induced Failure of Shell Structures

Directory of Open Access Journals (Sweden)

Jeong-Hoon Song

2013-01-01

Full Text Available A simplified implementation of the conventional extended finite element method (XFEM for dynamic fracture in thin shells is presented. Though this implementation uses the same linear combination of the conventional XFEM, it allows for considerable simplifications of the discontinuous displacement and velocity fields in shell finite elements. The proposed method is implemented for the discrete Kirchhoff triangular (DKT shell element, which is one of the most popular shell elements in engineering analysis. Numerical examples for dynamic failure of shells under impulsive loads including implosion and explosion are presented to demonstrate the effectiveness and robustness of the method.

Extending double modulation: combinatorial rules for identifying the modulations necessary for determining elasticities in metabolic pathways.

Science.gov (United States)

Giersch, C; Cornish-Bowden, A

1996-10-07

The double modulation method for determining the elasticities of pathway enzymes, originally devised by Kacser & Burns (Biochem. Soc. Trans. 7, 1149-1160, 1979), is extended to pathways of complex topological structure, including branching and feedback loops. An explicit system of linear equations for the unknown elasticities is derived. The constraints imposed on this linear system imply that modulations of more than one enzyme are not necessarily independent. Simple combinatorial rules are described for identifying without using any algebra the set of independent modulations that allow the determination of the elasticities of any enzyme. By repeated application, the minimum numbers of modulations required to determine the elasticities of all enzymes of a given pathway can be determined. The procedure is illustrated with numerous examples.

A flat triangular shell element with Loof nodes

DEFF Research Database (Denmark)

Poulsen, Peter Noe; Damkilde, Lars

1996-01-01

In the formulation of flat shell elements it is difficult to achieve inter-element compatibility between membrane and transverse displacements for non-coplanar elements. Many elements lack proper nodal degrees of freedom to model intersections making the assembly of elements troublesome. A flat...... triangular shell element is established by a combination of a new plate bending element DKTL and the well-known linear membrane strain element LST, and for this element the above-mentioned deficiences are avoided. The plate bending element DKTL is based on Discrete Kirchhoff Theory and Loof nodes. The nodal...

FASOR - A second generation shell of revolution code

Science.gov (United States)

Cohen, G. A.

1978-01-01

An integrated computer program entitled Field Analysis of Shells of Revolution (FASOR) currently under development for NASA is described. When completed, this code will treat prebuckling, buckling, initial postbuckling and vibrations under axisymmetric static loads as well as linear response and bifurcation under asymmetric static loads. Although these modes of response are treated by existing programs, FASOR extends the class of problems treated to include general anisotropy and transverse shear deformations of stiffened laminated shells. At the same time, a primary goal is to develop a program which is free of the usual problems of modeling, numerical convergence and ill-conditioning, laborious problem setup, limitations on problem size and interpretation of output. The field method is briefly described, the shell differential equations are cast in a suitable form for solution by this method and essential aspects of the input format are presented. Numerical results are given for both unstiffened and stiffened anisotropic cylindrical shells and compared with previously published analytical solutions.

Rayleigh wave effects in an elastic half-space.

Science.gov (United States)

Aggarwal, H. R.

1972-01-01

Consideration of Rayleigh wave effects in a homogeneous isotropic linearly elastic half-space subject to an impulsive uniform disk pressure loading. An approximate formula is obtained for the Rayleigh wave effects. It is shown that the Rayleigh waves near the center of loading arise from the portion of the dilatational and shear waves moving toward the axis, after they originate at the edge of the load disk. A study is made of the vertical displacement due to Rayleigh waves at points on the axis near the surface of the elastic half-space.

Response of orthotropic micropolar elastic medium due to time ...

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

namic response of anisotropic continuum has received the attention of ... linear theory of micropolar elasticity and bending of orthotropic micropolar ... medium due to time harmonic concentrated load, the continuum is divided into two half-.

Relativity, nuclear polarizability, and screening in sub-Coulomb elastic scattering

International Nuclear Information System (INIS)

Lynch, W.G.; Tsang, M.B.; Bhang, H.C.; Cramer, J.G.; Puigh, R.J.

Elastic scattering of p-shell nuclear projectiles from 208 Pb has been examined for deviations from Rutherford scattering. Four effects can be important: atomic screening, vacuum polarization, nuclear polarizability and a relativistic effect of dynamical origin. The presence of atomic screening, nuclear polarizability and the relativistic effect was observed thus constituting the first measurement of this relativistic effect using complex nuclei and the first measurement of this relativistic effect using complex nuclei and the first measurement of nuclear polarizability in an external Coulomb field

Hydrostatic pressure dependence of elastic constants for lead fluoride crystal

International Nuclear Information System (INIS)

Singh, R.K.; Rao, C.N.

1988-10-01

The variations of the second order elastic constants (SOEC) and longitudinal and shear moduli with hydrostatic pressure for the lead fluoride have been investigated theoretically, for the first time, by means of a three-body force potential (TBP) model. The significance of three-body interactions (TBI) has been clearly demonstrated in these investigations. The present TBP model has reproduced the pressure derivatives of the SOEC of PbF more satisfactorily than the shell model and other model calculations. (author). 24 refs, 3 figs, 2 tabs

Diffraction by an immersed elastic wedge

CERN Document Server

Croisille, Jean-Pierre

1999-01-01

This monograph presents the mathematical description and numerical computation of the high-frequency diffracted wave by an immersed elastic wave with normal incidence. The mathematical analysis is based on the explicit description of the principal symbol of the pseudo-differential operator connected with the coupled linear problem elasticity/fluid by the wedge interface. This description is subsequently used to derive an accurate numerical computation of diffraction diagrams for different incoming waves in the fluid, and for different wedge angles. The method can be applied to any problem of coupled waves by a wedge interface. This work is of interest for any researcher concerned with high frequency wave scattering, especially mathematicians, acousticians, engineers.

Response types and general stability conditions of linear aero-elastic system with two degrees-of-freedom

Czech Academy of Sciences Publication Activity Database

Náprstek, Jiří; Pospíšil, Stanislav

2012-01-01

Roč. 111, č. 1 (2012), s. 1-13 ISSN 0167-6105 R&D Projects: GA ČR(CZ) GA103/09/0094; GA AV ČR(CZ) IAA200710902 Institutional support: RVO:68378297 Keywords : aero-elastic system * self-excited vibration * instability * aero-elastic derivatives Subject RIV: JN - Civil Engineering Impact factor: 1.342, year: 2012

Quasi-estatic and dynamic elasto/viscoplastic analysis of plates and shells

International Nuclear Information System (INIS)

Dinis, L.M.S.

1981-01-01

The non-linear quasi-static and dynamic analysis of plates and shells is presented using the finite - element method for spatial discretization and the Central Finite Differences for the integration of the transient dynamic equation. The behaviour of the material is represented by the elasto/viscoplastic model of Perzyna together with approximations of the Von Mises yield surfaces for plates and shells. (Author) [pt

NIF Double Shell outer/inner shell collision experiments

Science.gov (United States)

Merritt, E. C.; Loomis, E. N.; Wilson, D. C.; Cardenas, T.; Montgomery, D. S.; Daughton, W. S.; Dodd, E. S.; Desjardins, T.; Renner, D. B.; Palaniyappan, S.; Batha, S. H.; Khan, S. F.; Smalyuk, V.; Ping, Y.; Amendt, P.; Schoff, M.; Hoppe, M.

2017-10-01

Double shell capsules are a potential low convergence path to substantial alpha-heating and ignition on NIF, since they are predicted to ignite and burn at relatively low temperatures via volume ignition. Current LANL NIF double shell designs consist of a low-Z ablator, low-density foam cushion, and high-Z inner shell with liquid DT fill. Central to the Double Shell concept is kinetic energy transfer from the outer to inner shell via collision. The collision determines maximum energy available for compression and implosion shape of the fuel. We present results of a NIF shape-transfer study: two experiments comparing shape and trajectory of the outer and inner shells at post-collision times. An outer-shell-only target shot measured the no-impact shell conditions, while an `imaging' double shell shot measured shell conditions with impact. The `imaging' target uses a low-Z inner shell and is designed to perform in similar collision physics space to a high-Z double shell but can be radiographed at 16keV, near the viable 2DConA BL energy limit. Work conducted under the auspices of the U.S. DOE by LANL under contract DE-AC52-06NA25396.

Nonplanar on-shell diagrams and leading singularities of scattering amplitudes

Energy Technology Data Exchange (ETDEWEB)

Chen, Baoyi; Cheung, Yeuk-Kwan E.; Li, Yunxuan; Xie, Ruofei; Xin, Yuan [Nanjing University, Department of Physics, Nanjing (China); Chen, Gang [Zhejiang Normal University, Department of Physics, Jinhua, Zhejiang (China); Nanjing University, Department of Physics, Nanjing (China)

2017-02-15

Bipartite on-shell diagrams are the latest tool in constructing scattering amplitudes. In this paper we prove that a Britto-Cachazo-Feng-Witten (BCFW) decomposable on-shell diagram process a rational top form if and only if the algebraic ideal comprised the geometrical constraints are shifted linearly during successive BCFW integrations. With a proper geometric interpretation of the constraints in the Grassmannian manifold, the rational top form integration contours can thus be obtained, and understood, in a straightforward way. All rational top form integrands of arbitrary higher loops leading singularities can therefore be derived recursively, as long as the corresponding on-shell diagram is BCFW decomposable. (orig.)

Dynamic plastic buckling of rings and cylindrical shells

International Nuclear Information System (INIS)

Jones, N.; Okawa, D.M.

1975-01-01

A theoretical analysis is developed to predict the dynamic plastic buckling of a long, impulsively loaded cylindrical shell. This theoretical work is used to examine various features of plastic buckling and to assess the importance of several approximations which previous authors have introduced in dynamic plastic buckling studies. In particular, the influence of a time-dependent circumferential membrane force, the sharpness of the peaks in the displacement and velocity amplification functions, the restrictions which are implicit when employing the Prandtl-Reuss equations in this class of problems, and the limitations due to elastic unloading are examined in some detail. (Auth.)

Scanning the parameter space of collapsing rotating thin shells

Science.gov (United States)

Rocha, Jorge V.; Santarelli, Raphael

2018-06-01

We present results of a comprehensive study of collapsing and bouncing thin shells with rotation, framing it in the context of the weak cosmic censorship conjecture. The analysis is based on a formalism developed specifically for higher odd dimensions that is able to describe the dynamics of collapsing rotating shells exactly. We analyse and classify a plethora of shell trajectories in asymptotically flat spacetimes. The parameters varied include the shell’s mass and angular momentum, its radial velocity at infinity, the (linear) equation-of-state parameter and the spacetime dimensionality. We find that plunges of rotating shells into black holes never produce naked singularities, as long as the matter shell obeys the weak energy condition, and so respects cosmic censorship. This applies to collapses of dust shells starting from rest or with a finite velocity at infinity. Not even shells with a negative isotropic pressure component (i.e. tension) lead to the formation of naked singularities, as long as the weak energy condition is satisfied. Endowing the shells with a positive isotropic pressure component allows for the existence of bouncing trajectories satisfying the dominant energy condition and fully contained outside rotating black holes. Otherwise any turning point occurs always inside the horizon. These results are based on strong numerical evidence from scans of numerous sections in the large parameter space available to these collapsing shells. The generalisation of the radial equation of motion to a polytropic equation-of-state for the matter shell is also included in an appendix.

A finite element model for nonlinear shells of revolution

International Nuclear Information System (INIS)

Cook, W.A.

1979-01-01

A shell-of-revolution model was developed to analyze impact problems associated with the safety analysis of nuclear material shipping containers. The nonlinear shell theory presented by Eric Reissner in 1972 was used to develop our model. Reissner's approach includes transverse shear deformation and moments turning about the middle surface normal. With these features, this approach is valid for both thin and thick shells. His theory is formulated in terms of strain and stress resultants that refer to the undeformed geometry. This nonlinear shell model is developed using the virtual work principle associated with Reissner's equilibrium equations. First, the virtual work principle is modified for incremental loading; then it is linearized by assuming that the nonlinear portions of the strains are known. By iteration, equilibrium is then approximated for each increment. A benefit of this approach is that this iteration process makes it possible to use nonlinear material properties. (orig.)

Fast-neutron elastic scattering from elemental vanadium

International Nuclear Information System (INIS)

Smith, A.B.; Guenther, P.T.; Lawson, R.D.

1988-03-01

Differential neutron elastic- and inelastic-scattering cross sections of vanadium were measured from 4.5 to 10 MeV. These results were combined with previous 1.5 to 4.0 MeV data from this laboratory, the 11.1 MeV elastic-scattering results obtained at Ohio University, and the reported neutron total cross sections to energies of ∼20.0 MeV, to form a data base which was interpreted in terms of the spherical optical-statistical model. A fit to the data was achieved by making both the strengths and geometries of the optical-model potential energy dependent. This energy dependence was large below ∼6.0 MeV. Above ∼6.0 MeV the energy dependencies are smaller, and similar to those characteristic of global models. Using the dispersion relationship and the method of moments, the optical-model potential energy deduced from 0.0 to 11.1 MeV neutron-scattering data was extrapolated to higher energies and to the bound-state regime. This extrapolation leads to predicted neutron total cross sections that are within 3% of the experimental values throughout the energy range 0.0 to 20.0 MeV. Furthermore, the values of the volume-integral-per-nucleon of the real potential are in excellent agreement with those needed to reproduce the observed binding energies of particle- and hole-states. The latter gives clear evidence of the Fermi surface anomaly. Using only the 0.0 to 11.1 MeV data, the predicted E < O behavior of the strength and radius of the real shell-model Woods-Saxon potential are somewhat different from those obtained by Mahaux and Sartor in their analysis of nuclei near closed shells. 61 refs., 9 figs., 2 tabs

Counter-rotational effects on stability of 2 + 1-dimensional thin-shell wormholes

Energy Technology Data Exchange (ETDEWEB)

Mazharimousavi, S.H.; Halilsoy, M. [Eastern Mediterranean University, Department of Physics, Gazimagusa (Turkey)

2014-09-15

The role of angular momentum in a 2 + 1-dimensional rotating thin-shell wormhole (TSW) is considered. Particular emphasis is given to stability when the shells (rings) are counter-rotating. We find that counter-rotating halves make the TSW supported by the equation of state of a linear gas more stable. Under a small velocity dependent perturbation, however, it becomes unstable. (orig.)

Rubber and gel origami: visco- and poro-elastic behavior of folded structures

Science.gov (United States)

Evans, Arthur; Bende, Nakul; Na, Junhee; Hayward, Ryan; Santangelo, Christian

2014-11-01

The Japanese art of origami is rapidly becoming a platform for material design, as researchers develop systematic methods to exploit the purely geometric rules that allow paper to folded without stretching. Since any thin sheet couples mechanics strongly to geometry, origami provides a natural template for generating length-scale independent structures from a variety of different materials. In this talk I discuss some of the implications of using polymeric sheets and shells over many length scales to create folded materials with tunable shapes and properties. These implications include visco-elastic snap-through transitions and poro-elastically driven micro origami. In each case, mechanical response, dynamics, and reversible folding is tuned through a combination of geometry and constitutive properties, demonstrating the efficacy of using origami principles for designing functional materials.

Simplified method for elastic plastic analysis of material presenting bilinear kinematic hardening

International Nuclear Information System (INIS)

Roche, R.

1983-12-01

A simplified method for elastic plastic analysis is presented. Material behavior is assumed to be elastic plastic with bilinear kinematic hardening. The proposed method give a strain-stress field fullfilling material constitutive equations, equations of equilibrium and continuity conditions. This strain-stress is obtained through two linear computations. The first one is the conventional elastic analysis of the body submitted to the applied load. The second one use tangent matrix (tangent Young's modulus and Poisson's ratio) for the determination of an additional stress due to imposed initial strain. Such a method suits finite elements computer codes, the most useful result being plastic strains resulting from the applied loading (load control or deformation control). Obviously, there is not unique solution, for stress-strain field is not depending only of the applied load, but of the load history. Therefore, less pessimistic solutions can be got by one or two additional linear computations [fr

The Application of Simulation Method in Isothermal Elastic Natural Gas Pipeline

Science.gov (United States)

Xing, Chunlei; Guan, Shiming; Zhao, Yue; Cao, Jinggang; Chu, Yanji

2018-02-01

This Elastic pipeline mathematic model is of crucial importance in natural gas pipeline simulation because of its compliance with the practical industrial cases. The numerical model of elastic pipeline will bring non-linear complexity to the discretized equations. Hence the Newton-Raphson method cannot achieve fast convergence in this kind of problems. Therefore A new Newton Based method with Powell-Wolfe Condition to simulate the Isothermal elastic pipeline flow is presented. The results obtained by the new method aregiven based on the defined boundary conditions. It is shown that the method converges in all cases and reduces significant computational cost.

Finite element elastic-plastic analysis of LMFBR components

International Nuclear Information System (INIS)

Levy, A.; Pifko, A.; Armen, H. Jr.

1978-01-01

The present effort involves the development of computationally efficient finite element methods for accurately predicting the isothermal elastic-plastic three-dimensional response of thick and thin shell structures subjected to mechanical and thermal loads. This work will be used as the basis for further development of analytical tools to be used to verify the structural integrity of liquid metal fast breeder reactor (LMFBR) components. The methods presented here have been implemented into the three-dimensional solid element module (HEX) of the Grumman PLANS finite element program. These methods include the use of optimal stress points as well as a variable number of stress points within an element. This allows monitoring the stress history at many points within an element and hence provides an accurate representation of the elastic-plastic boundary using a minimum number of degrees of freedom. Also included is an improved thermal stress analysis capability in which the temperature variation and corresponding thermal strain variation are represented by the same functional form as the displacement variation. Various problems are used to demonstrate these improved capabilities. (Auth.)

Prediction of mass excess, β-decay energy and neutron separation energy from the atomic mass formula with empirical shell terms

International Nuclear Information System (INIS)

Ando, Yoshihira; Uno, Masahiro; Yamada, Masami

1983-02-01

Recently we proposed two types of atomic mass formula (constant-shell-term formula, linear-shell-term formula). With use of these formulas, we calculate and tabulate mass excesses, neutron separation energies, and β-decay energies (β-decay and/or electron capture) for about 5000 nuclides. The mass excess values and their errors in the 1977 atomic mass evaluation by A.H. Wapstra and K. Bos which we used in constructing our formulas, are also tabulated for reference. The constant-shell-term formula is fitted to 1468 input mass data with the standard deviation of 626 keV and the linear-shell-term formula with 394 keV

Prediction of mass excess, #betta#-decay energy and neutron separation energy from the atomic mass formula with empirical shell terms

International Nuclear Information System (INIS)

Ando, Yoshihira; Uno, Masahiro; Yamada, Masami.

1983-02-01

Recently we proposed two types of atomic mass formula (constant-shell-term formula, linear-shell-term formula). With use of these formulas, we calculate and tabulate mass excesses, neutron separation energies, and #betta#-decay energies (#betta# - -decay and/or electron capture) for about 5000 nuclides. The mass excess values and their errors in the 1977 atomic mass evaluation by A.H. Wapstra and K. Bos which we used in constructing our formulas, are also tabulated for reference. The constant-shell-term formula is fitted to 1468 input mass data with the standard deviation of 626 keV and the linear-shell-term formula with 394 keV. (author)

Two-velocity elasticity theory and facet growth

OpenAIRE

Andreev, A. F.; Melnikovsky, L. A.

2002-01-01

We explain the linear growth of smooth solid helium facets by the presence of lattice point defects. To implement this task, the framework of very general two-velocity elasticity theory equations is developed. Boundary conditions for these equations for various surface types are derived. We also suggest additional experiments to justify the concept.

An analysis of hypercritical states in elastic and inelastic systems

Science.gov (United States)

Kowalczk, Maciej

The author raises a wide range of problems whose common characteristic is an analysis of hypercritical states in elastic and inelastic systems. the article consists of two basic parts. The first part primarily discusses problems of modelling hypercritical states, while the second analyzes numerical methods (so-called continuation methods) used to solve non-linear problems. The original approaches for modelling hypercritical states found in this article include the combination of plasticity theory and an energy condition for cracking, accounting for the variability and cyclical nature of the forms of fracture of a brittle material under a die, and the combination of plasticity theory and a simplified description of the phenomenon of localization along a discontinuity line. The author presents analytical solutions of three non-linear problems for systems made of elastic/brittle/plastic and elastic/ideally plastic materials. The author proceeds to discuss the analytical basics of continuation methods and analyzes the significance of the parameterization of non-linear problems, provides a method for selecting control parameters based on an analysis of the rank of a rectangular matrix of a uniform system of increment equations, and also provides a new method for selecting an equilibrium path originating from a bifurcation point. The author provides a general outline of continuation methods based on an analysis of the rank of a matrix of a corrective system of equations. The author supplements his theoretical solutions with numerical solutions of non-linear problems for rod systems and problems of the plastic disintegration of a notched rectangular plastic plate.

Incremental localized boundary-domain integro-differential equations of elastic damage mechanics for inhomogeneous body

OpenAIRE

Mikhailov, SE

2006-01-01

Copyright @ 2006 Tech Science Press A quasi-static mixed boundary value problem of elastic damage mechanics for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary homogeneous linear elasticity with frozen initial, secant or tangent elastic coe±cients, a boundary-domain integro-differential formulation of the elasto-plastic problem with respect to the displacement rates and their gradients is derived. Usin...

Investigations of the radial distributions of nucleons in 1fsub(7/2)-shell nuclei by elastic alpha particle scattering

International Nuclear Information System (INIS)

Gils, H.J.

1984-12-01

The radial size and shape of the distribution of nucleons - i.e. the sum of protons and neutrons - in atomic nuclei of the 1fsub(7/2) shell is investigated in the present work. The experimental basis of the studies are differential cross sections of elastic α particle scattering by sup(40,42,43,44,48)Ca, 50 Ti, 51 V, 52 Cr precisely measured over a wide angular range at the 104 MeV α particle beam from the Karlsruhe Isochronous Cyclotron. The experimental cross sections are analyzed using so-called 'model independent' optical potentials by which the data are very well reproduced. The error bands of these potentials are determined in a well-defined form from the analyses. The high sensitivity of the data to the radial form of the real optical potential justifies, in principle, that the experiments are a suitable tool for investigating nuclear density distributions. Some pre-informations on this question are obtained from the optical potential analyses. For a more direct access to the nuclear matter distributions - in particular to differences between neighbouring nuclei - a semimicroscopic reaction model is presented which on the one hand is based on a fully microscopic many body approach. On the other hand all quantities being not of particular interest for the results are treated in a phenomenological way. Thereby, it is possible to reproduce the experimental cross sections as well as by the 'model independent' potentials and to obtain full consistency between the two approaches. This has not been achieved by any other microscopic reaction model. (orig./HSI) [de

Materials and noncoplanar mesh designs for integrated circuits with linear elastic responses to extreme mechanical deformations.

Science.gov (United States)

Kim, Dae-Hyeong; Song, Jizhou; Choi, Won Mook; Kim, Hoon-Sik; Kim, Rak-Hwan; Liu, Zhuangjian; Huang, Yonggang Y; Hwang, Keh-Chih; Zhang, Yong-wei; Rogers, John A

2008-12-02

Electronic systems that offer elastic mechanical responses to high-strain deformations are of growing interest because of their ability to enable new biomedical devices and other applications whose requirements are impossible to satisfy with conventional wafer-based technologies or even with those that offer simple bendability. This article introduces materials and mechanical design strategies for classes of electronic circuits that offer extremely high stretchability, enabling them to accommodate even demanding configurations such as corkscrew twists with tight pitch (e.g., 90 degrees in approximately 1 cm) and linear stretching to "rubber-band" levels of strain (e.g., up to approximately 140%). The use of single crystalline silicon nanomaterials for the semiconductor provides performance in stretchable complementary metal-oxide-semiconductor (CMOS) integrated circuits approaching that of conventional devices with comparable feature sizes formed on silicon wafers. Comprehensive theoretical studies of the mechanics reveal the way in which the structural designs enable these extreme mechanical properties without fracturing the intrinsically brittle active materials or even inducing significant changes in their electrical properties. The results, as demonstrated through electrical measurements of arrays of transistors, CMOS inverters, ring oscillators, and differential amplifiers, suggest a valuable route to high-performance stretchable electronics.

Thin-shell wormhole solutions in Einstein-Hoffmann-Born-Infeld theory

Energy Technology Data Exchange (ETDEWEB)

Mazharimousavi, S. Habib, E-mail: habib.mazhari@emu.edu.tr [Department of Physics, Eastern Mediterranean University, G. Magusa, North Cyprus, Mersin 10 (Turkey); Halilsoy, M., E-mail: mustafa.halilsoy@emu.edu.tr [Department of Physics, Eastern Mediterranean University, G. Magusa, North Cyprus, Mersin 10 (Turkey); Amirabi, Z., E-mail: zahra.amirabi@emu.edu.tr [Department of Physics, Eastern Mediterranean University, G. Magusa, North Cyprus, Mersin 10 (Turkey)

2011-10-03

We adopt the Hoffmann-Born-Infeld's (HBI) double Lagrangian approach in general relativity to find black holes and investigate the possibility of viable thin-shell wormholes. By virtue of the non-linear electromagnetic parameter, the matching hypersurfaces of the two regions with two Lagrangians provide a natural, lower-bound radius for the thin-shell wormholes which provides the main motivation to the present study. In particular, the stability of thin-shell wormholes supported by normal matter in higher-dimensional Einstein-HBI-Gauss-Bonnet (EHBIGB) gravity is highlighted. -- Highlights: → We extend the Hoffmann-Born-Infeld Lagrangian to higher dimensions. → We found higher-dimensional black hole solutions for Einstein-Hoffmann-Born-Infeld-Gauss-Bonnet (EHBIGB) gravity. → We obtained thin-shell wormholes in the EHBIGB gravity which are supported by ordinary matter and stable.

Atomic mass prediction from the mass formula with empirical shell terms

International Nuclear Information System (INIS)

Uno, Masahiro; Yamada, Masami

1982-08-01

The mass-excess prediction of about 8000 nuclides was calculated from two types of the atomic mass formulas with empirical shell terms of Uno and Yamada. The theoretical errors to accompany the calculated mass excess are also presented. These errors have been obtained by a new statistical method. The mass-excess prediction includes the term of the gross feature of a nuclear mass surface, the shell terms and a small correction term for odd-odd nuclei. Two functional forms for the shell terms were used. The first is the constant form, and the sencond is the linear form. In determining the values of shell parameters, only the data of even-even and odd-A nuclei were used. A new statistical method was applied, in which the error inherent to the mass formula was taken account. The obtained shell parameters and the values of mass excess are shown in tables. (Kato, T.)

Using an elastic magnifier to increase power output and performance of heart-beat harvesters

Science.gov (United States)

Galbier, Antonio C.; Karami, M. Amin

2017-09-01

Embedded piezoelectric energy harvesting (PEH) systems in medical pacemakers have been a growing and innovative research area. The goal of these systems, at present, is to remove the pacemaker battery, which makes up 60%-80% of the unit, and replace it with a sustainable power source. This requires that energy harvesting systems provide sufficient power, 1-3 μW, for operating a pacemaker. The goal of this work is to develop, test, and simulate cantilevered energy harvesters with a linear elastic magnifier (LEM). This research hopes to provide insight into the interaction between pacemaker energy harvesters and the heart. By introducing the elastic magnifier into linear and nonlinear systems oscillations of the tip are encouraged into high energy orbits and large tip deflections. A continuous nonlinear model is presented for the bistable piezoelectric energy harvesting (BPEH) system and a one-degree-of-freedom linear mass-spring-damper model is presented for the elastic magnifier. The elastic magnifier will not consider the damping negligible, unlike most models. A physical model was created for the bistable structure and formed to an elastic magnifier. A hydrogel was designed for the experimental model for the LEM. Experimental results show that the BPEH coupled with a LEM (BPEH + LEM) produces more power at certain input frequencies and operates a larger bandwidth than a PEH, BPEH, and a standard piezoelectric energy harvester with the elastic magnifier (PEH + LEM). Numerical simulations are consistent with these results. It was observed that the system enters high-energy and high orbit oscillations and that, ultimately, BPEH systems implemented in medical pacemakers can, if designed properly, have enhanced performance if positioned over the heart.

Importance of elastic finite-size effects: Neutral defects in ionic compounds

Science.gov (United States)

Burr, P. A.; Cooper, M. W. D.

2017-09-01

Small system sizes are a well-known source of error in density functional theory (DFT) calculations, yet computational constraints frequently dictate the use of small supercells, often as small as 96 atoms in oxides and compound semiconductors. In ionic compounds, electrostatic finite-size effects have been well characterized, but self-interaction of charge-neutral defects is often discounted or assumed to follow an asymptotic behavior and thus easily corrected with linear elastic theory. Here we show that elastic effects are also important in the description of defects in ionic compounds and can lead to qualitatively incorrect conclusions if inadequately small supercells are used; moreover, the spurious self-interaction does not follow the behavior predicted by linear elastic theory. Considering the exemplar cases of metal oxides with fluorite structure, we show that numerous previous studies, employing 96-atom supercells, misidentify the ground-state structure of (charge-neutral) Schottky defects. We show that the error is eliminated by employing larger cells (324, 768, and 1500 atoms), and careful analysis determines that elastic, not electrostatic, effects are responsible. The spurious self-interaction was also observed in nonoxide ionic compounds irrespective of the computational method used, thereby resolving long-standing discrepancies between DFT and force-field methods, previously attributed to the level of theory. The surprising magnitude of the elastic effects is a cautionary tale for defect calculations in ionic materials, particularly when employing computationally expensive methods (e.g., hybrid functionals) or when modeling large defect clusters. We propose two computationally practicable methods to test the magnitude of the elastic self-interaction in any ionic system. In commonly studied oxides, where electrostatic effects would be expected to be dominant, it is the elastic effects that dictate the need for larger supercells: greater than 96 atoms.

Curvature-Induced Instabilities of Shells

Science.gov (United States)

Pezzulla, Matteo; Stoop, Norbert; Steranka, Mark P.; Bade, Abdikhalaq J.; Holmes, Douglas P.

2018-01-01

Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of spontaneous curvature and geometric frustration in curved shells remains poorly understood. Via a combination of precision experiments on elastomeric spherical shells, simulations, and theory, we show how a spontaneous curvature induces a rotational symmetry-breaking buckling as well as a snapping instability reminiscent of the Venus fly trap closure mechanism. The instabilities, and their dependence on geometry, are rationalized by reducing the spontaneous curvature to an effective mechanical load. This formulation reveals a combined pressurelike term in the bulk and a torquelike term in the boundary, allowing scaling predictions for the instabilities that are in excellent agreement with experiments and simulations. Moreover, the effective pressure analogy suggests a curvature-induced subcritical buckling in closed shells. We determine the critical buckling curvature via a linear stability analysis that accounts for the combination of residual membrane and bending stresses. The prominent role of geometry in our findings suggests the applicability of the results over a wide range of scales.

Data-Driven Problems in Elasticity

Science.gov (United States)

Conti, S.; Müller, S.; Ortiz, M.

2018-01-01

We consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problem consists of minimizing the distance between a given material data set and the subspace of compatible strain fields and stress fields in equilibrium. We find that the classical solutions are recovered in the case of linear elasticity. We identify conditions for convergence of Data-Driven solutions corresponding to sequences of approximating material data sets. Specialization to constant material data set sequences in turn establishes an appropriate notion of relaxation. We find that relaxation within this Data-Driven framework is fundamentally different from the classical relaxation of energy functions. For instance, we show that in the Data-Driven framework the relaxation of a bistable material leads to material data sets that are not graphs.

Computer Modeling of the Dynamic Strength of Metal-Plastic Cylindrical Shells Under Explosive Loading

Science.gov (United States)

Abrosimov, N. A.; Novosel'tseva, N. A.

2017-05-01

A technique for numerically analyzing the dynamic strength of two-layer metal-plastic cylindrical shells under an axisymmetric internal explosive loading is developed. The kinematic deformation model of the layered package is based on a nonclassical theory of shells. The geometric relations are constructed using relations of the simplest quadratic version of the nonlinear elasticity theory. The stress and strain tensors in the composite macrolayer are related by Hooke's law for an orthotropic body with account of degradation of the stiffness characteristics of the multilayer package due to local failure of some its elementary layers. The physical relations in the metal layer are formulated in terms of a differential theory of plasticity. An energy-correlated resolving system of dynamic equations for the metal-plastic cylindrical shells is derived by minimizing the functional of total energy of the shells as three-dimensional bodies. The numerical method for solving the initial boundary-value problem formulated is based on an explicit variational-difference scheme. The reliability of the technique considered is verified by comparing numerical results with experimental data. An analysis of the ultimate strains and strength of one-layer basalt-and glass-fiber-reinforced plastic and two-layer metalplastic cylindrical shells is carried out.

How tall can gelatin towers be? An introduction to elasticity and buckling

Science.gov (United States)

Taberlet, Nicolas; Ferrand, Jérémy; Camus, Élise; Lachaud, Léa; Plihon, Nicolas

2017-12-01

The stability of elastic towers is studied through simple hands-on experiments. Using gelatin-based stackable bricks, one can investigate the maximum height a simple structure can reach before collapsing. We show through experiments and by using the classical linear elastic theory that the main limitation to the height of such towers is the buckling of the elastic structures under their own weight. Moreover, the design and architecture of the towers can be optimized to greatly improve their resistance to self-buckling. To this aim, the maximum height of hollow and tapered towers is investigated. The experimental and theoretical developments presented in this paper can help students grasp the fundamental concepts in elasticity and mechanical stability.

Consequences of elastic anisotropy in patterned substrate heteroepitaxy.

Science.gov (United States)

Dixit, Gopal Krishna; Ranganathan, Madhav

2018-06-13

The role of elastic anisotropy on quantum dot formation and evolution on a pre-patterned substrate is evaluated within the framework of a continuum model. We first extend the formulation for surface evolution to take elastic anisotropy into account. Using a small slope approximation, we derive the evolution equation and show how it can be numerically implemented up to linear and second order for stripe and egg-carton patterned substrates using an accurate and efficient procedure. The semi--infinite nature of the substrate is used to solve the elasticity problem subject to other boundary conditions at the free surface and at the film--substrate interface. The positioning of the quantum dots with respect to the peaks and valleys of the pattern is explained by a competition between the length scale of the pattern and the wavelength of the Asaro--Tiller--Grinfeld instability, which is also affected by the elastic anisotropy. The alignment of dots is affected by a competition between the elastic anisotropy of the film and the pattern orientation. A domain of pattern inversion, wherein the quantum dots form exclusively in the valleys of the patterns is identified as a function of the average film thickness and the elastic anisotropy, and the time--scale for this inversion as function of height is analyzed. © 2018 IOP Publishing Ltd.

Effect of price elasticity of demand in monopolies with gradient adjustment

International Nuclear Information System (INIS)

Cavalli, Fausto; Naimzada, Ahmad

2015-01-01

Highlights: •A monopoly with isoelastic demand function is studied. •Reduced rationality monopolist uses gradient adjustment. •If marginal cost is small, increasing elasticity leads to stable dynamics. •For large marginal cost, dynamic can be unstable for both small and large elasticity. -- Abstract: We study a monopolistic market characterized by a constant elasticity demand function, in which the firm technology is described by a linear total cost function. The firm is assumed to be boundedly rational and to follow a gradient rule to adjust the production level in order to optimize its profit. We focus on what happens on varying the price elasticity of demand, studying the effect on the equilibrium stability. We prove that, depending on the relation between the market size and the marginal cost, two different scenarios are possible, in which elasticity has either a stabilizing or a mixed stabilizing/destabilizing effect

A Smoothed Finite Element-Based Elasticity Model for Soft Bodies

Directory of Open Access Journals (Sweden)

Juan Zhang

2017-01-01

Full Text Available One of the major challenges in mesh-based deformation simulation in computer graphics is to deal with mesh distortion. In this paper, we present a novel mesh-insensitive and softer method for simulating deformable solid bodies under the assumptions of linear elastic mechanics. A face-based strain smoothing method is adopted to alleviate mesh distortion instead of the traditional spatial adaptive smoothing method. Then, we propose a way to combine the strain smoothing method and the corotational method. With this approach, the amplitude and frequency of transient displacements are slightly affected by the distorted mesh. Realistic simulation results are generated under large rotation using a linear elasticity model without adding significant complexity or computational cost to the standard corotational FEM. Meanwhile, softening effect is a by-product of our method.

Mechanical characterization and non-linear elastic modeling of poly(glycerol sebacate) for soft tissue engineering.

Science.gov (United States)

Mitsak, Anna G; Dunn, Andrew M; Hollister, Scott J

2012-07-01

Scaffold tissue engineering strategies for repairing and replacing soft tissue aim to improve reconstructive and corrective surgical techniques whose limitations include suboptimal mechanical properties, fibrous capsule formation and volume loss due to graft resorption. An effective tissue engineering strategy requires a scaffolding material with low elastic modulus that behaves similarly to soft tissue, which has been characterized as a nonlinear elastic material. The material must also have the ability to be manufactured into specifically designed architectures. Poly(glycerol sebacate) (PGS) is a thermoset elastomer that meets these criteria. We hypothesize that the mechanical properties of PGS can be modulated through curing condition and architecture to produce materials with a range of stiffnesses. To evaluate this hypothesis, we manufactured PGS constructs cured under various conditions and having one of two architectures (solid or porous). Specimens were then tensile tested according to ASTM standards and the data were modeled using a nonlinear elastic Neo-Hookean model. Architecture and testing conditions, including elongation rate and wet versus dry conditions, affected the mechanical properties. Increasing curing time and temperature led to increased tangent modulus and decreased maximum strain for solid constructs. Porous constructs had lower nonlinear elastic properties, as did constructs of both architectures tested under simulated physiological conditions (wetted at 37 °C). Both solid and porous PGS specimens could be modeled well with the Neo-Hookean model. Future studies include comparing PGS properties to other biological tissue types and designing and characterizing PGS scaffolds for regenerating these tissues. Copyright © 2012 Elsevier Ltd. All rights reserved.

Variational linear algebraic equations method

International Nuclear Information System (INIS)

Moiseiwitsch, B.L.

1982-01-01

A modification of the linear algebraic equations method is described which ensures a variational bound on the phaseshifts for potentials having a definite sign at all points. The method is illustrated by the elastic scattering of s-wave electrons by the static field of atomic hydrogen. (author)

Cut-off frequencies of circumferential horizontal shear waves in various functionally graded cylinder shells.

Science.gov (United States)

Shen, Xiaoqin; Ren, Dawei; Cao, Xiaoshan; Wang, Ji

2018-03-01

In this study, cut-off frequencies of the circumferential SH waves in functionally graded piezoelectric-piezomagnetic material (FGPPM) cylinder shells with traction free, electrical and magnetic open boundary conditions are investigated analytically. The Wentzel-Kramers-Brillouin (WKB) method is employed for solving differential equations with variable coefficients for general cases. For comparison, Bessel functions and Kummer functions are used for solving cut-off frequency problems in homogenous and ideal FGPPM cylinder shells. It is shown that the WKB solution for the cut-off frequencies has good precise. The set of cut-off frequencies is a series of approximate arithmetic progressions, for which the difference is a function of the density and the effective elastic parameter. The relationship between the difference and the gradient coefficient is described. These results provide theoretical guidance for the non-destructive evaluation of curved shells based on the cut-off frequencies. Copyright © 2017 Elsevier B.V. All rights reserved.

Passive and active ventricular elastances of the left ventricle

Directory of Open Access Journals (Sweden)

Ng Eddie YK

2005-02-01

Full Text Available Abstract Background Description of the heart as a pump has been dominated by models based on elastance and compliance. Here, we are presenting a somewhat new concept of time-varying passive and active elastance. The mathematical basis of time-varying elastance of the ventricle is presented. We have defined elastance in terms of the relationship between ventricular pressure and volume, as: dP = EdV + VdE, where E includes passive (Ep and active (Ea elastance. By incorporating this concept in left ventricular (LV models to simulate filling and systolic phases, we have obtained the time-varying expression for Ea and the LV-volume dependent expression for Ep. Methods and Results Using the patient's catheterization-ventriculogram data, the values of passive and active elastance are computed. Ea is expressed as: ; Epis represented as: . Ea is deemed to represent a measure of LV contractility. Hence, Peak dP/dt and ejection fraction (EF are computed from the monitored data and used as the traditional measures of LV contractility. When our computed peak active elastance (Ea,max is compared against these traditional indices by linear regression, a high degree of correlation is obtained. As regards Ep, it constitutes a volume-dependent stiffness property of the LV, and is deemed to represent resistance-to-filling. Conclusions Passive and active ventricular elastance formulae can be evaluated from a single-beat P-V data by means of a simple-to-apply LV model. The active elastance (Ea can be used to characterize the ventricle's contractile state, while passive elastance (Ep can represent a measure of resistance-to-filling.

A Meta-analysis of the Price Elasticity of Gasoline Demand. A System of Equations Approach

NARCIS (Netherlands)

Brons, Martijn; Nijkamp, Peter; Pels, Eric; Rietveld, Piet

2006-01-01

Automobile gasoline demand can be expressed as a multiplicative function of fuel efficiency, mileage per car and car ownership. This implies a linear relationship between the price elasticity of total fuel demand and the price elasticities of fuel efficiency, mileage per car and car ownership. In

Material dimensionality effects on the nanoindentation behavior of Al/a-Si core-shell nanostructures

Energy Technology Data Exchange (ETDEWEB)

Fleming, Robert A. [Department of Mechanical Engineering, University of Arkansas, Fayetteville, AR 72701 (United States); Center for Advanced Surface Engineering, University of Arkansas, Fayetteville, AR 72701 (United States); Goss, Josue A. [Center for Advanced Surface Engineering, University of Arkansas, Fayetteville, AR 72701 (United States); Zou, Min, E-mail: mzou@uark.edu [Department of Mechanical Engineering, University of Arkansas, Fayetteville, AR 72701 (United States); Center for Advanced Surface Engineering, University of Arkansas, Fayetteville, AR 72701 (United States)

2017-08-01

Highlights: • Nanoindentation behavior of Al/a-Si core-shell nanostructures were studied. • 3D core confinement enables significant deformation recovery beyond elastic limit. • As the confinement is reduced, the deformation recovery is reduced or suppressed. • Atomistic simulations suggest core confinement affects dislocation dynamics. • 3D confinement has the highest percentage of dislocation removal after unloading. - Abstract: The nanoindentation behavior of hemispherical Al/a-Si core-shell nanostructures (CSNs), horizontally-aligned Al/a-Si core-shell nanorods (CSRs) with various lengths, and an Al/a-Si layered thin film has been studied to understand the effects of geometrical confinement of the Al core on the CSN deformation behavior. When loaded beyond the elastic limit, the CSNs have an unconventional load-displacement behavior with no residual displacement after unloading, resulting in no net shape change after indentation. This behavior is enabled by dislocation activities within the confined Al core, as indicated by discontinuous indentation signatures (load-drops and load-jumps) observed in the load-displacement data. When the geometrical confinement of the core is slightly reduced, as in the case of CSRs with the shortest rod length, the discontinuous indentation signatures and deformation resistance are heavily reduced. Further decreases in core confinement result in conventional nanoindentation behavior, regardless of geometry. Supporting molecular dynamics simulations show that dislocations nucleated in the core of a CSN are more effectively removed during unloading compared to CSRs, which supports the hypothesis that the unique deformation resistance of Al/a-Si CSNs are enabled by 3-dimensional confinement of the Al core.

Material dimensionality effects on the nanoindentation behavior of Al/a-Si core-shell nanostructures

International Nuclear Information System (INIS)

Fleming, Robert A.; Goss, Josue A.; Zou, Min

2017-01-01

Highlights: • Nanoindentation behavior of Al/a-Si core-shell nanostructures were studied. • 3D core confinement enables significant deformation recovery beyond elastic limit. • As the confinement is reduced, the deformation recovery is reduced or suppressed. • Atomistic simulations suggest core confinement affects dislocation dynamics. • 3D confinement has the highest percentage of dislocation removal after unloading. - Abstract: The nanoindentation behavior of hemispherical Al/a-Si core-shell nanostructures (CSNs), horizontally-aligned Al/a-Si core-shell nanorods (CSRs) with various lengths, and an Al/a-Si layered thin film has been studied to understand the effects of geometrical confinement of the Al core on the CSN deformation behavior. When loaded beyond the elastic limit, the CSNs have an unconventional load-displacement behavior with no residual displacement after unloading, resulting in no net shape change after indentation. This behavior is enabled by dislocation activities within the confined Al core, as indicated by discontinuous indentation signatures (load-drops and load-jumps) observed in the load-displacement data. When the geometrical confinement of the core is slightly reduced, as in the case of CSRs with the shortest rod length, the discontinuous indentation signatures and deformation resistance are heavily reduced. Further decreases in core confinement result in conventional nanoindentation behavior, regardless of geometry. Supporting molecular dynamics simulations show that dislocations nucleated in the core of a CSN are more effectively removed during unloading compared to CSRs, which supports the hypothesis that the unique deformation resistance of Al/a-Si CSNs are enabled by 3-dimensional confinement of the Al core.

The size-dependent vibration of embedded magneto-electro-elastic cylindrical nanoshells

International Nuclear Information System (INIS)

Ke, Liao-Liang; Wang, Yue-Sheng; Yang, Jie; Kitipornchai, Sritawat

2014-01-01

Based on the nonlocal Love’s shell theory, this paper develops an embedded magneto-electro-elastic (MEE) cylindrical nanoshell model. This model incorporates effects of the small scale parameter and thermo-electro-magnetic loadings. The surrounding elastic medium is described as the Winkler model characterized by the spring. By using this model and the Hamilton principle, the governing equations and boundary conditions are derived for free vibration of the embedded MEE cylindrical nanoshells. The Navier’s method is first utilized to obtain the analytical solution for the simply supported MEE nanoshell. Then, numerical solutions for MEE nanoshells under various boundary conditions are obtained by using the differential quadrature (DQ) method. A detailed parametric study is conducted to highlight the influences of the nonlocal parameter, temperature rise, external electric potential, external magnetic potential, spring constant, radius-to-thickness ratio and length-to-radius ratio on natural frequencies of MEE nanoshells. (paper)

Some fundamental definitions of the elastic parameters for homogeneous isotropic linear elastic materials in pavement design and analysis

CSIR Research Space (South Africa)

De Beer, Morris

2008-07-01

Full Text Available - wave and ρ the material density. The elastic moduli P-wave modulus, M, is defined so that M = K + 4µ / 3 and M can then be determined by Equation 11, with a known speed Vp P MV 2 ρ = (11) It should however also... gas (such as air within compacted road materials), the adiabatic bulk modulus KS is approximately given by pKS κ= (4) Where: κ is the adiabatic index, (sometimes calledγ ); p is the pressure. In a fluid (such as moisture...

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