Flow stress anisotropy caused by geometrically necessary boundaries

DEFF Research Database (Denmark)

Hansen, N.; Juul Jensen, D.

1992-01-01

of dislocations. A model has been proposed for this microstructural anisotropy based on the assumptions that (i) the average slip plane is at an angle of 45-degrees to the direction of the applied stress and that (ii) a strengthening parameter is the mean distance in the slip plane between the geometrically...... necessary boundaries. For different macroscopic arrangements of such boundaries, the model predictions are in good qualitative and quantitative agreement with experiments....

Sensor for Boundary Shear Stress in Fluid Flow

Science.gov (United States)

Bao, Xiaoqi; Badescu, Mircea; Sherrit, Stewart; Bar-Cohen, Yoseph; Lih, Shyh-Shiuh; Chang, Zensheu; Trease, Brian P.; Kerenyi, Kornel; Widholm, Scott E.; Ostlund, Patrick N.

2012-01-01

The formation of scour patterns at bridge piers is driven by the forces at the boundary of the water flow. In most experimental scour studies, indirect processes have been applied to estimate the shear stress using measured velocity profiles. The estimations are based on theoretical models and associated assumptions. However, the turbulence flow fields and boundary layer in the pier-scour region are very complex and lead to low-fidelity results. In addition, available turbulence models cannot account accurately for the bed roughness effect. Direct measurement of the boundary shear stress, normal stress, and their fluctuations are attractive alternatives. However, most direct-measurement shear sensors are bulky in size or not compatible to fluid flow. A sensor has been developed that consists of a floating plate with folded beam support and an optical grid on the back, combined with a high-resolution optical position probe. The folded beam support makes the floating plate more flexible in the sensing direction within a small footprint, while maintaining high stiffness in the other directions. The floating plate converts the shear force to displacement, and the optical probe detects the plate s position with nanometer resolution by sensing the pattern of the diffraction field of the grid through a glass window. This configuration makes the sensor compatible with liquid flow applications.

Grain boundary cavitation under reversed constant stress

International Nuclear Information System (INIS)

Hales, R.

1978-06-01

The growth of grain boundary cavities by diffusion processes has been examined for cyclic stresses. It is found that the time required to grow a void by a predetermined amount (tsub(t)) is always longer than the time required to shrink the same defect to its original size (tsub(c)) under reversed stress. The ratio tsub(c)/tsub(t) is a function of the magnitude of the applied stress and tensile hold time. Similar calculations have been performed for gas filled bubbles. Similar results to those for voids are found at long hold times, but a significantly different ratio of tsub(c)/tsub(t) is obtained at short times. (author)

Reynolds-Stress Budgets in an Impinging Shock Wave/Boundary-Layer Interaction

Science.gov (United States)

Vyas, Manan A.; Yoder, Dennis A.; Gaitonde, Datta V.

2018-01-01

Implicit large-eddy simulation (ILES) of a shock wave/boundary-layer interaction (SBLI) was performed. Comparisons with experimental data showed a sensitivity of the current prediction to the modeling of the sidewalls. This was found to be common among various computational studies in the literature where periodic boundary conditions were used in the spanwise direction, as was the case in the present work. Thus, although the experiment was quasi-two-dimensional, the present simulation was determined to be two-dimensional. Quantities present in the exact equation of the Reynolds-stress transport, i.e., production, molecular diffusion, turbulent transport, pressure diffusion, pressure strain, dissipation, and turbulent mass flux were calculated. Reynolds-stress budgets were compared with past large-eddy simulation and direct numerical simulation datasets in the undisturbed portion of the turbulent boundary layer to validate the current approach. The budgets in SBLI showed the growth in the production term for the primary normal stress and energy transfer mechanism was led by the pressure strain term in the secondary normal stresses. The pressure diffusion term, commonly assumed as negligible by turbulence model developers, was shown to be small but non-zero in the normal stress budgets, however it played a key role in the primary shear stress budget.

Matrix-type multiple reciprocity boundary element method for solving three-dimensional two-group neutron diffusion equations

International Nuclear Information System (INIS)

Itagaki, Masafumi; Sahashi, Naoki.

1997-01-01

The multiple reciprocity boundary element method has been applied to three-dimensional two-group neutron diffusion problems. A matrix-type boundary integral equation has been derived to solve the first and the second group neutron diffusion equations simultaneously. The matrix-type fundamental solutions used here satisfy the equation which has a point source term and is adjoint to the neutron diffusion equations. A multiple reciprocity method has been employed to transform the matrix-type domain integral related to the fission source into an equivalent boundary one. The higher order fundamental solutions required for this formulation are composed of a series of two types of analytic functions. The eigenvalue itself is also calculated using only boundary integrals. Three-dimensional test calculations indicate that the present method provides stable and accurate solutions for criticality problems. (author)

Grain boundary cavity growth under applied stress and internal pressure

International Nuclear Information System (INIS)

Mancuso, J.F.

1977-08-01

The growth of grain boundary cavities under applied stress and internal gas pressure was investigated. Methane gas filled cavities were produced by the C + 4H reversible CH4 reaction in the grain boundaries of type 270 nickel by hydrogen charging in an autoclave at 500 0 C with a hydrogen pressure of either 3.4 or 14.5 MPa. Intergranular fracture of nickel was achieved at a charging temperature of 300 0 C and 10.3 MPa hydrogen pressure. Cavities on the grain boundaries were observed in the scanning electron microscope after fracture. Photomicrographs of the cavities were produced in stereo pairs which were analyzed so as to correct for perspective distortion and also to determine the orientational dependence of cavity growth under an applied tensile stress

Modeling of grain boundary stresses in Alloy 600

Energy Technology Data Exchange (ETDEWEB)

Kozaczek, K.J. [Oak Ridge National Lab., TN (United States); Sinharoy, A.; Ruud, C.O. [Pennsylvania State Univ., University Park, PA (United States); Mcllree, A.R. [Electric Power Research Inst., Palo Alto, CA (United States)

1995-04-01

Corrosive environments combined with high stress levels and susceptible microstructures can cause intergranular stress corrosion cracking (IGSCC) of Alloy 600 components on both primary and secondary sides of pressurized water reactors. One factor affecting the IGSCC is intergranular carbide precipitation controlled by heat treatment of Alloy 600. This study is concerned with analysis of elastic stress fields in vicinity of M{sub 7}C{sub 3} and M{sub 23}C{sub 6} carbides precipitated in the matrix and at a grain boundary triple point. The local stress concentration which can lead to IGSCC initiation was studied using a two-dimensional finite element model. The intergranular precipitates are more effective stress raisers than the intragranular precipitates. The combination of the elastic property mismatch and the precipitate shape can result in a local stress field substantially different than the macroscopic stress. The maximum local stresses in the vicinity of the intergranular precipitate were almost twice as high as the applied stress.

Variational Homotopy Perturbation Method for Solving Higher Dimensional Initial Boundary Value Problems

Directory of Open Access Journals (Sweden)

Muhammad Aslam Noor

2008-01-01

Full Text Available We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method (VHPM. We use this method for solving higher dimensional initial boundary value problems with variable coefficients. The developed algorithm is quite efficient and is practically well suited for use in these problems. The proposed scheme finds the solution without any discritization, transformation, or restrictive assumptions and avoids the round-off errors. Several examples are given to check the reliability and efficiency of the proposed technique.

On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients

Science.gov (United States)

van Horssen, Wim T.; Wang, Yandong; Cao, Guohua

2018-06-01

In this paper, it is shown how characteristic coordinates, or equivalently how the well-known formula of d'Alembert, can be used to solve initial-boundary value problems for wave equations on fixed, bounded intervals involving Robin type of boundary conditions with time-dependent coefficients. A Robin boundary condition is a condition that specifies a linear combination of the dependent variable and its first order space-derivative on a boundary of the interval. Analytical methods, such as the method of separation of variables (SOV) or the Laplace transform method, are not applicable to those types of problems. The obtained analytical results by applying the proposed method, are in complete agreement with those obtained by using the numerical, finite difference method. For problems with time-independent coefficients in the Robin boundary condition(s), the results of the proposed method also completely agree with those as for instance obtained by the method of separation of variables, or by the finite difference method.

Stress engineering for the design of morphotropic phase boundary in piezoelectric material

Energy Technology Data Exchange (ETDEWEB)

Ohno, Tomoya, E-mail: ohno@mail.kitami-it.ac.jp [Department of Materials Science, Kitami Institute of Technology, 165 Kouen-cho, Kitami 090-8507 (Japan); Yanagida, Hiroshi; Maekawa, Kentaroh [Department of Materials Science, Kitami Institute of Technology, 165 Kouen-cho, Kitami 090-8507 (Japan); Arai, Takashi; Sakamoto, Naonori; Wakiya, Naoki; Suzuki, Hisao [Graduate School of Science and Technology, Shizuoka University, 3-5-1 Johoku, Hamamatsu, Shizuoka 432-8561 (Japan); Satoh, Shigeo [Graduate School of Science and Engineering, Ibaragi University, 4-12-1 Nakanarusawa-cho, Hitachi, Ibaragi 316-0033 (Japan); Matsuda, Takeshi [Department of Materials Science, Kitami Institute of Technology, 165 Kouen-cho, Kitami 090-8507 (Japan)

2015-06-30

Alkoxide-derived lead zirconate titanate thin films having Zr/Ti = 50/50 to 60/40 compositions with different residual stress conditions were deposited on a Si wafer to clarify the effects of the residual stress on the morphotropic phase boundary shift. The residual stress condition was controlled to − 0.1 to − 0.9 GPa by the design of the buffer layer structure on the Si wafer. Results show that the maximum effective piezoelectric constant d{sub 33} was obtained at 58/42 composition under − 0.9 GPa compressive residual stress condition. Moreover, the MPB composition shifted linearly to Zr-rich phase with increasing compressive residual stress. - Highlights: • The residual stress in lead zirconate titanate film on silicon was controlled. • The maximum residual stress in lead zirconate titanate film was − 0.9 GPa. • The morphotropic phase boundary shifted to zirconium rich phase by the strain.

Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity.

Science.gov (United States)

Atroshchenko, Elena; Bordas, Stéphane P A

2015-07-08

In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate the analogue of Somigliana stress identity, which can be used to obtain the stress and couple-stress fields inside the domain from the boundary values of the displacements, microrotation and stress and couple-stress tractions. Using these newly derived fundamental solutions, the boundary integral equations of both types are formulated and solved by the boundary element method. Simultaneous use of both types of equations (approach known as the dual boundary element method (BEM)) allows problems where parts of the boundary are overlapping, such as crack problems, to be treated and to do this for general geometry and loading conditions. The high accuracy of the boundary element method for both types of equations is demonstrated for a number of benchmark problems, including a Griffith crack problem and a plate with an edge crack. The detailed comparison of the BEM results and the analytical solution for a Griffith crack and an edge crack is given, particularly in terms of stress and couple-stress intensity factors, as well as the crack opening displacements and microrotations on the crack faces and the angular distributions of stresses and couple-stresses around the crack tip.

Effect of Couple Stresses on the Stress Intensity Factors for Two Parallel Cracks in an Infinite Elastic Medium under Tension

Directory of Open Access Journals (Sweden)

Shouetsu Itou

2012-01-01

Full Text Available Stresses around two parallel cracks of equal length in an infinite elastic medium are evaluated based on the linearized couple-stress theory under uniform tension normal to the cracks. Fourier transformations are used to reduce the boundary conditions with respect to the upper crack to dual integral equations. In order to solve these equations, the differences in the displacements and in the rotation at the upper crack are expanded through a series of functions that are zero valued outside the crack. The unknown coefficients in each series are solved in order to satisfy the boundary conditions inside the crack using the Schmidt method. The stresses are expressed in terms of infinite integrals, and the stress intensity factors can be determined using the characteristics of the integrands for an infinite value of the variable of integration. Numerical calculations are carried out for selected crack configurations, and the effect of the couple stresses on the stress intensity factors is revealed.

An Immersed Boundary Method for Solving the Compressible Navier-Stokes Equations with Fluid Structure Interaction

Science.gov (United States)

Brehm, Christoph; Barad, Michael F.; Kiris, Cetin C.

2016-01-01

An immersed boundary method for the compressible Navier-Stokes equation and the additional infrastructure that is needed to solve moving boundary problems and fully coupled fluid-structure interaction is described. All the methods described in this paper were implemented in NASA's LAVA solver framework. The underlying immersed boundary method is based on the locally stabilized immersed boundary method that was previously introduced by the authors. In the present paper this method is extended to account for all aspects that are involved for fluid structure interaction simulations, such as fast geometry queries and stencil computations, the treatment of freshly cleared cells, and the coupling of the computational fluid dynamics solver with a linear structural finite element method. The current approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems in 2D and 3D. As part of the validation procedure, results from the second AIAA aeroelastic prediction workshop are also presented. The current paper is regarded as a proof of concept study, while more advanced methods for fluid structure interaction are currently being investigated, such as geometric and material nonlinearities, and advanced coupling approaches.

Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography

NARCIS (Netherlands)

Christensen, M.H.; Hartong, J.; Obers, N.A.; Rollier, B.

2014-01-01

For a specific action supporting z = 2 Lifshitz geometries we identify the Lifshitz UV completion by solving for the most general solution near the Lifshitz boundary. We identify all the sources as leading components of bulk fields which requires a vielbein formalism. This includes two linear

Stress-assisted grain growth in nanocrystalline metals: Grain boundary mediated mechanisms and stabilization through alloying

International Nuclear Information System (INIS)

Zhang, Yang; Tucker, Garritt J.; Trelewicz, Jason R.

2017-01-01

The mechanisms of stress-assisted grain growth are explored using molecular dynamics simulations of nanoindentation in nanocrystalline Ni and Ni-1 at.% P as a function of grain size and deformation temperature. Grain coalescence is primarily confined to the high stress region beneath the simulated indentation zone in nanocrystalline Ni with a grain size of 3 nm. Grain orientation and atomic displacement vector mapping demonstrates that coalescence transpires through grain rotation and grain boundary migration, which are manifested in the grain interior and grain boundary components of the average microrotation. A doubling of the grain size to 6 nm and addition of 1 at.% P eliminates stress-assisted grain growth in Ni. In the absence of grain coalescence, deformation is accommodated by grain boundary-mediated dislocation plasticity and thermally activated in pure nanocrystalline Ni. By adding solute to the grain boundaries, the temperature-dependent deformation behavior observed in both the lattice and grain boundaries inverts, indicating that the individual processes of dislocation and grain boundary plasticity will exhibit different activity based on boundary chemistry and deformation temperature.

A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ Lie-Group Shooting Method

Directory of Open Access Journals (Sweden)

Chein-Shan Liu

2013-01-01

Full Text Available The boundary layer problem for power-law fluid can be recast to a third-order p-Laplacian boundary value problem (BVP. In this paper, we transform the third-order p-Laplacian into a new system which exhibits a Lie-symmetry SL(3,ℝ. Then, the closure property of the Lie-group is used to derive a linear transformation between the boundary values at two ends of a spatial interval. Hence, we can iteratively solve the missing left boundary conditions, which are determined by matching the right boundary conditions through a finer tuning of r∈[0,1]. The present SL(3,ℝ Lie-group shooting method is easily implemented and is efficient to tackle the multiple solutions of the third-order p-Laplacian. When the missing left boundary values can be determined accurately, we can apply the fourth-order Runge-Kutta (RK4 method to obtain a quite accurate numerical solution of the p-Laplacian.

Compressive intrinsic stress originates in the grain boundaries of dense refractory polycrystalline thin films

Energy Technology Data Exchange (ETDEWEB)

Magnfält, D., E-mail: danma@ifm.liu.se; Sarakinos, K. [Nanoscale Engineering Division, Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83 Linköping (Sweden); Fillon, A.; Abadias, G. [Institut P' , Département Physique et Mécanique des Matériaux, Université de Poitiers-CNRS-ENSMA, SP2MI, Téléport 2, Bd M. et P. Curie, F-86962 Chasseneuil-Futuroscope (France); Boyd, R. D.; Helmersson, U. [Plasma and Coatings Physics Division, Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83 Linköping (Sweden)

2016-02-07

Intrinsic stresses in vapor deposited thin films have been a topic of considerable scientific and technological interest owing to their importance for functionality and performance of thin film devices. The origin of compressive stresses typically observed during deposition of polycrystalline metal films at conditions that result in high atomic mobility has been under debate in the literature in the course of the past decades. In this study, we contribute towards resolving this debate by investigating the grain size dependence of compressive stress magnitude in dense polycrystalline Mo films grown by magnetron sputtering. Although Mo is a refractory metal and hence exhibits an intrinsically low mobility, low energy ion bombardment is used during growth to enhance atomic mobility and densify the grain boundaries. Concurrently, the lateral grain size is controlled by using appropriate seed layers on which Mo films are grown epitaxially. The combination of in situ stress monitoring with ex situ microstructural characterization reveals a strong, seemingly linear, increase of the compressive stress magnitude on the inverse grain size and thus provides evidence that compressive stress is generated in the grain boundaries of the film. These results are consistent with models suggesting that compressive stresses in metallic films deposited at high homologous temperatures are generated by atom incorporation into and densification of grain boundaries. However, the underlying mechanisms for grain boundary densification might be different from those in the present study where atomic mobility is intrinsically low.

Intrinsic Compressive Stress in Polycrystalline Films is Localized at Edges of the Grain Boundaries

Science.gov (United States)

Vasco, Enrique; Polop, Celia

2017-12-01

The intrinsic compression that arises in polycrystalline thin films under high atomic mobility conditions has been attributed to the insertion or trapping of adatoms inside grain boundaries. This compression is a consequence of the stress field resulting from imperfections in the solid and causes the thermomechanical fatigue that is estimated to be responsible for 90% of mechanical failures in current devices. We directly measure the local distribution of residual intrinsic stress in polycrystalline thin films on nanometer scales, using a pioneering method based on atomic force microscopy. Our results demonstrate that, at odds with expectations, compression is not generated inside grain boundaries but at the edges of gaps where the boundaries intercept the surface. We describe a model wherein this compressive stress is caused by Mullins-type surface diffusion towards the boundaries, generating a kinetic surface profile different from the mechanical equilibrium profile by the Laplace-Young equation. Where the curvatures of both profiles differ, an intrinsic stress is generated in the form of Laplace pressure. The Srolovitz-type surface diffusion that results from the stress counters the Mullins-type diffusion and stabilizes the kinetic surface profile, giving rise to a steady compression regime. The proposed mechanism of competition between surface diffusions would explain the flux and time dependency of compressive stress in polycrystalline thin films.

Evaluation of local stress and local hydrogen concentration at grain boundary using three-dimensional polycrystalline model

International Nuclear Information System (INIS)

Ebihara, Ken-ichi; Itakura, Mitsuhiro; Yamaguchi, Masatake; Kaburaki, Hideo; Suzudo, Tomoaki

2010-01-01

The decohesion model in which hydrogen segregating at grain boundaries reduces cohesive energy is considered to explain hydrogen embrittlement. Although there are several experimental and theoretical supports of this model, its total process is still unclear. In order to understand hydrogen embrittlement in terms of the decohesion model, therefore, it is necessary to evaluate stress and hydrogen concentration at grain boundaries under experimental conditions and to verify the grain boundary decohesion process. Under this consideration, we evaluated the stress and the hydrogen concentration at grain boundaries in the three-dimensional polycrystalline model which was generated by the random Voronoi tessellation. The crystallographic anisotropy was given to each grain. As the boundary conditions of the calculations, data extracted from the results calculated in the notched round-bar specimen model under the tensile test condition in which fracture of the steel specimen is observed was given to the polycrystalline model. As a result, it was found that the evaluated stress does not reach the fracture stress which was estimated under the condition of the evaluated hydrogen concentration by first principles calculations. Therefore, it was considered that the initiation of grain boundary fracture needs other factors except the stress concentration due to the crystallographic anisotropy. (author)

An efficient computer based wavelets approximation method to solve Fuzzy boundary value differential equations

Science.gov (United States)

Alam Khan, Najeeb; Razzaq, Oyoon Abdul

2016-03-01

In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.

[Effects on Stress, Problem Solving Ability and Quality of Life of as a Stress Management Program for Hospitalized Schizophrenic Patients: Based on the Stress, Appraisal-Coping Model of Lazarus & Folkman].

Science.gov (United States)

Park, Sun Ah; Sung, Kyung Mi

2016-08-01

The study was done to evaluate the effects a Stress Management Program (SMP) on stress, problem solving skills, and quality of life for hospitalized patients with Schizophrenia. A mixed method design was used: a combination of a repeated-measure design with a non-equivalent control group and qualitative data collection. The participants were 40 patients with schizophrenia admitted in three psychiatric hospitals. The experimental group (n=20) received the SMP twice a week for a total of 8 weeks. Study results revealed that the SMP was effective for stress (F=321.02, pproblem solving ability (F=246.28, peffective strategy to reduce patients' hospitalization stress, and improve problem solving skills and quality of life. Therefore, it is recommended that mental health nurses use this stress management program in clinical practice to assist adaptation to hospitalization for persons with schizophrenia.

Sensor for direct measurement of the boundary shear stress in fluid flow

Science.gov (United States)

Bao, Xiaoqi; Badescu, Mircea; Bar-Cohen, Yoseph; Lih, Shyh-Shiuh; Sherrit, Stewart; Chang, Zensheu; Chen, Beck; Widholm, Scott; Ostlund, Patrick

2011-04-01

The formation of scour patterns at bridge piers is driven by the forces at the boundary of the water flow. In most experimental scour studies, indirect processes have been applied to estimate the shear and normal stress using measured velocity profiles. The estimations are based on theoretical models and associated assumptions. However, the turbulence flow fields and boundary layer in the pier-scour region are very complex. In addition, available turbulence models cannot account accurately for the bed roughness effect. Direct measurement of the boundary shear and normal stress and their fluctuations are attractive alternatives. However, this approach is a challenging one especially for high spatial resolution and high fidelity measurements. The authors designed and fabricated a prototype miniature shear stress sensor including an EDM machined floating plate and a high-resolution optical encoder. Tests were performed both in air as well as operation in water with controlled flow. The sensor sensitivity, stability and signal-to-noise level were measured and evaluated. The detailed test results and a discussion of future work will be presented in this paper.

Problem of the Moving Boundary in Continuous Casting Solved by The Analytic-Numerical Method

Directory of Open Access Journals (Sweden)

Grzymkowski R.

2013-03-01

Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase - liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.

Problem of the Moving Boundary in Continuous Casting Solved by the Analytic-Numerical Method

Directory of Open Access Journals (Sweden)

R. Grzymkowski

2013-01-01

Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.

Structure of high and low shear-stress events in a turbulent boundary layer

Science.gov (United States)

Gomit, G.; de Kat, R.; Ganapathisubramani, B.

2018-01-01

Simultaneous particle image velocimetry (PIV) and wall-shear-stress sensor measurements were performed to study structures associated with shear-stress events in a flat plate turbulent boundary layer at a Reynolds number Reτ≈4000 . The PIV field of view covers 8 δ (where δ is the boundary layer thickness) along the streamwise direction and captures the entire boundary layer in the wall-normal direction. Simultaneously, wall-shear-stress measurements that capture the large-scale fluctuations were taken using a spanwise array of hot-film skin-friction sensors (spanning 2 δ ). Based on this combination of measurements, the organization of the conditional wall-normal and streamwise velocity fluctuations (u and v ) and of the Reynolds shear stress (-u v ) can be extracted. Conditional averages of the velocity field are computed by dividing the histogram of the large-scale wall-shear-stress fluctuations into four quartiles, each containing 25% of the occurrences. The conditional events corresponding to the extreme quartiles of the histogram (positive and negative) predominantly contribute to a change of velocity profile associated with the large structures and in the modulation of the small scales. A detailed examination of the Reynolds shear-stress contribution related to each of the four quartiles shows that the flow above a low wall-shear-stress event carries a larger amount of Reynolds shear stress than the other quartiles. The contribution of the small and large scales to this observation is discussed based on a scale decomposition of the velocity field.

A high-order boundary integral method for surface diffusions on elastically stressed axisymmetric rods

OpenAIRE

Li, Xiaofan; Nie, Qing

2009-01-01

Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratu...

Analysis of stress fields and elastic energies in the vicinity of nanograin boundaries using the disclination approach

Science.gov (United States)

Sukhanov, Ivan I.; Ditenberg, Ivan A.

2017-12-01

The paper provides a theoretical analysis of elastic stresses and elastic energy distribution in nanostructured metal materials in the vicinity of nanograin boundaries with a high partial disclination density. The analysis demonstrates the stress field distribution in disclination grain boundary configurations as a function of nanograin size, taking into account the superposition of these stresses in screening the disclination pile-ups. It is found that the principal stress tensor components reach maximum values only in disclination planes P ≈ E/25 and that the stress gradients peak at nodal points ∂P/∂x ≈ 0.08E nm-1. The shear stress components are localized within the physical grain size, and the specific elastic energy distribution for such configurations reveals characteristic local maxima which can be the cause for physical broadening of nanograin boundaries.

Simultaneous wall-shear-stress and wide-field PIV measurements in a turbulent boundary layer

Science.gov (United States)

Gomit, Guillaume; Fourrie, Gregoire; de Kat, Roeland; Ganapathisubramani, Bharathram

2015-11-01

Simultaneous particle image velocimetry (PIV) and hot-film shear stress sensor measurements were performed to study the large-scale structures associated with shear stress events in a flat plate turbulent boundary layer at a high Reynolds number (Reτ ~ 4000). The PIV measurement was performed in a streamwise-wall normal plane using an array of six high resolution cameras (4 ×16MP and 2 ×29MP). The resulting field of view covers 8 δ (where δ is the boundary layer thickness) in the streamwise direction and captures the entire boundary layer in the wall-normal direction. The spatial resolution of the measurement is approximately is approximately 70 wall units (1.8 mm) and sampled each 35 wall units (0.9 mm). In association with the PIV setup, a spanwise array of 10 skin-friction sensors (spanning one δ) was used to capture the footprint of the large-scale structures. This combination of measurements allowed the analysis of the three-dimensional conditional structures in the boundary layer. Particularly, from conditional averages, the 3D organisation of the wall normal and streamwise velocity components (u and v) and the Reynolds shear stress (-u'v') related to a low and high shear stress events can be extracted. European Research Council Grant No-277472-WBT.

Influence of yield stress on free convective boundary-layer flow of a non-Newtonian nanofluid past a vertical plate in a porous medium

International Nuclear Information System (INIS)

Hady, F. M.; Ibrahim, F. S.; Abdel-Gaied, S. M.; Eid, M. R.

2011-01-01

The effect of yield stress on the free convective heat transfer of dilute liquid suspensions of nanofluids flowing on a vertical plate saturated in porous medium under laminar conditions is investigated considering the nanofluid obeys the mathematical model of power-law. The model used for non-Newtonian nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing boundary- layer equations are cast into dimensionless system which is solved numerically using a deferred correction technique and Newton iteration. This solution depends on yield stress parameter Ω, a power-law index n, Lewis number Le, a buoyancy-ratio number Nr, a Brownian motion number Nb, and a thermophoresis number Nt. Analyses of the results found that the reduced Nusselt and Sherwood numbers are decreasing functions of the higher yield stress parameter for each dimensionless numbers, n and Le, except the reduced Sherwood number is an increasing function of higher Nb for different values of yield stress parameter

Thermoplasticity of coupled bodies in the case of stress-dependent heat transfer

Science.gov (United States)

Kilikovskaya, O. A.

1987-01-01

The problem of the thermal stresses in coupled deformable bodies is formulated for the case where the heat-transfer coefficient at the common boundary depends on the stress-strain state of the bodies (e.g., is a function of the normal pressure at the common boundary). Several one-dimensional problems are solved in this formulation. Among these problems is the determination of the thermal stresses in an n-layer plate and in a two-layer cylinder.

The Bree problem with different yield stresses on-load and off-load and application to creep ratcheting

International Nuclear Information System (INIS)

Bradford, R.A.W.; Ure, J.; Chen, H.F.

2014-01-01

The ratchet boundaries and ratchet strains are derived for the Bree problem and an elastic-perfectly plastic material with different yield stresses on-load and off-load. The Bree problem consists of a constant uniaxial primary membrane stress and a cycling thermal bending stress. The ratchet problem with differing yield stresses is also solved for a modified loading in which both the primary membrane and thermal bending stresses cycle in-phase. The analytic solutions for the ratchet boundaries are compared with the results of deploying the linear matching method (LMM) and excellent agreement is found. Whilst these results are of potential utility for purely elastic–plastic behaviour, since yield stresses will often differ at the two ends of the cycle, the solution is also proposed as a means of assessing creep ratcheting via a creep ductility exhaustion approach. -- Highlights: • The Bree problem is solved for differing yield stresses on and off load. • The modified Bree problem with cycling primary load is also solved. • These solutions can be applied to creep ratcheting using a pseudo-yield stress

On the stress investigation at the edges of the fixed elastic semi-strip

Directory of Open Access Journals (Sweden)

N. Vaysfeld

2016-10-01

Full Text Available The stress state of the elastic fixed semi-strip with the regarding of the singularities at its edge is investigated in the article. The initial boundary problem is reduced to a vector boundary problem in the transformation’s domain by the use of integral Fourier transformation. The one-dimensional vector boundary problem is solved exactly with the help of matrix differential calculations and Green’s matrix apparatus. The problem’s solving was focused at the solving of the singular integral equation (SIE with the two fixed singularities at the ends of the integration’s interval. The symbol of SIE was constructed and the generalized method of the SIE solving was applied. The stress’ distributions of the semi-strip are investigated

Influences of triple junctions on stress-assisted grain boundary motion in nanocrystalline materials

International Nuclear Information System (INIS)

Aramfard, Mohammad; Deng, Chuang

2014-01-01

Stress-assisted grain boundary motion is among the most studied modes of microstructural evolution in crystalline materials. In this study, molecular dynamics simulations were used to systematically investigate the influences of triple junctions on the stress-assisted motion of symmetric tilt grain boundaries in Cu by considering a honeycomb nanocrystalline model. It was found that the grain boundary motion in nanocrystalline models was highly sensitive to the loading mode, and a strong coupling effect which was prevalent in bicrystal models was only observed when simple shear was applied. In addition, the coupling factor extracted from the honeycomb model was found to be larger and more sensitive to temperature change than that from bicrystal models for the same type of grain boundary under the same loading conditions. Furthermore, the triple junctions seemed to exhibit unusual asymmetric pinning effects to the migrating grain boundary and the constraints by the triple junctions and neighboring grains led to remarkable non-linear grain boundary motion in directions both parallel and normal to the applied shear, which was in stark contrast to that observed in bicrystal models. In addition, dislocation nucleation and propagation, which were absent in the bicrystal model, were found to play an important role on shear-induced grain boundary motion when triple junctions were present. In the end, a generalized model for shear-assisted grain boundary motion was proposed based on the findings from this research. (paper)

Temperature and stress distribution in pressure vessel by the boundary element method

International Nuclear Information System (INIS)

Alujevic, A.; Apostolovic, D.

1990-01-01

The aim of this paper is to demonstrate the applicability of boundary element method for the solution of temperatures and thermal stresses in the body of reactor pressure vessel of the NPP Krsko . In addition to the theory of boundary elements for thermo-elastic continua (2D, 3D) results are given of a numerically evaluated meridional cross-section. (author)

Generalised functions method in the boundary value problems of elastodynamics by stationary running loads

International Nuclear Information System (INIS)

Alexeyeva, L.A.

2001-01-01

Investigation of diffraction processes of seismic waves on underground tunnels and pipelines with use of mathematical methods is related to solving boundary value problems (BVP) for hyperbolic system of differential equations in domains with cylindrical cavities when seismic disturbances propagate along boundaries with subsonic or transonic speeds. Also such classes of problems appear when it's necessary to study the behavior of underground constructions and Stress-strain State of environment. But in this case the velocities of running loads are less than velocities of wave propagation in surrounding medium. At present similar problems were solved only for constructions of circular cylindrical form with use of methods of full and not full dividing of variables. For cylindrical constructions of complex cross section strong mathematical theories for solving these problems were absent.(author)

Effect of residual stress and hardening on grain boundary sliding in welds of low-carbon stainless steels with surface machining

International Nuclear Information System (INIS)

Mori, Hiroaki; Mochizuki, Masahito; Nishimoto, Kazutoshi; Katsuyama, Jinya

2007-01-01

To clarify the effects of residual stress and hardening on intergranular stress corrosion cracking (IGSCC) behavior in welds of low-carbon austenitic stainless steels with surface machining, residual stress and hardness were evaluated by 3-dimentional thermo elastic-plastic analysis and grain boundary sliding behavior was examined using a constant strain rate tensile test. It was revealed that grain boundary sliding occurred in the material at 561K by the tensile test with the numerically simulated tensile residual stress due to welding and surface machining. In addition, it was clarified that the grain boundary energy is raised by the grain boundary sliding. On the basis of these results, it was concluded that the cause of IGSCC in the welds of low-carbon austenitic stainless steel with surface hardening is the increase in grain boundary energy due to grain boundary sliding accelerated by residual stress of multi pass welding and surface hardening. (author)

Effect of residual stress and hardening on grain boundary sliding in welds of low-carbon stainless steels with surface machining

International Nuclear Information System (INIS)

Mori, Hiroaki; Mochizuki, Masahito; Nishimoto, Kazutoshi; Katsuyama, Jinya

2008-01-01

To clarify the effects of residual stress and hardening on intergranular stress corrosion cracking (IGSCC) behavior in welds of low-carbon austenitic stainless steels with surface machining, residual stress and hardness were evaluated by 3-dimentional thermo elastic-plastic analysis and grain boundary sliding behavior was examined using a constant strain rate tensile test. It was revealed that grain boundary sliding occurred in the material at 561K by the tensile test with the numerically simulated tensile residual stress due to multi-pass welding and surface machining. In addition, it was clarified that the grain boundary energy is raised by the grain boundary sliding. On the basis of these results, it was concluded that the cause of IGSCC in the welds of low-carbon austenitic stainless steel with surface hardening is the increase in grain boundary energy due to grain boundary sliding induced by residual stress of multi pass welding and surface hardening. (author)

Reflection and transmission of seismic waves under initial stress at the earth's core-mantle boundary

Directory of Open Access Journals (Sweden)

Sukhendu Dey

1980-01-01

Full Text Available In the present paper the influence of the initial stress is shown on the reflection and transmission of P waves at the core-mantle boundary. Taking a particular value of the inherent initial stress, the variations of reflection and transmission coefficients with respect to the angle of emergence are represented by graphs. These graphs when compared with those having no initial stress show that the effect of the initial stress is to produce a reflected P and S waves with numerically higher amplitudes but a transmitted P wave with smaller amplitude. A method is also indicated in this paper to calculate the actual value of the initial stress near the core-mantle boundary by measuring the amplitudes of incident and reflected P waves.

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

Science.gov (United States)

Biala, T A; Jator, S N

2015-01-01

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

Analytical solutions of couple stress fluid flows with slip boundary conditions

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Devakar M.

2014-09-01

Full Text Available In the present article, the exact solutions for fundamental flows namely Couette, Poiseuille and generalized Couette flows of an incompressible couple stress fluid between parallel plates are obtained using slip boundary conditions. The effect of various parameters on velocity for each problem is discussed. It is found that, for each of the problems, the solution in the limiting case as couple stresses approaches to zero is similar to that of classical viscous Newtonian fluid. The results indicate that, the presence of couple stresses decreases the velocity of the fluid.

Reducing Teacher Stress by Implementing Collaborative Problem Solving in a School Setting

Science.gov (United States)

Schaubman, Averi; Stetson, Erica; Plog, Amy

2011-01-01

Student behavior affects teacher stress levels and the student-teacher relationship. In this pilot study, teachers were trained in Collaborative Problem Solving (CPS), a cognitive-behavioral model that explains challenging behavior as the result of underlying deficits in the areas of flexibility/adaptability, frustration tolerance, and problem…

Shear-coupled grain-boundary migration dependence on normal strain/stress

Science.gov (United States)

Combe, N.; Mompiou, F.; Legros, M.

2017-08-01

In specific conditions, grain-boundary (GB) migration occurs in polycrystalline materials as an alternative vector of plasticity compared to the usual dislocation activity. The shear-coupled GB migration, the expected most efficient GB based mechanism, couples the GB motion to an applied shear stress. Stresses on GB in polycrystalline materials seldom have, however, a unique pure shear component. This work investigates the influence of a normal strain on the shear coupled migration of a Σ 13 (320 )[001 ] GB in a copper bicrystal using atomistic simulations. We show that the yield shear stress inducing the GB migration strongly depends on the applied normal stress. Beyond, the application of a normal stress on this GB qualitatively modifies the GB migration: while the Σ 13 (320 )[001 ] GB shear couples following the 〈110 〉 migration mode without normal stress, we report the observation of the 〈010 〉 mode under a sufficiently high tensile normal stress. Using the nudge elastic band method, we uncover the atomistic mechanism of this 〈010 〉 migration mode and energetically characterize it.

Numerical evaluation of state boundary surface through rotation of principal stress axes in sand

International Nuclear Information System (INIS)

Sadrnejad, S. A.

2001-01-01

In applying shear stress to saturated soil with arbitrary stress paths, the prediction of the exact value of strains is difficult because of mainly its stress path dependent nature. Rotation of the principal stress axes during shearing of the soil is a feature of stress paths associated with many field loading situations. A proper understanding of the effects of principal stress rotation on soil behavior can be provided if the anisotropy existing prior to stress rotation and induced anisotropy due to plastic flow in soil are clearly understood and modeled. A multi laminate based model for soil is developed and used to compute and present the influence of rotation of principal stress axes on the plastic behavior of soil. This is fulfilled by distributing the effects of boundary condition changes into several predefined sampling orientations at one point and summing the micro-results up as the macro-result. The validity of the presented model examined by comparing numerical and test results showing the mentioned aspect. In this paper, the state boundary surface is numerically obtained by a multi laminate based model capable of predicting the behavior of sand under the influences of rotation of the direction of principal stress axes and induced anisotropy. the predicted numerical results are tally in agreement with experiments

Large scale structures in a turbulent boundary layer and their imprint on wall shear stress

Science.gov (United States)

Pabon, Rommel; Barnard, Casey; Ukeiley, Lawrence; Sheplak, Mark

2015-11-01

Experiments were performed on a turbulent boundary layer developing on a flat plate model under zero pressure gradient flow. A MEMS differential capacitive shear stress sensor with a 1 mm × 1 mm floating element was used to capture the fluctuating wall shear stress simultaneously with streamwise velocity measurements from a hot-wire anemometer traversed in the wall normal direction. Near the wall, the peak in the cross correlation corresponds to an organized motion inclined 45° from the wall. In the outer region, the peak diminishes in value, but is still significant at a distance greater than half the boundary layer thickness, and corresponds to a structure inclined 14° from the wall. High coherence between the two signals was found for the low-frequency content, reinforcing the belief that large scale structures have a vital impact on wall shear stress. Thus, estimation of the wall shear stress from the low-frequency velocity signal will be performed, and is expected to be statistically significant in the outer boundary layer. Additionally, conditionally averaged mean velocity profiles will be presented to assess the effects of high and low shear stress. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1315138.

Stress Wave Propagation in Soils Modelled by the Boundary Element Method

DEFF Research Database (Denmark)

Rasmussen, K. M.

This thesis deals with different aspects of the boundary element method (BEM) applied to stress wave propagation problems in soils. Among other things BEM formulations for coupled FEM and BEM, moving loads, direct BEM and indirect BEM are presented. For all the formulations both analytical...

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

Science.gov (United States)

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

2014-01-01

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

Prediction of wall shear stresses in transitional boundary layers using near-wall mean velocity profiles

International Nuclear Information System (INIS)

Jeon, Woo Pyung; Shin, Sung Ho; Kang, Shin Hyoung

2000-01-01

The local wall shear stress in transitional boundary layer was estimated from the near-wall mean velocity data using the principle of Computational Preston tube Method(CPM). The previous DNS and experimental databases of transitional boundary layers were used to demonstrate the accuracy of the method and to provide the applicable range of wall unit y + . The skin friction coefficients predicted by the CPM agreed well with those from previous studies. To reexamine the applicability of the CPM, near-wall hot-wire measurements were conducted in developing transitional boundary layers on a flat plate with different freestream turbulence intensities. The intermittency profiles across the transitional boundary layers were reasonably obtained from the conditional sampling technique. An empirical correlation between the representative intermittency near the wall and the free parameter K 1 of the extended wall function of CPM has been newly proposed using the present and other experimental data. The CPM has been verified as a useful tool to measure the wall shear stress in transitional boundary layer with reasonable accuracy

Boundary integral equation methods in eigenvalue problems of elastodynamics and thin plates

CERN Document Server

Kitahara, M

1985-01-01

The boundary integral equation (BIE) method has been used more and more in the last 20 years for solving various engineering problems. It has important advantages over other techniques for numerical treatment of a wide class of boundary value problems and is now regarded as an indispensable tool for potential problems, electromagnetism problems, heat transfer, fluid flow, elastostatics, stress concentration and fracture problems, geomechanical problems, and steady-state and transient electrodynamics.In this book, the author gives a complete, thorough and detailed survey of the method. It pro

On a class of problems on interaction of stress concentrators of different types with an elastic semi-infinite plate

Science.gov (United States)

Mkhitaryan, S. M.

2018-04-01

A class of mixed boundary-value problems of mathematical theory of elasticity dealing with interaction between stress concentrators of different types (such as cracks, absolutely rigid thin inclusions, punches, and stringers) and an elastic semi-infinite plate is considered. The method of Mellin integral transformation is used to reduce solving these problems to solving singular integral equations (SIE). After the governing SIE are solved, the following characteristics of the problem are determined: tangential contact stresses under stringers, dislocation density on the crack edges, breaking stresses outside the cracks on their line of location, the stress intensity factor (SIF), crack openings, jumps of contact stresses on the edges of inclusions.

SIMULATION OF THE stress-strain state of excavation BOUNDARIES in fractured massifs

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Nizomov Dzhahongir Nizomovich

2012-07-01

Any limiting process, namely, if or and any results are in line with the isotropic medium. The proposed algorithm and calculation pattern may be used to research the concentrated stresses alongside the boundaries of hydrotechnical engineering facilities.

Solving potential field problems in composite media with complicated geometries

International Nuclear Information System (INIS)

Yeh, H.

1977-01-01

Recently, Yeh developed a method of solving potential field problems for complicated geometries and theorems of piecewise continuous eigenfunctions which can be used to solve boundary-value problems in composite media by the separation of variables. This paper shows that by a proper arrangement of matching conditions and boundary conditions, this method and these theorems can be applied simultaneously so that the problems in composite media with complicated geometries can be solved. To illustrate this, a heat-conduction problem in a composite cylinder with an abrupt change in cross-section area is solved. Also presented in this paper are the method of handling the nonhomogeneous boundary conditions for composite media and the extension of one of the above-mentioned theorems to include imperfect contact on material boundaries

Influence of plastic slip localization on grain boundary stress fields and microcrack nucleation

International Nuclear Information System (INIS)

Sauzay, Maxime; Vor, Kokleang

2013-01-01

Slip localization is widely observed in metallic polycrystals after tensile deformation, cyclic deformation (persistent slip bands) or pre-irradiation followed by tensile deformation (channels). Such strong deformation localized in thin slip bands induces local stress concentrations in the quasi-elastic matrix around, at the intersections between slip bands and grain boundaries where microcracks are often observed. Since the work of Stroh, such stress fields have been modeled using the dislocation pile-up theory which leads to stress singularities similar to the LEFM ones. The Griffith criterion has then been widely applied, leading usually to strong underestimations of the macroscopic stress for microcrack nucleation. In fact, slip band thickness is finite: 50-1000 nm depending on material, temperature and loading conditions. Then, many slip planes are plastically activated through the thickness. Stress fields have probably been overestimated using the pile-up theory which assumes that all dislocations are located on the same atomic plane. To evaluate more realistic stress fields, crystalline finite element (FE) computations are carried out using microstructure inputs (slip band aspect ratio and spacing). Slip bands (low critical resolved shear stress) are embedded in an elastic matrix. The following results are obtained concerning grain boundary normal stress fields: - strong influence of slip band thickness close to the slip band corner, which is not accounted for by the pile-up theory. But far away, the thickness has a negligible effect and the predicted stress fields are close to the one predicted by the pile-up theory, - analytical formulae are deduced from the numerous FE computation results which allows the prediction of surface/bulk slips as well as grain boundary stress fields. Slip band plasticity parameters, slip band length and thickness, Schmid factor and remote stress are taken into account. The dependence with respect to the various parameters can

A New Displacement-based Approach to Calculate Stress Intensity Factors With the Boundary Element Method

Directory of Open Access Journals (Sweden)

Marco Gonzalez

Full Text Available Abstract The analysis of cracked brittle mechanical components considering linear elastic fracture mechanics is usually reduced to the evaluation of stress intensity factors (SIFs. The SIF calculation can be carried out experimentally, theoretically or numerically. Each methodology has its own advantages but the use of numerical methods has become very popular. Several schemes for numerical SIF calculations have been developed, the J-integral method being one of the most widely used because of its energy-like formulation. Additionally, some variations of the J-integral method, such as displacement-based methods, are also becoming popular due to their simplicity. In this work, a simple displacement-based scheme is proposed to calculate SIFs, and its performance is compared with contour integrals. These schemes are all implemented with the Boundary Element Method (BEM in order to exploit its advantages in crack growth modelling. Some simple examples are solved with the BEM and the calculated SIF values are compared against available solutions, showing good agreement between the different schemes.

A comparative study on stress and compliance based structural topology optimization

Science.gov (United States)

Hailu Shimels, G.; Dereje Engida, W.; Fakhruldin Mohd, H.

2017-10-01

Most of structural topology optimization problems have been formulated and solved to either minimize compliance or weight of a structure under volume or stress constraints, respectively. Even if, a lot of researches are conducted on these two formulation techniques separately, there is no clear comparative study between the two approaches. This paper intends to compare these formulation techniques, so that an end user or designer can choose the best one based on the problems they have. Benchmark problems under the same boundary and loading conditions are defined, solved and results are compared based on these formulations. Simulation results shows that the two formulation techniques are dependent on the type of loading and boundary conditions defined. Maximum stress induced in the design domain is higher when the design domains are formulated using compliance based formulations. Optimal layouts from compliance minimization formulation has complex layout than stress based ones which may lead the manufacturing of the optimal layouts to be challenging. Optimal layouts from compliance based formulations are dependent on the material to be distributed. On the other hand, optimal layouts from stress based formulation are dependent on the type of material used to define the design domain. High computational time for stress based topology optimization is still a challenge because of the definition of stress constraints at element level. Results also shows that adjustment of convergence criterions can be an alternative solution to minimize the maximum stress developed in optimal layouts. Therefore, a designer or end user should choose a method of formulation based on the design domain defined and boundary conditions considered.

A high-order boundary integral method for surface diffusions on elastically stressed axisymmetric rods.

Science.gov (United States)

Li, Xiaofan; Nie, Qing

2009-07-01

Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratures along with an extrapolation technique, leading to an arbitrarily high-order quadrature; in addition, a high-order (temporal) integration factor method, based on explicit representation of the mean curvature, is used to reduce the stability constraint on time-step. To apply this method to a periodic (in axial direction) and axi-symmetric elastically stressed cylinder, we also present a fast and accurate summation method for the periodic Green's functions of isotropic elasticity. Using the high-order boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a self-similar assumption. In the presence of elastic stress, we show that a finite time, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated.

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

Structure and properties of fluid-filled grain boundaries under stress in geological materials. Geologica Ultraiectina (290)

NARCIS (Netherlands)

van Noort, R.

2008-01-01

Two of the three processes making up the deformation mechanism of intergranular pressure solution, being dissolution and diffusion, take place in the grain boundary fluid phase. Hence, the structure and physical properties of wet grain boundaries under stress can be expected to influence the

General stability of composite panels reinforced with flexible rods taking account of the side boundary conditions

Science.gov (United States)

Dudchenko, A. A.; Elpat'evskii, A. N.

1995-07-01

Reinforced panels are the basic load-bearing elements of various structures. Optimization of massive structures requires consideration of deformation of the panel cross-sections. This is particularly important in determining the bearing strength at buckling. The load scheme, conditions for fixation of the panel cross-section, and bend-torsional stiffness taking account of the deformation of the rod cross-section affect the buckling load in real structures. The stress distribution prior to buckling must be known to solve the buckling problem properly. The stress in the panel is proportional to the active load. The stress distribution is assumed to be known according to our previous method [1]. The load scheme and panel dimensions are shown in Fig. 1. The stress distribution in the panel prior to buckling can be found using Eqs. (1)-(3). A view of the cross-section is given in Fig. 1. The displacements in the panel at buckling for the boundary area are found using Eqs. (4)-(6), while the stresses in the skin and stiffness are found using Eq. (7). Roots k1 and k2 are those of the characteristic equation and β is a dimensionless coordinate. The problem was solved using variational theory. The potential energy is given by Eqs. (8) and (9) by orihogonalization of Eqs. (5). The basic equations are converted to Eqs. (10) by evaluation of the components in Eqs. (8) and (9). Its calculation (11) gives the compression load. Optimization of parameter α gives the critical strength P1 = 6.93 kN (without taking account of the boundary area) and P2 = 5.31 kN (taking account of the boundary area).

Social problem solving strategies and posttraumatic stress disorder in the aftermath of intimate partner violence.

Science.gov (United States)

Reich, Catherine M; Blackwell, Náthali; Simmons, Catherine A; Beck, J Gayle

2015-05-01

Social factors are often associated with the development or maintenance of posttraumatic stress disorder (PTSD) in the aftermath of interpersonal traumas. However, social problem solving strategies have received little attention. The current study explored the role of social problem solving styles (i.e., rational approaches, impulsive/careless strategies, or avoidance strategies) as intermediary variables between abuse exposure and PTSD severity among intimate partner violence survivors. Avoidance problem solving served as an intermediating variable for the relationship between three types of abuse and PTSD severity. Rational and impulsive/careless strategies were not associated with abuse exposure. These findings extend the current understanding of social problem solving among interpersonal trauma survivors and are consistent with more general avoidance coping research. Future research might examine whether avoidance problem solving tends to evolve in the aftermath of trauma or whether it represents a longstanding risk factor for PTSD development. Published by Elsevier Ltd.

The use of MACSYMA for solving elliptic boundary value problems

Science.gov (United States)

Thejll, Peter; Gilbert, Robert P.

1990-01-01

A boundary method is presented for the solution of elliptic boundary value problems. An approach based on the use of complete systems of solutions is emphasized. The discussion is limited to the Dirichlet problem, even though the present method can possibly be adapted to treat other boundary value problems.

THE CALCULATION OF STRESS-STRAIN STATE OF THREE-LAYER BEAM TAKING INTO ACCOUNT EDGE EFFECTS

Directory of Open Access Journals (Sweden)

Kh. M. Muselemov

2015-01-01

Full Text Available The work is dedicated to the calculation of the stress-strain state (SSS of the three-layer beam (TLB subject to boundary effects.In this paper, a system of differential equations of equilibrium of the threelayer beam. To solve these equations, it is necessary to know the 12 boundary conditions, co-which depend on support conditions and loading of sandwich beams under study. This system of equations is solved by the application package of mathematical modeling "Maple 5.4." The solution of this system we obtain expressions for determining de-formations and stress all components (bearing layers and filler, a three-layer beam anywhere under specified conditions of fastening the ends of the beam and its loading. 

Stress-free states of continuum dislocation fields : Rotations, grain boundaries, and the Nye dislocation density tensor

NARCIS (Netherlands)

Limkumnerd, Surachate; Sethna, James P.

We derive general relations between grain boundaries, rotational deformations, and stress-free states for the mesoscale continuum Nye dislocation density tensor. Dislocations generally are associated with long-range stress fields. We provide the general form for dislocation density fields whose

Integral Method of Boundary Characteristics: Neumann Condition

Science.gov (United States)

Kot, V. A.

2018-05-01

A new algorithm, based on systems of identical equalities with integral and differential boundary characteristics, is proposed for solving boundary-value problems on the heat conduction in bodies canonical in shape at a Neumann boundary condition. Results of a numerical analysis of the accuracy of solving heat-conduction problems with variable boundary conditions with the use of this algorithm are presented. The solutions obtained with it can be considered as exact because their errors comprise hundredths and ten-thousandths of a persent for a wide range of change in the parameters of a problem.

Moving Griffith crack in an orthotropic strip with punches at boundary faces

Directory of Open Access Journals (Sweden)

S. Mukherjee

2005-01-01

Full Text Available Integral transform technique is employed to solve the elastodynamic problem of steady-state propagation of a Griffith crack centrally situated along the midplane of orthotropic strip of finite thickness 2h and subjected to point loading with centrally situated moving punches under constant pressure along the boundaries of the layer. The problem is reduced to the solution of a pair of simultaneous singular integral equations with Cauchy-type singularities which have finally been solved through the finite Hilbert transform technique. For large h, analytical expression for the stress intensity factor at the crack tip is obtained. Graphical plots of the numerical results are also presented.

Lidar-Observed Stress Vectors and Veer in the Atmospheric Boundary Layer

DEFF Research Database (Denmark)

Berg, Jacob; Mann, Jakob; Patton, Edward G.

2013-01-01

This study demonstrates that a pulsed wind lidar is a reliable instrument for measuring angles between horizontal vectors of significance in the atmospheric boundary layer. Three different angles are considered: the wind turning, the angle between the stress vector and the mean wind direction......, and the angle between the stress vector and the vertical gradient of the mean velocity vector. The latter is assumed to be zero by the often applied turbulent-viscosity hypothesis, so that the stress vector can be described through the vertical gradient of velocity. In the atmospheric surface layer, where...... the Coriolis force is negligible, this is supposedly a good approximation. High-resolution large-eddy simulation data show that this is indeed the case even beyond the surface layer. In contrast, through analysis of WindCube lidar measurements supported by sonic measurements, the study shows that it is only...

β-distribution for Reynolds stress and turbulent heat flux in relaxation turbulent boundary layer of compression ramp

Science.gov (United States)

Hu, YanChao; Bi, WeiTao; Li, ShiYao; She, ZhenSu

2017-12-01

A challenge in the study of turbulent boundary layers (TBLs) is to understand the non-equilibrium relaxation process after sep-aration and reattachment due to shock-wave/boundary-layer interaction. The classical boundary layer theory cannot deal with the strong adverse pressure gradient, and hence, the computational modeling of this process remains inaccurate. Here, we report the direct numerical simulation results of the relaxation TBL behind a compression ramp, which reveal the presence of intense large-scale eddies, with significantly enhanced Reynolds stress and turbulent heat flux. A crucial finding is that the wall-normal profiles of the excess Reynolds stress and turbulent heat flux obey a β-distribution, which is a product of two power laws with respect to the wall-normal distances from the wall and from the boundary layer edge. In addition, the streamwise decays of the excess Reynolds stress and turbulent heat flux also exhibit power laws with respect to the streamwise distance from the corner of the compression ramp. These results suggest that the relaxation TBL obeys the dilation symmetry, which is a specific form of self-organization in this complex non-equilibrium flow. The β-distribution yields important hints for the development of a turbulence model.

Thermodynamic effect of elastic stress on grain boundary segregation of phosphorus in a low alloy steel

International Nuclear Information System (INIS)

Zheng, Lei; Lejček, Pavel; Song, Shenhua; Schmitz, Guido; Meng, Ye

2015-01-01

Grain boundary (GB) segregation of P in 2.25Cr1Mo steel induced by elastic stress shows that the P equilibrium concentration, after reaching the non-equilibrium concentration maximum at critical time, returns to its initial thermal equilibrium level. This finding confirms the interesting phenomenon that the effect of elastic stress on GB segregation of P is significant in kinetics while slight in thermodynamics. Through extending the “pressure” in classical theory of chemical potential to the “elastic stress”, the thermodynamic effect of elastic stress on GB segregation is studied, and the relationship between elastic stress and segregation Gibbs energy is formulated. The formulas reveal that the difference in the segregation Gibbs energy between the elastically-stressed and non-stressed states depends on the excess molar volume of GB segregation and the magnitude of elastic stress. Model calculations in segregation Gibbs energy confirm that the effect of elastic stress on the thermodynamics of equilibrium GB segregation is slight, and the theoretical analyses considerably agree with the experimental results. The confirmation indicates that the nature of the thermodynamic effect is well captured. - Highlights: • GB segregation of P after stress aging returns to its initial thermal equilibrium level. • Relationship between elastic stress and segregation energy is formulated. • Thermodynamic effect relies on excess molar volume and magnitude of elastic stress. • Effect of elastic stress on Gibbs energy of GB segregation is estimated to be slight. • Complete theory of the effect of elastic stress on grain boundary segregation is setup

Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics

Directory of Open Access Journals (Sweden)

Dang Quang A

2013-02-01

Full Text Available In this paper we consider a mixed boundary value problem for biharmonic equation of the Airy stress function which models a crack problem of a solid elastic plate. An iterative method for reducing the problem to a sequence of mixed problems for Poisson equations is proposed and investigated. The convergence of the method is established theoretically and illustrated on many numerical experiments.

Performance improvement of extended boundary node method for solving elliptic boundary-value problems

International Nuclear Information System (INIS)

Saitoh, Ayumu; Kamitani, Atsushi; Takayama, Teruou; Nakamura, Hiroaki

2016-01-01

The extended boundary-node method (X-BNM) with the hierarchical-matrix (H-matrix) method has been developed and its performance has been investigated numerically. The results of computations show that the solver speed of the X-BNM with the H-matrix method is much faster than that of the standard X-BNM for the case where the number of boundary nodes exceeds a certain limit. Furthermore, the accuracy of the X-BNM with the H-matrix method is almost equal to that of the standard X-BNM. From these results, it is found that the H-matrix method is useful as the acceleration technique of the X-BNM. (author)

Magnetohydrodynamic boundary layer flow past a porous substrate with Beavers-Joseph boundary condition

International Nuclear Information System (INIS)

Jat, R.N.; Chaudhary, Santosh

2009-01-01

The flow of an electrically conducting fluid past a porous substrate attached to the flat plate with Beavers-Joseph boundary condition under the influence of a uniform transverse magnetic field has been studied. Taking suitable similar variables, the momentum equation is transformed to ordinary differential equation and solved by standard techniques. The energy equation is solved by considering two boundary layers, one in the porous substrate and the other above the porous substrate. The velocity and temperature distributions along with Nusselt number are discussed numerically and presented through graphs. (author)

Analysis of residual stresses in a long hollow cylinder

International Nuclear Information System (INIS)

Tokovyy, Yuriy V.; Ma, Chien-Ching

2011-01-01

This paper presents an analytical method for solving the axisymmetric stress problem for a long hollow cylinder subjected to locally-distributed residual (incompatible) strains. This method is based on direct integration of the equilibrium and compatibility equations, which thereby have been reduced to the set of two governing equations for two key functions with corresponding boundary and integral conditions. The governing equations were solved by making use of the Fourier integral transformation. Application of the method is illustrated with an analysis of the welding residual stresses in a butt-welded thick-walled pipe. - Highlights: → A solution to the axisymmetric stress problem for a hollow cylinder is constructed. → The cylinder is subjected to a field of locally-distributed residual strains. → The method is based on direct integration of the equilibrium equations. → An application of our solution to analysis of welding residual stresses is considered.

Practical stress evaluation method of RC slab for bending moment in consideration of additional in-plane stress caused by boundary condition

International Nuclear Information System (INIS)

Kobayashi, Toshio; Adachi, Naohito; Masuda, Kiyoshi

1998-01-01

In a design of a thick RC slab such as a basemat of a nuclear reactor building, the design method as same as for RC column is usually used. In this method, bending moment and axial force which are obtained by linear Finite Element Method (FEM) for external force are considered. But the assumption for linear FEM in which concrete participates for tensile stress is different from that for reinforcement design in which concrete does not participate for tensile stress. This difference of the assumption results that in-plane tensile strain at the center of the slab depth in the reinforcement design is larger than that in linear FEM. Some effects will appear in stress distribution if this tensile strain is constrained by boundary condition. In this paper, a practical method to evaluate the boundary constrain effects for this in-plane tensile strain is proposed and a simulation analysis of a thick reinforced concrete slab with a large opening for out-of-plane force is also reported. (author)

Boundary element analysis of stress singularity in dissimilar metals by friction welding

International Nuclear Information System (INIS)

Chung, N. Y.; Park, C. H.

2012-01-01

Friction welded dissimilar metals are widely applied in automobiles, rolling stocks, machine tools, and various engineering fields. Dissimilar metals have several advantages over homogeneous metals, including high strength, material property, fatigue endurance, impact absorption, high reliability, and vibration reduction. Due to the increased use of these metals, understanding their behavior under stress conditions is necessary, especially the analysis of stress singularity on the interface of friction-welded dissimilar metals. To establish a strength evaluation method and a fracture criterion, it is necessary to analyze stress singularity on the interface of dissimilar metals with welded flashes by friction welding under various loads and temperature conditions. In this paper, a method analyzing stress singularity for the specimens with and without flashes set in friction welded dissimilar metals is introduced using the boundary element method. The stress singularity index (λ) and the stress singularity factor (Γ) at the interface edge are computed from the stress analysis results. The shape and flash thickness, interface length, residual stress, and load are considered in the computation. Based on these results, the variations of interface length (c) and the ratio of flash thickness (t2 t1) greatly influence the stress singularity factors at the interface edge of friction welded dissimilar metals. The stress singularity factors will be a useful fracture parameter that considers stress singularity on the interface of dissimilar metals

Solving fuzzy two-point boundary value problem using fuzzy Laplace transform

OpenAIRE

Ahmad, Latif; Farooq, Muhammad; Ullah, Saif; Abdullah, Saleem

2014-01-01

A natural way to model dynamic systems under uncertainty is to use fuzzy boundary value problems (FBVPs) and related uncertain systems. In this paper we use fuzzy Laplace transform to find the solution of two-point boundary value under generalized Hukuhara differentiability. We illustrate the method for the solution of the well known two-point boundary value problem Schrodinger equation, and homogeneous boundary value problem. Consequently, we investigate the solutions of FBVPs under as a ne...

A Reynolds stress model for near-wall turbulence

Science.gov (United States)

Durbin, P. A.

1993-01-01

The paper formulates a tensorially consistent near-wall second-order closure model. Redistributive terms in the Reynolds stress equations are modeled by an elliptic relaxation equation in order to represent strongly nonhomogeneous effects produced by the presence of walls; this replaces the quasi-homogeneous algebraic models that are usually employed, and avoids the need for ad hoc damping functions. The model is solved for channel flow and boundary layers with zero and adverse pressure gradients. Good predictions of Reynolds stress components, mean flow, skin friction, and displacement thickness are obtained in various comparisons to experimental and direct numerical simulation data. The model is also applied to a boundary layer flowing along a wall with a 90-deg, constant-radius, convex bend.

Anxiety, Depression, Problem Solving and Stress Management in Patients with Ankylosing Spondylitis

Directory of Open Access Journals (Sweden)

Yasemin Özkan

2018-04-01

Full Text Available Objective: This study aims to determine anxiety, depression, self-esteem, stress management and problem solving skills in ankylosing spondylitis (AS patients compared to healthy subjects. Materials and Methods: The study involves 33 patients with AS according to the Modified New York Criteria and 31 healthy subjects as control group. A socio-demographic data form, the Hospital Anxiety and Depression Scale (HADS, the Rosenberg Self-Esteem Scale (RSES, the Problem Solving Inventory (PSI and the Coping Orientation to Problems Experienced (COPE scale were used to evaluate participants. Results: The mean ages of the patients and the control were 36.3±10.9 and 33.6±6.2 years respectively with no significant difference between the two groups (p>0.05. On the HADS scale, AS patients showed significantly higher anxiety and depression scores (p<0.05. AS patients had significantly lower self-esteem as determined by the RSES scores (p<0.05. When the study groups were compared using the PSI, a significant difference was observed only in the “approach-avoidance style” subscale. A positive correlation between Bath Ankylosing Spondylitis Disease Activity Index (BASDAI and RSES was reported and there was a very strong negative correlation between BASDAI and overall PSI scores. A negative correlation was found between humor, mental disengagement and behavioral disengagement and BASDAI scores (p<0.05. Conclusion: Being a chronic rheumatic disease, AS not only limits daily living activities due to its physical manifestations but also causes psychological problems such as depression ve anxiety. However, it does not seem to impair problem solving skills and the ability to cope with stress significantly. It might be helpful to evaluate AS patients using a holistic approach and to be aware of the factors that are associated with difficulties in their social interactions.

Solving free-plasma-boundary problems with the SIESTA MHD code

Science.gov (United States)

Sanchez, R.; Peraza-Rodriguez, H.; Reynolds-Barredo, J. M.; Tribaldos, V.; Geiger, J.; Hirshman, S. P.; Cianciosa, M.

2017-10-01

SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for 3D magnetic configurations. It is an iterative code that uses the solution obtained by the VMEC code to provide a background coordinate system and an initial guess of the solution. The final solution that SIESTA finds can exhibit magnetic islands and stochastic regions. In its original implementation, SIESTA addressed only fixed-boundary problems. This fixed boundary condition somewhat restricts its possible applications. In this contribution we describe a recent extension of SIESTA that enables it to address free-plasma-boundary situations, opening up the possibility of investigating problems with SIESTA in which the plasma boundary is perturbed either externally or internally. As an illustration, the extended version of SIESTA is applied to a configuration of the W7-X stellarator.

A numerical method for solving the 3D unsteady incompressible Navier Stokes equations in curvilinear domains with complex immersed boundaries

Science.gov (United States)

Ge, Liang; Sotiropoulos, Fotis

2007-08-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow

Investigation of the stability of blocks around underground openings by using the boundary element method

Directory of Open Access Journals (Sweden)

Murat Ünal

2002-03-01

Full Text Available In this study, a two-dimensional software was developed by using the boundary element method, in order to model and solve the rock mechanics problems encountered in surface and underground excavations. Stability of rock wedges formed at the roof of underground excavations were investigated in detail by using this software. The behaviour of the symmetric wedge on different joint stiffnesses was studied using a modified boundary element software. Then the results obtained were discussed and compared with the analytical solution, considering the surface tractions, shear stresses (developed along the discontinuity, wedge displacements and strains (along the wedge height.

Difference method for solving a nonlocal boundary value problem for a degenerating third-order pseudo-parabolic equation with variable coefficients

Science.gov (United States)

Beshtokov, M. Kh.

2016-10-01

A nonlocal boundary value problem for a degenerating third-order pseudo-parabolic equation with variable coefficients is considered. For solving this problem, a priori estimates in the differential and difference forms are obtained. The a priori estimates imply the uniqueness and stability of the solution on a layer with respect to the initial data and the right-hand side and the convergence of the solution of the difference problem to the solution of the differential problem.

Reynolds stress structures in a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation.

Science.gov (United States)

Atkinson, C.; Sekimoto, A.; Jiménez, J.; Soria, J.

2018-04-01

Mean Reynolds stress profiles and instantaneous Reynolds stress structures are investigated in a self-similar adverse pressure gradient turbulent boundary layer (APG-TBL) at the verge of separation using data from direct numerical simulations. The use of a self-similar APG-TBL provides a flow domain in which the flow gradually approaches a constant non-dimensional pressure gradient, resulting in a flow in which the relative contribution of each term in the governing equations is independent of streamwise position over a domain larger than two boundary layer thickness. This allows the flow structures to undergo a development that is less dependent on the upstream flow history when compared to more rapidly decelerated boundary layers. This APG-TBL maintains an almost constant shape factor of H = 2.3 to 2.35 over a momentum thickness based Reynolds number range of Re δ 2 = 8420 to 12400. In the APG-TBL the production of turbulent kinetic energy is still mostly due to the correlation of streamwise and wall-normal fluctuations, 〈uv〉, however the contribution form the other components of the Reynolds stress tensor are no longer negligible. Statistical properties associated with the scale and location of sweeps and ejections in this APG-TBL are compared with those of a zero pressure gradient turbulent boundary layer developing from the same inlet profile, resulting in momentum thickness based range of Re δ 2 = 3400 to 3770. In the APG-TBL the peak in both the mean Reynolds stress and the production of turbulent kinetic energy move from the near wall region out to a point consistent with the displacement thickness height. This is associated with a narrower distribution of the Reynolds stress and a 1.6 times higher relative number of wall-detached negative uv structures. These structures occupy 5 times less of the boundary layer volume and show a similar reduction in their streamwise extent with respect to the boundary layer thickness. A significantly lower percentage

A study on the bonding residual thermal stress analysis of dissimilar materials using boundary element method

International Nuclear Information System (INIS)

Yi, Won; Yu, Yeong Chul; Jeong, Eui Seob; Lee, Chang Ho

1995-01-01

It is very important to evaluate the bonding residual thermal stress in dissimilar materials such as LSI package. In this study, the bonding residual thermal stress was calculated using the boundary element method, varing with the sub-element, geometry of specimen and adhesive thickness. The present results reveal a stress singularity at the edge of the interface, therefore the bonding strength of metal/resin interface can be estimated by taking into account it.

Stress-constrained truss topology optimization problems that can be solved by linear programming

DEFF Research Database (Denmark)

Stolpe, Mathias; Svanberg, Krister

2004-01-01

We consider the problem of simultaneously selecting the material and determining the area of each bar in a truss structure in such a way that the cost of the structure is minimized subject to stress constraints under a single load condition. We show that such problems can be solved by linear...... programming to give the global optimum, and that two different materials are always sufficient in an optimal structure....

The mediating effects of self-esteem and coronary-prone behavior on problem solving and affect under low and high stress.

Science.gov (United States)

Hubbs-Tait, L; Blodgett, C J

1989-01-01

Self-esteem and coronary-prone behavior were identified as two personality constructs related to different stress responses. It was hypothesized that in the case of low self-esteem Type A subjects the conflicting stress responses would have a particularly adverse effect on problem-solving behavior, mood, and self-perception. Subjects were 32 Type A and 32 Type B males evenly divided into high and low self-esteem groups. Half of the subjects in each group solved 10 matrix problems under high stress, half under low stress. Compared with high self-esteem Type As, low self-esteem Type As under high stress became more hostile and perceived themselves as more tense and more hurried. They also tended to make more errors. Results are interpreted as implying that low and high self-esteem Type A subjects are not psychologically homogeneous. It is suggested that the two groups may differ substantially in terms of cardiovascular risk.

Bed slope effects on turbulent wave boundary layers: 2. Comparison with skewness, asymmetry, and other effects

DEFF Research Database (Denmark)

Fuhrman, David R.; Fredsøe, Jørgen; Sumer, B. Mutlu

2009-01-01

currents or undertow). The effects from each of the four components are isolated and quantified using a standard set of bed shear stress quantities, allowing their easy comparison. For conditions representing large shallow-water waves on steep slopes, the results suggest that converging-diverging effects......A numerical model solving incompressible Reynolds-averaged Navier-Stokes equations, combined with a two-equation k-omega model for turbulence closure, is used to systematically compare the relative strength of bed shear stress quantities and boundary layer streaming under wave motions from four...... from beach slope may make a significant onshore bed load contribution. Generally, however, the results suggest wave skewness (in addition to conventional steady streaming) as the most important onshore contribution outside the surf zone. Streaming induced within the wave boundary layer is also...

Boundary value problems and partial differential equations

CERN Document Server

Powers, David L

2005-01-01

Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering.* CD with animations and graphics of solutions, additional exercises and chapter review questions* Nearly 900 exercises ranging in difficulty* Many fully worked examples

Effects of stress management training and problem solving on quality of life and life expectancy among infertile women

Directory of Open Access Journals (Sweden)

Mohammad Reza Zarbakhsh Bahri

2013-08-01

Full Text Available Introduction: This study aims to evaluate the effectiveness of stress management training and problem-solving training on quality of life and life expectancy of infertile women was conducted.Material and Methods: The method of this study was experimental with pretest – posttest design with a control group. population of 400 infertile women who referred to infertility center in Rasht were randomized to 250 of them were selected and the quality of life and life expectancy of the study were the 45 members of the quality of life and life expectancy lower were more randomly in three groups of 15 people, including two experimental groups and one control group were replaced. Each experimental groups were trained for 10 sessions of 90 minutes, respectively, stress management and problem-solving. Upon completion of the training program, participants were assessed again.Results: The result of present study showed that there was a significant difference between the experimental groups and control group in the scores of quality of life and life expectancy (p0.05.Conclusion: Stress management and problem solving training were effective on life expectancy and quality of life of infertile women but there was no significant difference between the effectiveness of these two methods on life expectancy and quality of life of infertile women.

Stress tensor of a quark moving through N=4 thermal plasma

International Nuclear Information System (INIS)

Friess, Joshua J.; Gubser, Steven S.; Michalogiorgakis, Georgios; Pufu, Silviu S.

2007-01-01

We develop the linear equations that describe graviton perturbations of AdS 5 -Schwarzschild generated by a string trailing behind an external quark moving with constant velocity. Solving these equations allows us to evaluate the stress tensor in the boundary gauge theory. Components of the stress tensor exhibit directional structures in Fourier space at both large and small momenta. We comment on the possible relevance of our results to relativistic heavy-ion collisions

Grain boundary segregation and intergranular stress corrosion cracking susceptibility of austenitic stainless steels in high temperature water

International Nuclear Information System (INIS)

Shoji, T.; Yamaki, K.; Ballinger, R.G.; Hwang, I.S.

1992-01-01

The effects of grain boundary segregation on intergranular stress corrosion cracking of austenitic stainless steels in high temperature water have been examined as a function of heat treatment. The materials investigated were: (1) two commercial purity Type 304; (2) low sulfur Type 304; (3) nuclear grade Type 304; (4) ultra high purity Type 304L; and (5) Type 316L and Type 347L. Specimens were solution treated at 1050 degrees C for 0.5 hour and given a sensitization heat treatment at 650 degrees C for 50 hours. Some of the specimens were then subjected to an aging heat treatment at 850 degrees C for from one to ten hours to cause Cr recovery at the grain boundaries. The effects of heat treatments on degree of sensitization and grain boundary segregation were evaluated by Electrochemical Potentiokinetic Reactivation (EPR) and Coriou tests, respectively. The susceptibility to stress corrosion (SCC) was evaluated using slow strain rate tests technique (SSRT) in high temperature water. SSRT tests were performed in an aerated pure water (8 ppm dissolved oxygen) at 288 degrees C at a strain rate of 1.33 x 10 -6 /sec. Susceptibility to intergranular stress corrosion cracking was compared with degree of sensitization and grain boundary segregation. The results of the investigation indicate that EPR is not always an accurate indicator of SCC susceptibility. The Coriou test provides a more reliable measure of SCC susceptibility especially for 304L, 304NG, 316L, and 347L stainless steels. The results also indicate that grain boundary segregation as well as degree of sensitization must be considered in the determination of SCC susceptibility

Derivation Method for the Foundation Boundaries of Hydraulic Numerical Simulation Models Based on the Elastic Boussinesq Solution

Directory of Open Access Journals (Sweden)

Jintao Song

2015-01-01

Full Text Available The foundation boundaries of numerical simulation models of hydraulic structures dominated by a vertical load are investigated. The method used is based on the stress formula for fundamental solutions to semi-infinite space body elastic mechanics under a vertical concentrated force. The limit method is introduced into the original formula, which is then partitioned and analyzed according to the direction of the depth extension of the foundation. The point load will be changed to a linear load with a length of 2a. Inverse proportion function assumptions are proposed at parameter a and depth l of the calculation points to solve the singularity questions of elastic stress in a semi-infinite space near the ground. Compared with the original formula, changing the point load to a linear load with a length of 2a is more reasonable. Finally, the boundary depth criterion of a hydraulic numerical simulation model is derived and applied to determine the depth boundary formula for gravity dam numerical simulations.

Boundary element method for modelling creep behaviour

International Nuclear Information System (INIS)

Zarina Masood; Shah Nor Basri; Abdel Majid Hamouda; Prithvi Raj Arora

2002-01-01

A two dimensional initial strain direct boundary element method is proposed to numerically model the creep behaviour. The boundary of the body is discretized into quadratic element and the domain into quadratic quadrilaterals. The variables are also assumed to have a quadratic variation over the elements. The boundary integral equation is solved for each boundary node and assembled into a matrix. This matrix is solved by Gauss elimination with partial pivoting to obtain the variables on the boundary and in the interior. Due to the time-dependent nature of creep, the solution has to be derived over increments of time. Automatic time incrementation technique and backward Euler method for updating the variables are implemented to assure stability and accuracy of results. A flowchart of the solution strategy is also presented. (Author)

Extremely high wall-shear stress events in a turbulent boundary layer

Science.gov (United States)

Pan, Chong; Kwon, Yongseok

2018-04-01

The present work studies the fluctuating characteristics of the streamwise wall-shear stress in a DNS of a turbulent boundary layer at Re τ =1500 from a structural view. The two-dimensional field of the fluctuating friction velocity u‧ τ (x,z) is decomposed into the large- and small-scale components via a recently proposed scale separation algorithm, Quasi-bivariate Variational Mode Decomposition (QB-VMD). Both components are found to be dominated by streak-like structures, which can be regarded as the wall signature of the inner-layer streaks and the outer-layer LSMs, respectively. Extreme positive/negative wall-shear stress fluctuation events are detected in the large-scale component. The former’s occurrence frequency is nearly one order of magnitude higher than the latter; therefore, they contribute a significant portion of the long tail of the wall-shear stress distribution. Both two-point correlations and conditional averages show that these extreme positive wall-shear stress events are embedded in the large-scale positive u‧ τ streaks. They seem to be formed by near-wall ‘splatting’ process, which are related to strong finger-like sweeping (Q4) events originated from the outer-layer positive LSMs.

Solution of a Problem Linear Plane Elasticity with Mixed Boundary Conditions by the Method of Boundary Integrals

Directory of Open Access Journals (Sweden)

Nahed S. Hussein

2014-01-01

Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of …eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.

An approximate moving boundary method for American option pricing

NARCIS (Netherlands)

Chockalingam, A.; Muthuraman, K.

2015-01-01

We present a method to solve the free-boundary problem that arises in the pricing of classical American options. Such free-boundary problems arise when one attempts to solve optimal-stopping problems set in continuous time. American option pricing is one of the most popular optimal-stopping problems

Hydrodynamic structure of the boundary layers in a rotating cylindrical cavity with radial inflow

International Nuclear Information System (INIS)

Herrmann-Priesnitz, Benjamín; Torres, Diego A.; Calderón-Muñoz, Williams R.; Salas, Eduardo A.; Vargas-Uscategui, Alejandro; Duarte-Mermoud, Manuel A.

2016-01-01

A flow model is formulated to investigate the hydrodynamic structure of the boundary layers of incompressible fluid in a rotating cylindrical cavity with steady radial inflow. The model considers mass and momentum transfer coupled between boundary layers and an inviscid core region. Dimensionless equations of motion are solved using integral methods and a space-marching technique. As the fluid moves radially inward, entraining boundary layers develop which can either meet or become non-entraining. Pressure and wall shear stress distributions, as well as velocity profiles predicted by the model, are compared to numerical simulations using the software OpenFOAM. Hydrodynamic structure of the boundary layers is governed by a Reynolds number, Re, a Rossby number, Ro, and the dimensionless radial velocity component at the periphery of the cavity, U_o. Results show that boundary layers merge for Re > 0.1, and boundary layers become predominantly non-entraining for low Ro, low Re, and high U_o. Results may contribute to improve the design of technology, such as heat exchange devices, and turbomachinery.

Hydrodynamic structure of the boundary layers in a rotating cylindrical cavity with radial inflow

Energy Technology Data Exchange (ETDEWEB)

Herrmann-Priesnitz, Benjamín, E-mail: bherrman@ing.uchile.cl; Torres, Diego A. [Department of Mechanical Engineering, Universidad de Chile, Beauchef 851, Santiago (Chile); Advanced Mining Technology Center, Universidad de Chile, Av. Tupper 2007, Santiago (Chile); Calderón-Muñoz, Williams R. [Department of Mechanical Engineering, Universidad de Chile, Beauchef 851, Santiago (Chile); Energy Center, Universidad de Chile, Av. Tupper 2007, Santiago (Chile); Salas, Eduardo A. [CSIRO-Chile International Centre of Excellence, Apoquindo 2827, Floor 12, Santiago (Chile); Vargas-Uscategui, Alejandro [Department of Mechanical Engineering, Universidad de Chile, Beauchef 851, Santiago (Chile); CSIRO-Chile International Centre of Excellence, Apoquindo 2827, Floor 12, Santiago (Chile); Duarte-Mermoud, Manuel A. [Advanced Mining Technology Center, Universidad de Chile, Av. Tupper 2007, Santiago (Chile); Department of Electrical Engineering, Universidad de Chile, Av. Tupper 2007, Santiago (Chile)

2016-03-15

A flow model is formulated to investigate the hydrodynamic structure of the boundary layers of incompressible fluid in a rotating cylindrical cavity with steady radial inflow. The model considers mass and momentum transfer coupled between boundary layers and an inviscid core region. Dimensionless equations of motion are solved using integral methods and a space-marching technique. As the fluid moves radially inward, entraining boundary layers develop which can either meet or become non-entraining. Pressure and wall shear stress distributions, as well as velocity profiles predicted by the model, are compared to numerical simulations using the software OpenFOAM. Hydrodynamic structure of the boundary layers is governed by a Reynolds number, Re, a Rossby number, Ro, and the dimensionless radial velocity component at the periphery of the cavity, U{sub o}. Results show that boundary layers merge for Re < < 10 and Ro > > 0.1, and boundary layers become predominantly non-entraining for low Ro, low Re, and high U{sub o}. Results may contribute to improve the design of technology, such as heat exchange devices, and turbomachinery.

Consequences of boundary-spanning demands and resources for work-to-family conflict and perceived stress.

Science.gov (United States)

Voydanoff, Patricia

2005-10-01

Using work-family border theory, this article examines relationships between boundary-spanning demands and resources and work-to-family conflict and perceived stress. The analysis uses data from 2,109 respondents from the 2002 National Study of the Changing Workforce. The demands that were positively related to work-to-family conflict and perceived stress were commuting time, bringing work home, job contacts at home, and work-family multitasking. Work-family multitasking partially explained the effects of bringing work home and job contacts at home on conflict and stress. For resources, time off for family responsibilities and a supportive work-family culture showed negative associations with conflict and stress. Work-to-family conflict partially mediated relationships between several demands and resources and perceived stress. Copyright (c) 2005 APA, all rights reserved.

Direct measurements of wall shear stress by buried wire gages in a shock-wave boundary-layer interaction region

Science.gov (United States)

Murthy, V. S.; Rose, W. C.

1977-01-01

Detailed measurements of wall shear stress (skin friction) were made with specially developed buried wire gages in the interaction regions of a Mach 2.9 turbulent boundary layer with externally generated shocks. Separation and reattachment points inferred by these measurements support the findings of earlier experiments which used a surface oil flow technique and pitot profile measurements. The measurements further indicate that the boundary layer tends to attain significantly higher skin-friction values downstream of the interaction region as compared to upstream. Comparisons between measured wall shear stress and published results of some theoretical calculation schemes show that the general, but not detailed, behavior is predicted well by such schemes.

On flows of viscoelastic fluids under threshold-slip boundary conditions

Science.gov (United States)

Baranovskii, E. S.

2018-03-01

We investigate a boundary-value problem for the steady isothermal flow of an incompressible viscoelastic fluid of Oldroyd type in a 3D bounded domain with impermeable walls. We use the Fujita threshold-slip boundary condition. This condition states that the fluid can slip along a solid surface when the shear stresses reach a certain critical value; otherwise the slipping velocity is zero. Assuming that the flow domain is not rotationally symmetric, we prove an existence theorem for the corresponding slip problem in the framework of weak solutions. The proof uses methods for solving variational inequalities with pseudo-monotone operators and convex functionals, the method of introduction of auxiliary viscosity, as well as a passage-to-limit procedure based on energy estimates of approximate solutions, Korn’s inequality, and compactness arguments. Also, some properties and estimates of weak solutions are established.

Convection of wall shear stress events in a turbulent boundary layer

Science.gov (United States)

Pabon, Rommel; Mills, David; Ukeiley, Lawrence; Sheplak, Mark

2017-11-01

The fluctuating wall shear stress is measured in a zero pressure gradient turbulent boundary layer of Reτ 1700 simultaneously with velocity measurements using either hot-wire anemometry or particle image velocimetry. These experiments elucidate the patterns of large scale structures in a single point measurement of the wall shear stress, as well as their convection velocity at the wall. The wall shear stress sensor is a CS-A05 one-dimensional capacitice floating element from Interdisciplinary Consulting Corp. It has a nominal bandwidth from DC to 5 kHz and a floating element size of 1 mm in the principal sensing direction (streamwise) and 0.2 mm in the cross direction (spanwise), allowing the large scales to be well resolved in the current experimental conditions. In addition, a two sensor array of CS-A05 aligned in the spanwise direction with streamwise separations O (δ) is utilized to capture the convection velocity of specific scales of the shear stress through a bandpass filter and peaks in the correlation. Thus, an average wall normal position for the corresponding convecting event can be inferred at least as high as the equivalent local streamwise velocity. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1315138.

Closed-form solution for piezoelectric layer with two collinear cracks parallel to the boundaries

Directory of Open Access Journals (Sweden)

B. M. Singh

2006-01-01

Full Text Available We consider the problem of determining the stress distribution in an infinitely long piezoelectric layer of finite width, with two collinear cracks of equal length and parallel to the layer boundaries. Within the framework of reigning piezoelectric theory under mode III, the cracked piezoelectric layer subjected to combined electromechanical loading is analyzed. The faces of the layers are subjected to electromechanical loading. The collinear cracks are located at the middle plane of the layer parallel to its face. By the use of Fourier transforms we reduce the problem to solving a set of triple integral equations with cosine kernel and a weight function. The triple integral equations are solved exactly. Closed form analytical expressions for stress intensity factors, electric displacement intensity factors, and shape of crack and energy release rate are derived. As the limiting case, the solution of the problem with one crack in the layer is derived. Some numerical results for the physical quantities are obtained and displayed graphically.

Spatio-temporal characteristics of large scale motions in a turbulent boundary layer from direct wall shear stress measurement

Science.gov (United States)

Pabon, Rommel; Barnard, Casey; Ukeiley, Lawrence; Sheplak, Mark

2016-11-01

Particle image velocimetry (PIV) and fluctuating wall shear stress experiments were performed on a flat plate turbulent boundary layer (TBL) under zero pressure gradient conditions. The fluctuating wall shear stress was measured using a microelectromechanical 1mm × 1mm floating element capacitive shear stress sensor (CSSS) developed at the University of Florida. The experiments elucidated the imprint of the organized motions in a TBL on the wall shear stress through its direct measurement. Spatial autocorrelation of the streamwise velocity from the PIV snapshots revealed large scale motions that scale on the order of boundary layer thickness. However, the captured inclination angle was lower than that determined using the classic method by means of wall shear stress and hot-wire anemometry (HWA) temporal cross-correlations and a frozen field hypothesis using a convection velocity. The current study suggests the large size of these motions begins to degrade the applicability of the frozen field hypothesis for the time resolved HWA experiments. The simultaneous PIV and CSSS measurements are also used for spatial reconstruction of the velocity field during conditionally sampled intense wall shear stress events. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1315138.

Intrinsic stress in ZrN thin films: Evaluation of grain boundary contribution from in situ wafer curvature and ex situ x-ray diffraction techniques

International Nuclear Information System (INIS)

Koutsokeras, L. E.; Abadias, G.

2012-01-01

Low-mobility materials, like transition metal nitrides, usually undergo large residual stress when sputter-deposited as thin films. While the origin of stress development has been an active area of research for high-mobility materials, atomistic processes are less understood for low-mobility systems. In the present work, the contribution of grain boundary to intrinsic stress in reactively magnetron-sputtered ZrN films is evaluated by combining in situ wafer curvature measurements, providing information on the overall biaxial stress, and ex situ x-ray diffraction, giving information on elastic strain (and related stress) inside crystallites. The thermal stress contribution was also determined from the in situ stress evolution during cooling down, after deposition was stopped. The stress data are correlated with variations in film microstructure and growth energetics, in the 0.13-0.42 Pa working pressure range investigated, and discussed based on existing stress models. At low pressure (high energetic bombardment conditions), a large compressive stress is observed due to atomic peening, which induces defects inside crystallites but also promotes incorporation of excess atoms in the grain boundary. Above 0.3-0.4 Pa, the adatom surface mobility is reduced, leading to the build-up of tensile stress resulting from attractive forces between under-dense neighbouring column boundary and possible void formation, while crystallites can still remain under compressive stress.

Finite-volume discretizations and immersed boundaries

NARCIS (Netherlands)

Y.J. Hassen (Yunus); B. Koren (Barry)

2009-01-01

htmlabstractIn this chapter, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed `Cartesian' grid. The essence of the present method

Finite-volume discretizations and immersed boundaries

NARCIS (Netherlands)

Y.J. Hassen (Yunus); B. Koren (Barry)

2010-01-01

textabstractIn this chapter, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed Cartesian grid. The essence of the present method is

Hybrid immersed boundary method for airfoils with a trailing-edge flap

DEFF Research Database (Denmark)

Zhu, Wei Jun; Behrens, Tim; Shen, Wen Zhong

2013-01-01

In this paper, a hybrid immersed boundary technique has been developed for simulating turbulent flows past airfoils with moving trailing-edge flaps. Over the main fixed part of the airfoil, the equations are solved using a standard body-fitted finite volume technique, whereas the moving trailing......-edge flap is simulated using the immersed boundary method on a curvilinear mesh. An existing in-house-developed flow solver is employed to solve the incompressible Reynolds-Averaged Navier-Stokes equations together with the k-ω turbulence model. To achieve consistent wall boundary conditions at the immersed...... boundaries the k-ωturbulence model is modified and adapted to the local conditions associated with the immersed boundary method. The obtained results show that the hybrid approach is an efficient and accurate method for solving turbulent flows past airfoils with a trailing-edge flap and that flow control...

Parallel Fast Multipole Boundary Element Method for crustal dynamics

International Nuclear Information System (INIS)

Quevedo, Leonardo; Morra, Gabriele; Mueller, R Dietmar

2010-01-01

Crustal faults and sharp material transitions in the crust are usually represented as triangulated surfaces in structural geological models. The complex range of volumes separating such surfaces is typically three-dimensionally meshed in order to solve equations that describe crustal deformation with the finite-difference (FD) or finite-element (FEM) methods. We show here how the Boundary Element Method, combined with the Multipole approach, can revolutionise the calculation of stress and strain, solving the problem of computational scalability from reservoir to basin scales. The Fast Multipole Boundary Element Method (Fast BEM) tackles the difficulty of handling the intricate volume meshes and high resolution of crustal data that has put classical Finite 3D approaches in a performance crisis. The two main performance enhancements of this method: the reduction of required mesh elements from cubic to quadratic with linear size and linear-logarithmic runtime; achieve a reduction of memory and runtime requirements allowing the treatment of a new scale of geodynamic models. This approach was recently tested and applied in a series of papers by [1, 2, 3] for regional and global geodynamics, using KD trees for fast identification of near and far-field interacting elements, and MPI parallelised code on distributed memory architectures, and is now in active development for crustal dynamics. As the method is based on a free-surface, it allows easy data transfer to geological visualisation tools where only changes in boundaries and material properties are required as input parameters. In addition, easy volume mesh sampling of physical quantities enables direct integration with existing FD/FEM code.

A numerical solution of a singular boundary value problem arising in boundary layer theory.

Science.gov (United States)

Hu, Jiancheng

2016-01-01

In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.

Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. II - Wall shear stress

Science.gov (United States)

Liou, M. S.; Adamson, T. C., Jr.

1980-01-01

Asymptotic methods are used to calculate the shear stress at the wall for the interaction between a normal shock wave and a turbulent boundary layer on a flat plate. A mixing length model is used for the eddy viscosity. The shock wave is taken to be strong enough that the sonic line is deep in the boundary layer and the upstream influence is thus very small. It is shown that unlike the result found for laminar flow an asymptotic criterion for separation is not found; however, conditions for incipient separation are computed numerically using the derived solution for the shear stress at the wall. Results are compared with available experimental measurements.

Utilizing the meso-scale grain boundary stress to estimate the onset of delamination in 2099-T861 aluminium–lithium

International Nuclear Information System (INIS)

McDonald, Russell J; Beaudoin, Armand J

2010-01-01

Aluminium–lithium alloys provide a lower density and higher stiffness alternative to other high strength aluminium alloys. However, many Al–Li alloys exhibit a non-traditional failure mechanism called delamination, which refers to the failure of the elongated grain boundary interface. In this investigation, delaminations were observed after cyclic deformation of both uniaxial and torsion experiments. A cyclically stable rate-independent crystal plasticity framework with kinematic hardening was developed to address many experimental trends of stabilized cyclic plasticity. Utilizing this framework, meso-scale grain boundary interface stresses were estimated with uniform deformation and bi-crystal models. These models are computationally amenable to investigate both orientation dependence and the statistical nature of the grain boundary stresses for a given bulk texture and nominal loading. A coupled shear-normal Findley-based damage parameter was formulated to quantitatively characterize the nucleation of delamination consistently with experimental trends

The effect of grain boundary chemistry on the slip transmission process through grain boundaries in Ni3Al

International Nuclear Information System (INIS)

Robertson, I.M.; Lee, T.C.; Subramanian, R.; Birnbaum, H.K.

1992-01-01

This paper reports on the conditions established in disordered FCC systems for predicting the slip system that will be activated by a grain boundary to relieve a local stress concentration that have been applied to the ordered FCC alloy Ni 3 Al. The slip transfer behavior in hypo-stoichiometric Ni 3 Al with (0.2 at. %B) and without boron was directly observed by performing the deformation experiments in situ in the transmission electron microscope. In the boron-free and boron-doped alloys, lattice dislocations were incorporated in the grain boundary, but did not show evidence of dissociation to grain boundary dislocations or of movement in the grain boundary plane. The stress concentration associated with the dislocation pileup at the grain boundary are relieved by the emission of dislocations from the grain boundary in the boron-doped alloy. The slip system initiated in the adjoining grain obeyed the conditions established for disordered FCC systems. In the boron-free alloy, the primary stress relief mechanism was grain-boundary cracking, although dislocation emission from the grain boundary also occurred and accompanied intergranular crack advance

The Role of Three-Dimensional Boundary Stresses in Limiting the Occurrence and Size of Experimental Landslides

Science.gov (United States)

Prancevic, Jeffrey P.; Lamb, Michael P.; Palucis, Marisa C.; Venditti, Jeremy G.

2018-01-01

The occurrence of seepage-induced shallow landslides on hillslopes and steep channel beds is important for landscape evolution and natural hazards. Infinite-slope stability models have been applied for seven decades, but sediment beds generally require higher water saturation levels than predicted for failure, and controlled experiments are needed to test models. We initiated 90 landslides in a 5 m long laboratory flume with a range in sediment sizes (D = 0.7, 2, 5, and 15 mm) and hillslope angles (θ = 20° to 43°), resulting in subsurface flow that spanned the Darcian and turbulent regimes, and failures that occurred with subsaturated and supersaturated sediment beds. Near complete saturation was required for failure in most experiments, with water levels far greater than predicted by infinite-slope stability models. Although 3-D force balance models predict that larger landslides are less stable, observed downslope landslide lengths were typically only several decimeters, not the entire flume length. Boundary stresses associated with short landslides can explain the increased water levels required for failure, and we suggest that short failures are tied to heterogeneities in granular properties. Boundary stresses also limited landslide thicknesses, and landslides progressively thinned on lower gradient hillslopes until they were one grain diameter thick, corresponding to a change from near-saturated to supersaturated sediment beds. Thus, landslides are expected to be thick on steep hillslopes with large frictional stresses acting on the boundaries, whereas landslides should be thin on low-gradient hillslopes or in channel beds with a critical saturation level that is determined by sediment size.

Application of He's variational iteration method to the fifth-order boundary value problems

International Nuclear Information System (INIS)

Shen, S

2008-01-01

Variational iteration method is introduced to solve the fifth-order boundary value problems. This method provides an efficient approach to solve this type of problems without discretization and the computation of the Adomian polynomials. Numerical results demonstrate that this method is a promising and powerful tool for solving the fifth-order boundary value problems

An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

Science.gov (United States)

Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

2018-06-01

This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

Application of a 2-D approximation technique for solving stress analyses problem in FEM

Directory of Open Access Journals (Sweden)

H Khawaja

2016-10-01

Full Text Available With the advent of computational techniques and methods like finite element method, complex engineering problems are no longer difficult to solve. These methods have helped engineers and designers to simulate and solve engineering problems in much more details than possible with experimental techniques. However, applying these techniques is not a simple task and require lots of acumen, understanding, and experience in obtaining a solution that is as close to an exact solution as possible with minimum computer resources. In this work using the finite element (FE method, stress analyzes of the low-pressure turbine of a small turbofan engine is carried out by employing two different techniques. Initially, a complete solid model of the turbine is prepared which is then finite element modelled with the eight-node brick element. Stresses are calculated using this model. Subsequently, the same turbine is modelled with four-node shell element for calculation of stresses. Material properties, applied loads (inertial, aerodynamic, and thermal, and constraints were same for both the cases. Authors have developed a “2-D approximation technique” to approximate a 3-D problem into a 2-D problem to study the saving invaluable computational time and resources. In this statistics technique, the 3-D domain of variable thickness is divided into many small areas of constant thickness. It is ensured that the value of the thickness for each sub-area is the correct representative thickness of that sub area, and it is within three sigma limit. The results revealed that technique developed is accurate, less time consuming and computational effort saving; the stresses obtained by 2-D technique are within five percent of 3-D results. The solution is obtained in CPU time which is six times less than the 3-D model. Similarly, the number of nodes and elements are more than ten times less than that of the 3-D model. ANSYS ® was used in this work.

Computation of airfoil buffet boundaries

Science.gov (United States)

Levy, L. L., Jr.; Bailey, H. E.

1981-01-01

The ILLIAC IV computer has been programmed with an implicit, finite-difference code for solving the thin layer compressible Navier-Stokes equation. Results presented for the case of the buffet boundaries of a conventional and a supercritical airfoil section at high Reynolds numbers are found to be in agreement with experimentally determined buffet boundaries, especially at the higher freestream Mach numbers and lower lift coefficients where the onset of unsteady flows is associated with shock wave-induced boundary layer separation.

Direct approach for solving nonlinear evolution and two-point

Indian Academy of Sciences (India)

Time-delayed nonlinear evolution equations and boundary value problems have a wide range of applications in science and engineering. In this paper, we implement the differential transform method to solve the nonlinear delay differential equation and boundary value problems. Also, we present some numerical examples ...

Tricritical Ising model with a boundary

International Nuclear Information System (INIS)

De Martino, A.; Moriconi, M.

1998-03-01

We study the integrable and supersymmetric massive φ (1,3) deformation of the tricritical Ising model in the presence of a boundary. We use constraints from supersymmetry in order to compute the exact boundary S-matrices, which turn out to depend explicitly on the topological charge of the supersymmetry algebra. We also solve the general boundary Yang-Baxter equation and show that in appropriate limits the general reflection matrices go over the supersymmetry preserving solutions. Finally, we briefly discuss the possible connection between our reflection matrices and boundary perturbations within the framework of perturbed boundary conformal field theory. (author)

Intergranular fracture stress and phosphorus grain boundary segregation of a Mn-Ni-Mo steel

International Nuclear Information System (INIS)

Naudin, C.; Frund, J.M.; Pineau, A.

1999-01-01

Nuclear Reactor Pressure Vessel (RPV) steel A508 class 3 which is a low alloyed steel is not usually sensitive to reversible temper embrittlement when properly heat treated. However heterogeneous zones may be present in particular near the inner side of the vessel. These zones result from the segregation of the alloying elements (C, Mn, Ni, Mo) and impurities (S, P) taking place during solidification of the material. They are called segregated zones (or ghost lines). They can reach 2 mm thick along the radius and 30 mm long through the circumferential direction. Their susceptibility to reversible temper embrittlement is mainly due to grain boundary phosphorus segregation triggering brittle intergranular fracture when the material is tested at low temperature. In this material like in other steels the influence of some other alloying elements (Mo, Mn...) is clearly significant and should also be taken into account. But phosphorus effect has proved to be predominant. The aim of the present study is therefore to find out a quantitative relationship between grain boundary phosphorus segregation and critical intergranular fracture stress. A synthetic steel with a chemical composition representative of an average segregated zone was prepared for the present study. A number of heat treatments were applied to reach different embrittlement conditions. Then brittle fracture properties were obtained by performing cryogenic fracture tests on notched tensile specimens while the corresponding grain boundary phosphorus levels were measured by Auger electron spectroscopy. Systematic fractographic observations were carried out. Moreover an attempt to determine the influence of temperature on the critical intergranular fracture stress was made

A moving boundary problem and orthogonal collocation in solving a dynamic liquid surfactant membrane model including osmosis and breakage

Directory of Open Access Journals (Sweden)

E.C. Biscaia Junior

2001-06-01

Full Text Available A dynamic kinetic-diffusive model for the extraction of metallic ions from aqueous liquors using liquid surfactant membranes is proposed. The model incorporates undesirable intrinsic phenomena such as swelling and breakage of the emulsion globules that have to be controlled during process operation. These phenomena change the spatial location of the chemical reaction during the course of extraction, resulting in a transient moving boundary problem. The orthogonal collocation method was used to transform the partial differential equations into an ordinary differential equation set that was solved by an implicit numerical routine. The model was found to be numerically stable and reliable in predicting the behaviour of zinc extraction with acidic extractant for long residence times.

Thermodynamic effect of elastic stress on grain boundary segregation of phosphorus in a low alloy steel

Czech Academy of Sciences Publication Activity Database

Zheng, L.; Lejček, Pavel; Song, S.; Schmitz, G.; Meng, Y.

2015-01-01

Roč. 647, Oct (2015), s. 172-178 ISSN 0925-8388 R&D Projects: GA ČR GAP108/12/0144 Institutional support: RVO:68378271 Keywords : grain boundaries * segregation * elastic stress * thermodynamics * chemical potential * molar volume Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.014, year: 2015

Shooting method for solution of boundary-layer flows with massive blowing

Science.gov (United States)

Liu, T.-M.; Nachtsheim, P. R.

1973-01-01

A modified, bidirectional shooting method is presented for solving boundary-layer equations under conditions of massive blowing. Unlike the conventional shooting method, which is unstable when the blowing rate increases, the proposed method avoids the unstable direction and is capable of solving complex boundary-layer problems involving mass and energy balance on the surface.

Polyakov's quantized string with boundary terms

International Nuclear Information System (INIS)

Durhuus, B.; Olesen, P.; Petersen, J.L.

1981-11-01

The authors compute the boundary terms needed in Polyakov's method for calculating averages of functionals defined on surfaces. The method used is due to Seeley, who found recursive relations yielding the boundary terms. These relations are solved for a general second order elliptic differential operator. This solution is then applied to Polyakov's problem. (Auth.)

The Effect of Social Problem Solving Skills in the Relationship between Traumatic Stress and Moral Disengagement among Inner-City African American High School Students

Science.gov (United States)

Coker, Kendell L.; Ikpe, Uduakobong N.; Brooks, Jeannie S.; Page, Brian; Sobell, Mark B.

2014-01-01

This study examined the relationship between traumatic stress, social problem solving, and moral disengagement among African American inner-city high school students. Participants consisted of 45 (25 males and 20 females) African American students enrolled in grades 10 through 12. Mediation was assessed by testing for the indirect effect using the confidence interval derived from 10,000 bootstrapped resamples. The results revealed that social problem-solving skills have an indirect effect on the relationship between traumatic stress and moral disengagement. The findings suggest that African American youth that are negatively impacted by trauma evidence deficits in their social problem solving skills and are likely to be at an increased risk to morally disengage. Implications for culturally sensitive and trauma-based intervention programs are also provided. PMID:25071874

The Effect of Social Problem Solving Skills in the Relationship between Traumatic Stress and Moral Disengagement among Inner-City African American High School Students.

Science.gov (United States)

Coker, Kendell L; Ikpe, Uduakobong N; Brooks, Jeannie S; Page, Brian; Sobell, Mark B

2014-06-01

This study examined the relationship between traumatic stress, social problem solving, and moral disengagement among African American inner-city high school students. Participants consisted of 45 (25 males and 20 females) African American students enrolled in grades 10 through 12. Mediation was assessed by testing for the indirect effect using the confidence interval derived from 10,000 bootstrapped resamples. The results revealed that social problem-solving skills have an indirect effect on the relationship between traumatic stress and moral disengagement. The findings suggest that African American youth that are negatively impacted by trauma evidence deficits in their social problem solving skills and are likely to be at an increased risk to morally disengage. Implications for culturally sensitive and trauma-based intervention programs are also provided.

Implicit Large-Eddy Simulations of Zero-Pressure Gradient, Turbulent Boundary Layer

Science.gov (United States)

Sekhar, Susheel; Mansour, Nagi N.

2015-01-01

A set of direct simulations of zero-pressure gradient, turbulent boundary layer flows are conducted using various span widths (62-630 wall units), to document their influence on the generated turbulence. The FDL3DI code that solves compressible Navier-Stokes equations using high-order compact-difference scheme and filter, with the standard recycling/rescaling method of turbulence generation, is used. Results are analyzed at two different Re values (500 and 1,400), and compared with spectral DNS data. They show that a minimum span width is required for the mere initiation of numerical turbulence. Narrower domains ((is) less than 100 w.u.) result in relaminarization. Wider spans ((is) greater than 600 w.u.) are required for the turbulent statistics to match reference DNS. The upper-wall boundary condition for this setup spawns marginal deviations in the mean velocity and Reynolds stress profiles, particularly in the buffer region.

The Boundary Function Method. Fundamentals

Science.gov (United States)

Kot, V. A.

2017-03-01

The boundary function method is proposed for solving applied problems of mathematical physics in the region defined by a partial differential equation of the general form involving constant or variable coefficients with a Dirichlet, Neumann, or Robin boundary condition. In this method, the desired function is defined by a power polynomial, and a boundary function represented in the form of the desired function or its derivative at one of the boundary points is introduced. Different sequences of boundary equations have been set up with the use of differential operators. Systems of linear algebraic equations constructed on the basis of these sequences allow one to determine the coefficients of a power polynomial. Constitutive equations have been derived for initial boundary-value problems of all the main types. With these equations, an initial boundary-value problem is transformed into the Cauchy problem for the boundary function. The determination of the boundary function by its derivative with respect to the time coordinate completes the solution of the problem.

Second-order wave diffraction by a circular cylinder using scaled boundary finite element method

International Nuclear Information System (INIS)

Song, H; Tao, L

2010-01-01

The scaled boundary finite element method (SBFEM) has achieved remarkable success in structural mechanics and fluid mechanics, combing the advantage of both FEM and BEM. Most of the previous works focus on linear problems, in which superposition principle is applicable. However, many physical problems in the real world are nonlinear and are described by nonlinear equations, challenging the application of the existing SBFEM model. A popular idea to solve a nonlinear problem is decomposing the nonlinear equation to a number of linear equations, and then solves them individually. In this paper, second-order wave diffraction by a circular cylinder is solved by SBFEM. By splitting the forcing term into two parts, the physical problem is described as two second-order boundary-value problems with different asymptotic behaviour at infinity. Expressing the velocity potentials as a series of depth-eigenfunctions, both of the 3D boundary-value problems are decomposed to a number of 2D boundary-value sub-problems, which are solved semi-analytically by SBFEM. Only the cylinder boundary is discretised with 1D curved finite-elements on the circumference of the cylinder, while the radial differential equation is solved completely analytically. The method can be extended to solve more complex wave-structure interaction problems resulting in direct engineering applications.

Three dimensional, thermal stress analysis of a welded plate

International Nuclear Information System (INIS)

Koening, H.A.; Lai, C.K.-F.; Morral, J.E.

1985-01-01

A general finite element thermal stress analysis has been developed. The analysis can be uncoupled to solve either the heat transfer problem or the stress problem independently and it can accommodate non-linear material behavior, initial states of stress and strain, and moving boundary conditions. A unique feature of the model it that it properly accounts for the latent heat effect during phase changes. Applying the moving heat flux boundary condition to simulate arc welding, the model has been used to predict the transient thermal mechanical response of a welded plate. It is the absorption and liberation of latent heat in the fusion zone of a weld which complicates numerical methods of treating welding. For pure materials and eutectic alloys the latent heat effect is less of a problem because phase changes take place at a specific temperature. But for most alloys, phase changes take place over a range of temperatures bounded by the solidus, T S , and liquidus, T L , and the latent heat effect occurs continuously over the temperature range. (author)

Electromagnetic wave theory for boundary-value problems an advanced course on analytical methods

CERN Document Server

Eom, Hyo J

2004-01-01

Electromagnetic wave theory is based on Maxwell's equations, and electromagnetic boundary-value problems must be solved to understand electromagnetic scattering, propagation, and radiation. Electromagnetic theory finds practical applications in wireless telecommunications and microwave engineering. This book is written as a text for a two-semester graduate course on electromagnetic wave theory. As such, Electromagnetic Wave Theory for Boundary-Value Problems is intended to help students enhance analytic skills by solving pertinent boundary-value problems. In particular, the techniques of Fourier transform, mode matching, and residue calculus are utilized to solve some canonical scattering and radiation problems.

Elastic crack-tip stress field in a semi-strip

Directory of Open Access Journals (Sweden)

Victor Reut

2018-04-01

Full Text Available In this article the plain elasticity problem for a semi-strip with a transverse crack is investigated in the different cases of the boundary conditions at the semi-strips end. Unlike many works dedicated to this subject, the fixed singularities in the singular integral equation�s kernel are considered. The integral transformations� method is applied by the generalized scheme to reduce the initial problem to a one-dimensional problem. The one-dimensional problem is formulated as the vector boundary value problem which is solved with the help of matrix differential calculations and Green�s matrix apparatus. The solution of the problem is reduced to the solving of the system of three singular integral equations. Depending on the conditions given on the short edge of the semi-strip, the constructed singular integral equation can have one, or two fixed singularities. A special method is applied to solve this equation in regard of the singularities existence. Hence the system of the singular integral equations (SSIE is solved with the help of the generalized method. The stress intensity factors (SIF are investigated for different lengths of crack. The novelty of this work is in the application of new approach allowing the consideration of the fixed singularities in the problem about a transverse crack in the elastic semi-strip. The comparison of the numerical results� accuracy during the usage of the different approaches to the solving of SSIE is worked out

Influence of structural parameter included in nonlocal rock mass model on stress concentration around circular tunnel

Science.gov (United States)

Lavrikov, SV; Mikenina, OA; Revuzhenko, AF

2018-03-01

A model of elastic body, including local curvature of elementary volume, is matched with a nonlocal model with a linear structural parameter in the differential approximation. The problem on deformation of rock mass around a circular cross section tunnel is solved numerically. The contours of the calculated stresses are plotted. It is shown that inclusion of local bends in the model results in expansion of influence zone of the tunnel and reduces stress concentration factor at the tunnel boundary.

Boundary Element Solution of Geometrical Inverse Heat Conduction Problems for Development of IR CAT Scan

International Nuclear Information System (INIS)

Choi, C. Y.; Park, C. T.; Kim, T. H.; Han, K. N.; Choe, S. H.

1995-01-01

A geometrical inverse heat conduction problem is solved for the development of Infrared Computerized-Axial-Tomography (IR CAT) Scan by using a boundary element method in conjunction with regularization procedure. In this problem, an overspecified temperature condition by infrared scanning is provided on the surface, and is used together with other conditions to solve the position of an unknown boundary (cavity). An auxiliary problem is introduced in the solution of this problem. By defining a hypothetical inner boundary for the auxiliary problem domain, the cavity is located interior to the domain and its position is determined by solving a potential problem. Boundary element method with regularization procedure is used to solve this problem, and the effects of regularization on the inverse solution method are investigated by means of numerical analysis

A Numerical Model of Anisotropic Mass Transport Through Grain Boundary Networks

Science.gov (United States)

Wang, Yibo

Tin (Sn) thin films are commonly used in electronic circuit applications as coatings on contacts and solders for joining components. It is widely observed, for some such system, that whiskers---long, thin crystalline structures---emerge and grow from the film. The Sn whisker phenomenon has become a highly active research area since Sn whiskers have caused a large amount of damage and loss in manufacturing, military, medical and power industries. Though lead (Pb) addition to Sn has been used to solve this problem for over five decades, the adverse environmental and health effects of Pb have motivated legislation to severely constrain Pb use in society. People are researching and seeking the reasons which cause whiskers and corresponding methods to solve the problem. The contributing factors to cause a Sn whisker are potentially many and much still remains unknown. Better understanding of fundamental driving forces should point toward strategies to improve (a) the accuracy with which we can predict whisker formation, and (b) our ability to mitigate the phenomenon. This thesis summarizes recent important research achievements in understanding Sn whisker formation and growth, both experimentally and theoretically. Focus is then placed on examining the role that anisotropy in grain boundary diffusivity plays in determining whisker characteristics (specifically, whether they form and, if so, where on a surface). To study this aspect of the problem and to enable future studies on stress driven grain boundary diffusion, this thesis presents a numerical anisotropic mass transport model. In addition to presenting details of the model and implementation, model predictions for a set of increasingly complex grain boundary networks are discussed. Preliminary results from the model provide evidence that anisotropic grain boundary diffusion may be a primary driving mechanism in whisker formation.

Polyakov's quantized string with boundary terms

International Nuclear Information System (INIS)

Durhuus, B.; Olesen, P.; Petersen, J.L.

1982-01-01

We compute the boundary terms due to the conformal anomaly which are needed in Polyakov's method of calculating averages of functionals defined on surfaces. The method we use is due to Seeley, who found recursive relations yielding the boundary terms. We solve these relations for a general second-order elliptic differential operator. This solution is then applied to Polyakov's problem. (orig.)

Stress State of Elastic Thick-Walled Ring With Self-Balanced Pressures Distributed on Its Internal and External Borders

Directory of Open Access Journals (Sweden)

Kravchuk Aleksandr Stepanovich

2015-10-01

Full Text Available For the first time with the help of the theory of analytic functions and Kolosov-Muskhelishvili formulas the problem of the two-dimensional theory of elasticity for a thickwalled ring with the uneven pressures, acting on its borders, was solved. The pressure on the inner and outer boundaries is represented by Fourier series. The authors represent the two complex functions which solve boundary problem in the form of Laurent series. The logarithmic terms in these series are absent because the boundary problem has the self-balancing loads on each boundary of ring. The coefficients in the Laurent series are calculated by the boundary conditions. Firstly, the equations were obtained in the general form. But the hypothesis about even distributions of pressures at borders of ring was used for constructing an example. It leads to the fact that all coefficients of analytic functions represented in Laurent series have to be only real. As a solving example, the representation of pressures in equivalent hypotrochoids was used. The application of the computer algebra system Mathematica greatly simplifies the calculation of the distribution of stresses and displacements in ring. It does not require manual formal separation of real and imaginary parts in terms of Kolosov-Muskhelishvili to display the distribution of the physical parameters. It separates them only for calculated numbers with the help of built-in functions.

Three dimensional grain boundary modeling in polycrystalline plasticity

Science.gov (United States)

Yalçinkaya, Tuncay; Özdemir, Izzet; Fırat, Ali Osman

2018-05-01

At grain scale, polycrystalline materials develop heterogeneous plastic deformation fields, localizations and stress concentrations due to variation of grain orientations, geometries and defects. Development of inter-granular stresses due to misorientation are crucial for a range of grain boundary (GB) related failure mechanisms, such as stress corrosion cracking (SCC) and fatigue cracking. Local crystal plasticity finite element modelling of polycrystalline metals at micron scale results in stress jumps at the grain boundaries. Moreover, the concepts such as the transmission of dislocations between grains and strength of the grain boundaries are not included in the modelling. The higher order strain gradient crystal plasticity modelling approaches offer the possibility of defining grain boundary conditions. However, these conditions are mostly not dependent on misorientation of grains and can define only extreme cases. For a proper definition of grain boundary behavior in plasticity, a model for grain boundary behavior should be incorporated into the plasticity framework. In this context, a particular grain boundary model ([l]) is incorporated into a strain gradient crystal plasticity framework ([2]). In a 3-D setting, both bulk and grain boundary models are implemented as user-defined elements in Abaqus. The strain gradient crystal plasticity model works in the bulk elements and considers displacements and plastic slips as degree of freedoms. Interface elements model the plastic slip behavior, yet they do not possess any kind of mechanical cohesive behavior. The physical aspects of grain boundaries and the performance of the model are addressed through numerical examples.

Solution of moving boundary problems with implicit boundary condition

International Nuclear Information System (INIS)

Moyano, E.A.

1990-01-01

An algorithm that solves numerically a model for studying one dimensional moving boundary problems, with implicit boundary condition, is described. Landau's transformation is used, in order to work with a fixed number of nodes at each instant. Then, it is necessary to deal with a parabolic partial differential equation, whose diffusive and convective terms have variable coefficients. The partial differential equation is implicitly discretized, using Laasonen's scheme, always stable, instead of employing Crank-Nicholson sheme, as it has been done by Ferris and Hill. Fixed time and space steps (Δt, Δξ) are used, and the iteration is made with variable positions of the interface, i.e. varying δs until a boundary condition is satisfied. The model has the same features of the oxygen diffusion in absorbing tissue. It would be capable of estimating time variant radiation treatments of cancerous tumors. (Author) [es

Bed slope effects on turbulent wave boundary layers: 1. Model validation and quantification of rough-turbulent results

DEFF Research Database (Denmark)

Fuhrman, David R.; Fredsøe, Jørgen; Sumer, B. Mutlu

2009-01-01

measurements for steady streaming induced by a skewed free stream velocity signal is also provided. We then simulate a series of experiments involving oscillatory flow in a convergent-divergent smooth tunnel, and a good match with respect to bed shear stresses and streaming velocities is achieved......A numerical model solving incompressible Reynolds-averaged Navier-Stokes equations, combined with a two-equation k-omega turbulence closure, is used to study converging-diverging effects from a sloping bed on turbulent (oscillatory) wave boundary layers. Bed shear stresses from the numerical model....... The streaming is conceptually explained using analogies from steady converging and diffuser flows. A parametric study is undertaken to assess both the peak and time-averaged bed shear stresses in converging and diverging half periods under rough-turbulent conditions. The results are presented as friction factor...

A nonlinear boundary integral equations method for the solving of quasistatic elastic contact problem with Coulomb friction

Directory of Open Access Journals (Sweden)

Yurii M. Streliaiev

2016-06-01

Full Text Available Three-dimensional quasistatic contact problem of two linearly elastic bodies' interaction with Coulomb friction taken into account is considered. The boundary conditions of the problem have been simplified by the modification of the Coulomb's law of friction. This modification is based on the introducing of a delay in normal contact tractions that bound tangent contact tractions in the Coulomb's law of friction expressions. At this statement the problem is reduced to a sequence of similar systems of nonlinear integral equations describing bodies' interaction at each step of loading. A method for an approximate solution of the integral equations system corresponded to each step of loading is applied. This method consists of system regularization, discretization of regularized system and iterative process application for solving the discretized system. A numerical solution of a contact problem of an elastic sphere with an elastic half-space interaction under increasing and subsequently decreasing normal compressive force has been obtained.

An analytical boundary element integral approach to track the boundary of a moving cavity using electrical impedance tomography

International Nuclear Information System (INIS)

Khambampati, Anil Kumar; Kim, Sin; Lee, Bo An; Kim, Kyung Youn

2012-01-01

This paper is about locating the boundary of a moving cavity within a homogeneous background from the voltage measurements recorded on the outer boundary. An inverse boundary problem of a moving cavity is formulated by considering a two-phase vapor–liquid flow in a pipe. The conductivity of the flow components (vapor and liquid) is assumed to be constant and known a priori while the location and shape of the inclusion (vapor) are the unknowns to be estimated. The forward problem is solved using the boundary element method (BEM) with the integral equations solved analytically. A special situation is considered such that the cavity changes its location and shape during the time taken to acquire a full set of independent measurement data. The boundary of a cavity is assumed to be elliptic and is parameterized with Fourier series. The inverse problem is treated as a state estimation problem with the Fourier coefficients that represent the center and radii of the cavity as the unknowns to be estimated. An extended Kalman filter (EKF) is used as an inverse algorithm to estimate the time varying Fourier coefficients. Numerical experiments are shown to evaluate the performance of the proposed method. Through the results, it can be noticed that the proposed BEM with EKF method is successful in estimating the boundary of a moving cavity. (paper)

A finite-volume method for convection problems with embedded moving boundaries

NARCIS (Netherlands)

Y.J. Hassen (Yunus); B. Koren (Barry)

2009-01-01

htmlabstractAn accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. Moving interior boundary conditions are embedded in the fixed-grid fluxes in the direct neighborhood of the moving boundaries. Tailor-made limiters are

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.

Boundary Layer Flow and Heat Transfer of FMWCNT/Water Nanofluids over a Flat Plate

Directory of Open Access Journals (Sweden)

Mohammad Reza Safaei

2016-09-01

Full Text Available In the present study, the heat transfer and flow of water/FMWCNT (functionalized multi-walled carbon nanotube nanofluids over a flat plate was investigated using a finite volume method. Simulations were performed for velocity ranging from 0.17 mm/s to 1.7 mm/s under laminar regime and nanotube concentrations up to 0.2%. The 2-D governing equations were solved using an in-house FORTRAN code. For a specific free stream velocity, the presented results showed that increasing the weight percentage of nanotubes increased the Nusselt number. However, an increase in the solid weight percentage had a negligible effect on the wall shear stress. The results also indicated that increasing the free stream velocity for all cases leads to thinner boundary layer thickness, while increasing the FMWCNT concentration causes an increase in the boundary layer thickness.

The coordination of boundary tones and its interaction with prominence.

Science.gov (United States)

Katsika, Argyro; Krivokapić, Jelena; Mooshammer, Christine; Tiede, Mark; Goldstein, Louis

2014-05-01

This study investigates the coordination of boundary tones as a function of stress and pitch accent. Boundary tone coordination has not been experimentally investigated previously, and the effect of prominence on this coordination, and whether it is lexical (stress-driven) or phrasal (pitch accent-driven) in nature is unclear. We assess these issues using a variety of syntactic constructions to elicit different boundary tones in an Electromagnetic Articulography (EMA) study of Greek. The results indicate that the onset of boundary tones co-occurs with the articulatory target of the final vowel. This timing is further modified by stress, but not by pitch accent: boundary tones are initiated earlier in words with non-final stress than in words with final stress regardless of accentual status. Visual data inspection reveals that phrase-final words are followed by acoustic pauses during which specific articulatory postures occur. Additional analyses show that these postures reach their achievement point at a stable temporal distance from boundary tone onsets regardless of stress position. Based on these results and parallel findings on boundary lengthening reported elsewhere, a novel approach to prosody is proposed within the context of Articulatory Phonology: rather than seeing prosodic (lexical and phrasal) events as independent entities, a set of coordination relations between them is suggested. The implications of this account for prosodic architecture are discussed.

Deformation of a geo-medium with considering for internal self-balancing stresses

Science.gov (United States)

Lavrikov, S. V.; Revuzhenko, A. F.

2016-11-01

Based on the general concept of rock as a medium with inner sources and sinks of energy, the authors consider an approach to mathematical modeling of a geo-medium with account for internal self-balancing stresses. The description of stresses and strains at the level of microstructural elements and macrovolume of the medium uses methods of non-Archimedean analysis. The model allows describing the accumulation of elastic energy in the form of internal self-balancing stresses. A finite element algorithm and a software program for solving plane boundary-value problems have been developed. The calculated data on rock specimen compression are given. It is shown that the behavior of plastic deformation zones depends on the pre-assigned initial microstresses.

Investigations on grain boundary segregation energy of phosphorus in 12Cr1MoV steel under elastic stress

Czech Academy of Sciences Publication Activity Database

Zheng, L.; Fu, Y.; Lejček, Pavel; Song, S.; Schmitz, G.; Meng, Y.

2016-01-01

Roč. 18, č. 4 (2016), 506-510 ISSN 1438-1656 R&D Projects: GA ČR GAP108/12/0144 Institutional support: RVO:68378271 Keywords : grain boundary segregation, * stress effect, * phosphorus, * steel Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 2.319, year: 2016

A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems

Directory of Open Access Journals (Sweden)

S. S. Motsa

2013-01-01

Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.

Modified Differential Transform Method for Two Singular Boundary Values Problems

Directory of Open Access Journals (Sweden)

Yinwei Lin

2014-01-01

Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.

Nucleation of small angle boundaries

CSIR Research Space (South Africa)

Nabarro, FRN

1996-12-01

Full Text Available The internal stresses induced by the strain gradients in an array of lattice cells delineated by low-angle dislocation boundaries are partially relieved by the creation of new low-angle boundaries. This is shown to be a first-order transition...

Implementation of a boundary element method to solve for the near field effects of an array of WECs

Science.gov (United States)

Oskamp, J. A.; Ozkan-Haller, H. T.

2010-12-01

When Wave Energy Converters (WECs) are installed, they affect the shoreline wave climate by removing some of the wave energy which would have reached the shore. Before large WEC projects are launched, it is important to understand the potential coastal impacts of these installations. The high cost associated with ocean scale testing invites the use of hydrodynamic models to play a major role in estimating these effects. In this study, a wave structure interaction program (WAMIT) is used to model an array of WECs. The program predicts the wave field throughout the array using a boundary element method to solve the potential flow fluid problem, taking into account the incident waves, the power dissipated, and the way each WEC moves and interacts with the others. This model is appropriate for a small domain near the WEC array in order to resolve the details in the interactions, but not extending to the coastline (where the far-field effects must be assessed). To propagate these effects to the coastline, the waves leaving this small domain will be used as boundary conditions for a larger model domain which will assess the shoreline effects caused by the array. The immediate work is concerned with setting up the WAMIT model for a small array of point absorbers. A 1:33 scale lab test is planned and will provide data to validate the WAMIT model on this small domain before it is nested with the larger domain to estimate shoreline effects.

Generation of sheared poloidal flows by electrostatic and magnetic Reynolds stress in the boundary plasma of HT-7 tokamak

International Nuclear Information System (INIS)

Xu, G.S.; Wan, B.N.; Li, J.

2005-01-01

The radial profiles of electrostatic and magnetic Reynolds stress (Maxwell stress) have been measured in the plasma boundary region of HT-7 tokamak. Experimental results show that the radial gradient of electrostatic Reynolds stress (ERS) changes sign across the last closed flux surface, and the neoclassical flow damping and the damping due to charge exchange processes are balanced by the radial gradient of ERS, which sustains the equilibrium sheared flow structure in a steady state. The contribution of magnetic Reynolds stress was found unimportant in a low β plasma. Detailed analyses indicate that the propagation properties of turbulence in radial and poloidal directions and the profiles of potential fluctuation level are responsible for the radial structure of ERS. (author)

Dynamic Stress Concentration at the Boundary of an Incision at the Plate Under the Action of Weak Shock Waves

Directory of Open Access Journals (Sweden)

Mikulich Olena

2017-09-01

Full Text Available This paper proposes the novel technique for analysis of dynamic stress state of multi-connected infinite plates under the action of weak shock waves. For solution of the problem it uses the integral and discrete Fourier transforms. Calculation of transformed dynamic stresses at the incisions of plates is held using the boundary-integral equation method and the theory of complex variable functions. The numerical implementation of the developed algorithm is based on the method of mechanical quadratures and collocation technique. For calculation of originals of the dynamic stresses it uses modified discrete Fourier transform. The algorithm is effective in the analysis of the dynamic stress state of defective plates.

Efficient algorithms for analyzing the singularly perturbed boundary value problems of fractional order

Science.gov (United States)

Sayevand, K.; Pichaghchi, K.

2018-04-01

In this paper, we were concerned with the description of the singularly perturbed boundary value problems in the scope of fractional calculus. We should mention that, one of the main methods used to solve these problems in classical calculus is the so-called matched asymptotic expansion method. However we shall note that, this was not achievable via the existing classical definitions of fractional derivative, because they do not obey the chain rule which one of the key elements of the matched asymptotic expansion method. In order to accommodate this method to fractional derivative, we employ a relatively new derivative so-called the local fractional derivative. Using the properties of local fractional derivative, we extend the matched asymptotic expansion method to the scope of fractional calculus and introduce a reliable new algorithm to develop approximate solutions of the singularly perturbed boundary value problems of fractional order. In the new method, the original problem is partitioned into inner and outer solution equations. The reduced equation is solved with suitable boundary conditions which provide the terminal boundary conditions for the boundary layer correction. The inner solution problem is next solved as a solvable boundary value problem. The width of the boundary layer is approximated using appropriate resemblance function. Some theoretical results are established and proved. Some illustrating examples are solved and the results are compared with those of matched asymptotic expansion method and homotopy analysis method to demonstrate the accuracy and efficiency of the method. It can be observed that, the proposed method approximates the exact solution very well not only in the boundary layer, but also away from the layer.

Adaptive boundary conditions for exterior flow problems

CERN Document Server

Boenisch, V; Wittwer, S

2003-01-01

We consider the problem of solving numerically the stationary incompressible Navier-Stokes equations in an exterior domain in two dimensions. This corresponds to studying the stationary fluid flow past a body. The necessity to truncate for numerical purposes the infinite exterior domain to a finite domain leads to the problem of finding appropriate boundary conditions on the surface of the truncated domain. We solve this problem by providing a vector field describing the leading asymptotic behavior of the solution. This vector field is given in the form of an explicit expression depending on a real parameter. We show that this parameter can be determined from the total drag exerted on the body. Using this fact we set up a self-consistent numerical scheme that determines the parameter, and hence the boundary conditions and the drag, as part of the solution process. We compare the values of the drag obtained with our adaptive scheme with the results from using traditional constant boundary conditions. Computati...

Boundary element analysis of active mountain building and stress heterogeneity proximal to the 2015 Nepal earthquake

Science.gov (United States)

Thompson, T. B.; Meade, B. J.

2015-12-01

The Himalayas are the tallest mountains on Earth with ten peaks exceeding 8000 meters, including Mt. Everest. The geometrically complex fault system at the Himalayan Range Front produces both great relief and great earthquakes, like the recent Mw=7.8 Nepal rupture. Here, we develop geometrically accurate elastic boundary element models of the fault system at the Himalayan Range Front including the Main Central Thrust, South Tibetan Detachment, Main Frontal Thrust, Main Boundary Thrust, the basal detachment, and surface topography. Using these models, we constrain the tectonic driving forces and frictional fault strength required to explain Quaternary fault slip rate estimates. These models provide a characterization of the heterogeneity of internal stress in the region surrounding the 2015 Nepal earthquake.

On the role of infiltration and exfiltration in swash zone boundary layer dynamics

Science.gov (United States)

Pintado-Patiño, José Carlos; Torres-Freyermuth, Alec; Puleo, Jack A.; Pokrajac, Dubravka

2015-09-01

Boundary layer dynamics are investigated using a 2-D numerical model that solves the Volume-Averaged Reynolds-Averaged Navier-Stokes equations, with a VOF-tracking scheme and a k - ɛ turbulence closure. The model is validated with highly resolved data of dam break driven swash flows over gravel impermeable and permeable beds. The spatial gradients of the velocity, bed shear stress, and turbulence intensity terms are investigated with reference to bottom boundary layer (BL) dynamics. Numerical results show that the mean vorticity responds to flow divergence/convergence at the surface that result from accelerating/decelerating portions of the flow, bed shear stress, and sinking/injection of turbulence due to infiltration/exfiltration. Hence, the zero up-crossing of the vorticity is employed as a proxy of the BL thickness inside the shallow swash zone flows. During the uprush phase, the BL develops almost instantaneously with bore arrival and fluctuates below the surface due to flow instabilities and related horizontal straining. In contrast, during the backwash phase, the BL grows quasi-linearly with less influence of surface-induced forces. However, the infiltration produces a reduction of the maximum excursion and duration of the swash event. These effects have important implications for the BL development. The numerical results suggest that the BL growth rate deviates rapidly from a quasi-linear trend if the infiltration is dominant during the initial backwash phase and the flat plate boundary layer theory may no longer be applicable under these conditions.

The coordination of boundary tones and its interaction with prominence1

Science.gov (United States)

Katsika, Argyro; Krivokapić, Jelena; Mooshammer, Christine; Tiede, Mark; Goldstein, Louis

2014-01-01

This study investigates the coordination of boundary tones as a function of stress and pitch accent. Boundary tone coordination has not been experimentally investigated previously, and the effect of prominence on this coordination, and whether it is lexical (stress-driven) or phrasal (pitch accent-driven) in nature is unclear. We assess these issues using a variety of syntactic constructions to elicit different boundary tones in an Electromagnetic Articulography (EMA) study of Greek. The results indicate that the onset of boundary tones co-occurs with the articulatory target of the final vowel. This timing is further modified by stress, but not by pitch accent: boundary tones are initiated earlier in words with non-final stress than in words with final stress regardless of accentual status. Visual data inspection reveals that phrase-final words are followed by acoustic pauses during which specific articulatory postures occur. Additional analyses show that these postures reach their achievement point at a stable temporal distance from boundary tone onsets regardless of stress position. Based on these results and parallel findings on boundary lengthening reported elsewhere, a novel approach to prosody is proposed within the context of Articulatory Phonology: rather than seeing prosodic (lexical and phrasal) events as independent entities, a set of coordination relations between them is suggested. The implications of this account for prosodic architecture are discussed. PMID:25300341

Exact solutions to plaquette Ising models with free and periodic boundaries

International Nuclear Information System (INIS)

Mueller, Marco; Johnston, Desmond A.; Janke, Wolfhard

2017-01-01

An anisotropic limit of the 3d plaquette Ising model, in which the plaquette couplings in one direction were set to zero, was solved for free boundary conditions by Suzuki (1972) , who later dubbed it the fuki-nuke, or “no-ceiling”, model. Defining new spin variables as the product of nearest-neighbour spins transforms the Hamiltonian into that of a stack of (standard) 2d Ising models and reveals the planar nature of the magnetic order, which is also present in the fully isotropic 3d plaquette model. More recently, the solution of the fuki-nuke model was discussed for periodic boundary conditions, which require a different approach to defining the product spin transformation, by Castelnovo et al. (2010) . We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fuki-nuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.

Analytic approximations to nonlinear boundary value problems modeling beam-type nano-electromechanical systems

Energy Technology Data Exchange (ETDEWEB)

Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics

2017-06-01

Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.

The effect of inhomogeneous initial stress on Love wave propagation in layered magneto-electro-elastic structures

International Nuclear Information System (INIS)

Zhang, J; Shen, Y P; Du, J K

2008-01-01

The effect of inhomogeneous initial stress on Love wave propagation in layered magneto-electro-elastic structures is investigated in this paper. The coupled magneto-electro-elastic field equations are solved by adopting the Wentzel–Kramers–Brillouin (WKB) approximate approach. Then the phase velocity can be calculated by applying boundary and continuity conditions. A specific example of a structure consisting of a CoFe 2 O 4 layer and a BaTiO 3 substrate is used to illustrate the influence of inhomogeneous initial stress on the phase velocity, corresponding coupled magneto-electric factor and stress fields. The different influence between constant initial stress and inhomogeneous initial stress is discussed and the results are expected to be helpful for the preparation and application of Love wave sensors

Axisymmetric MHD stability of sharp-boundary Tokamaks

International Nuclear Information System (INIS)

Rebhan, E.; Salat, A.

1976-09-01

For a sharp-boundary, constant pressure plasma model of axisymmetric equilibria the MHD stability problem of axisymmetric perturbations is solved by analytic reduction to a one-dimensional problem on the boundary and subsequent numerical treatment, using the energy principle. The stability boundaries are determined for arbitrary aspect ratio, arbitrary βsub(p) and elliptical, triangular and rectangular plasma cross-sections, wall stabilization not being taken into account. It is found that the axisymmetric stability strongly depends on the plasma shape and is almost independent of the safety factor q. (orig.) [de

Do organizational practices matter in role stress processes? A study of direct and moderating effects for marketing-oriented boundary spanners

NARCIS (Netherlands)

J. Singh (Jagdip); W.J.M.I. Verbeke (Willem); G.K. Rhoads (Gary)

1996-01-01

textabstractPrevious research and meta-analyses suggest that the influence of organizational variables on boundary role stress processes is weak and marginal. Using the emerging work in organizational practices and configurations, the authors reexamine this relationship by addressing three critical

Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materials

Science.gov (United States)

Li, Qiang; Popov, Valentin L.

2018-03-01

Recently proposed formulation of the boundary element method for adhesive contacts has been generalized for contacts of power-law graded materials with and without adhesion. Proceeding from the fundamental solution for single force acting on the surface of an elastic half space, first the influence matrix is obtained for a rectangular grid. The inverse problem for the calculation of required stress in the contact area from a known surface displacement is solved using the conjugate-gradient technique. For the transformation between the stresses and displacements, the Fast Fourier Transformation is used. For the adhesive contact of graded material, the detachment criterion based on the energy balance is proposed. The method is validated by comparison with known exact analytical solutions as well as by proving the independence of the mesh size and the grid orientation.

Stress-sensitive tissue regeneration in viscoelastic biomaterials subjected to modulated tensile strain.

Science.gov (United States)

Belfiore, Laurence A; Floren, Michael L; Paulino, Alexandre T; Belfiore, Carol J

2011-09-01

This research contribution addresses the mechanochemistry of intra-tissue mass transfer for nutrients, oxygen, growth factors, and other essential ingredients that anchorage-dependent cells require for successful proliferation on biocompatible surfaces. The unsteady state reaction-diffusion equation (i.e., modified diffusion equation) is solved according to the von Kármán-Pohlhausen integral method of boundary layer analysis when nutrient consumption and tissue regeneration are stimulated by harmonically imposed stress. The mass balance with diffusion and stress-sensitive kinetics represents a rare example where the Damköhler and Deborah numbers appear together in an effort to simulate the development of mass transfer boundary layers in porous viscoelastic biomaterials. The Boltzmann superposition integral is employed to calculate time-dependent strain in terms of the real and imaginary components of dynamic compliance for viscoelastic solids that transmit harmonic excitation to anchorage-dependent cells. Rates of nutrient consumption under stress-free conditions are described by third-order kinetics which include local mass densities of nutrients, oxygen, and attached cells that maintain dynamic equilibrium with active protein sites in the porous matrix. Thinner nutrient mass transfer boundary layers are stabilized at shorter dimensionless diffusion times when the stress-free intra-tissue Damköhler number increases above its initial-condition-sensitive critical value. The critical stress-sensitive intra-tissue Damköhler number, above which it is necessary to consider the effect of harmonic strain on nutrient consumption and tissue regeneration, is proportional to the Deborah number and corresponds to a larger fraction of the stress-free intra-tissue Damköhler number in rigid biomaterials. Copyright © 2011 Elsevier B.V. All rights reserved.

DESIGN AND EXAMINATION OF ALGORITHMS FOR SOLVING THE KNAPSACK PROBLEM

Directory of Open Access Journals (Sweden)

S. Kantsedal

2015-07-01

Full Text Available The use of methods of branches and boundaries as well as the methods of dynamic programming at solving the problem of «knapsack» is grounded. The main concepts are expounded. The methods and algorithms development for solving the above specified problem are described. Recommendations on practical application of constructed algorithms based on their experimental investigation and carrying out charactheristics comparison are presented.

Nonlinear vibration of a traveling belt with non-homogeneous boundaries

Science.gov (United States)

Ding, Hu; Lim, C. W.; Chen, Li-Qun

2018-06-01

Free and forced nonlinear vibrations of a traveling belt with non-homogeneous boundary conditions are studied. The axially moving materials in operation are always externally excited and produce strong vibrations. The moving materials with the homogeneous boundary condition are usually considered. In this paper, the non-homogeneous boundaries are introduced by the support wheels. Equilibrium deformation of the belt is produced by the non-homogeneous boundaries. In order to solve the equilibrium deformation, the differential and integral quadrature methods (DIQMs) are utilized to develop an iterative scheme. The influence of the equilibrium deformation on free and forced nonlinear vibrations of the belt is explored. The DIQMs are applied to solve the natural frequencies and forced resonance responses of transverse vibration around the equilibrium deformation. The Galerkin truncation method (GTM) is utilized to confirm the DIQMs' results. The numerical results demonstrate that the non-homogeneous boundary conditions cause the transverse vibration to deviate from the straight equilibrium, increase the natural frequencies, and lead to coexistence of square nonlinear terms and cubic nonlinear terms. Moreover, the influence of non-homogeneous boundaries can be exacerbated by the axial speed. Therefore, non-homogeneous boundary conditions of axially moving materials especially should be taken into account.

Revisit boundary conditions for the self-adjoint angular flux formulation

Energy Technology Data Exchange (ETDEWEB)

Wang, Yaqi [Idaho National Lab. (INL), Idaho Falls, ID (United States); Gleicher, Frederick N. [Idaho National Lab. (INL), Idaho Falls, ID (United States)

2015-03-01

We revisit the boundary conditions for SAAF. We derived the equivalent parity variational form ready for coding up. The more rigorous approach of evaluating odd parity should be solving the odd parity equation coupled with the even parity. We proposed a symmetric reflecting boundary condition although neither positive definiteness nor even-odd decoupling is achieved. A simple numerical test verifies the validity of these boundary conditions.

Suction of MHD boundary layer flows

International Nuclear Information System (INIS)

Rao, B.N.

1985-01-01

The boundary layer growth with tensor electrical conductivity and the transpiration number has been examined using local nonsimilarity solutions method. It is found that suction will cause the increase in wall shearing stress and decrease in thicknesses of the boundary layer. (Auth.)

Stress in piezoelectric hollow sphere with thermal gradient

International Nuclear Information System (INIS)

Saadatfar, M.; Rastgoo, A.

2008-01-01

The piezoelectric phenomenon has been exploited in science and engineering for decades. Recent advances in smart structures technology have led to a resurgence of interest in piezoelectricity, and in particular, in the solution of fundamental boundary value problems. In this paper, we develop an analytic solution to the axisymmetric problem of a radially polarized, spherically isotropic piezoelectric hollow sphere. The sphere is subjected to uniform internal pressure, or uniform external pressure, or both and thermal gradient. There is a constant thermal difference between its inner and outer surfaces. An analytic solution to the governing equilibrium equations (a coupled system of second-order ordinary differential equations) is obtained. On application of the boundary conditions, the problem is reduced to solving a system of linear algebraic equations. Finally, the stress distributions in the sphere are obtained numerically for two piezoceramics

Three-dimensional study of grain boundary engineering effects on intergranular stress corrosion cracking of 316 stainless steel in high temperature water

Science.gov (United States)

Liu, Tingguang; Xia, Shuang; Bai, Qin; Zhou, Bangxin; Zhang, Lefu; Lu, Yonghao; Shoji, Tetsuo

2018-01-01

The intergranular cracks and grain boundary (GB) network of a GB-engineered 316 stainless steel after stress corrosion cracking (SCC) test in high temperature high pressure water of reactor environment were investigated by two-dimensional and three-dimensional (3D) characterization in order to expose the mechanism that GB-engineering mitigates intergranular SCC. The 3D microstructure shown that the essential characteristic of the GB-engineered microstructure is formation of many large twin-boundaries as a result of multiple-twinning, which results in the formation of large grain-clusters. The large grain-clusters played a key role to the improvement of intergranular SCC resistance by GB-engineering. The main intergranular cracks propagated in a zigzag along the outer boundaries of these large grain-clusters because all inner boundaries of the grain-clusters were twin-boundaries (∑3) or twin-related boundaries (∑3n) which had much lower susceptibility to SCC than random boundaries. These large grain-clusters had tree-ring-shaped topology structure and very complex morphology. They got tangled so that difficult to be separated during SCC, resulting in some large crack-bridges retained in the crack surface.

Uniaxial stress-driven coupled grain boundary motion in hexagonal close-packed metals: A molecular dynamics study

International Nuclear Information System (INIS)

Zong, Hongxiang; Ding, Xiangdong; Lookman, Turab; Li, Ju; Sun, Jun

2015-01-01

Stress-driven grain boundary (GB) migration has been evident as a dominant mechanism accounting for plastic deformation in crystalline solids. Using molecular dynamics (MD) simulations on a Ti bicrystal model, we show that a uniaxial stress-driven coupling is associated with the recently observed 90° GB reorientation in shock simulations and nanopillar compression measurements. This is not consistent with the theory of shear-induced coupled GB migration. In situ atomic configuration analysis reveals that this GB motion is accompanied by the glide of two sets of parallel dislocation arrays, and the uniaxial stress-driven coupling is explained through a composite action of symmetrically distributed dislocations and deformation twins. In addition, the coupling factor is calculated from MD simulations over a wide range of temperatures. We find that the coupled motion can be thermally damped (i.e., not thermally activated), probably due to the absence of the collective action of interface dislocations. This uniaxial coupled mechanism is believed to apply to other hexagonal close-packed metals

A methodology for on-line calculation of temperature and thermal stress under non-linear boundary conditions

International Nuclear Information System (INIS)

Botto, D.; Zucca, S.; Gola, M.M.

2003-01-01

In the literature many works have been written dealing with the task of on-line calculation of temperature and thermal stress for machine components and structures, in order to evaluate fatigue damage accumulation and estimate residual life. One of the most widespread methodologies is the Green's function technique (GFT), by which machine parameters such as fluid temperatures, pressures and flow rates are converted into metal temperature transients and thermal stresses. However, since the GFT is based upon the linear superposition principle, it cannot be directly used in the case of varying heat transfer coefficients. In the present work, a different methodology is proposed, based upon CMS for temperature transient calculation and upon the GFT for the related thermal stress evaluation. This new approach allows variable heat transfer coefficients to be accounted for. The methodology is applied for two different case studies, taken from the literature: a thick pipe and a nozzle connected to a spherical head, both subjected to multiple convective boundary conditions

The disconnection mechanism of coupled migration and shear at grain boundaries

International Nuclear Information System (INIS)

Khater, H.A.; Serra, A.; Pond, R.C.; Hirth, J.P.

2012-01-01

The mechanism of coupled migration and shear is studied in a range of [0 0 0 1] tilt boundaries in hexagonal close-packed metal using atomic-scale computer simulation. Symmetrical tilt boundaries spanning the low- and high-angle regimes and comprising regular arrays of grain boundary dislocations are simulated. For each misorientation, θ, the perfect boundary (pristine) is investigated as well as one containing a disconnection. Both types of structures are subjected to incremental applied strains to determine the stress that produces coupled migration and shear. The stress for motion in the pristine case, entailing nucleation, is higher than the Peierls stress for motion when disconnections are present. We conclude that the applied stresses in our simulations exert a Peach–Koehler force on pre-existing disconnections, thereby providing a feasible mechanism with a well-defined driving force that produces coupled migration and shear. This mechanism is feasible for the lower-angle boundaries studied, and facile for the high-angle cases.

Post-traumatic stress disorder symptoms in emotionally distressed individuals referred for a depression prevention intervention: relationship to problem-solving skills.

Science.gov (United States)

Kasckow, J; Brown, C; Morse, J; Begley, A; Bensasi, S; Reynolds, C F

2012-11-01

This study examined the rates of syndromal and subthreshold post-traumatic stress disorder (PTSD) and PTSD symptom scores in participants with symptoms of emotional distress, subsyndromal depression, and a history of traumatic exposure. Participants had been referred to a study of an indicated depression prevention intervention using problem-solving therapy in primary care. We hypothesized that higher severity of PTSD symptom scores would predict poorer problem-solving skills. In addition, some reports have suggested that there are higher rates of PTSD in minority populations relative to Caucasians; thus we hypothesized that race would also predict problem-solving skills in these individuals. We examined the rates of traumatic exposure, syndromal, and subthreshold PTSD. In those exposed to trauma, we performed a multiple linear regression to examine the effects of PTSD symptoms, depression symptoms, race, age, and gender on social problem-solving skills. Of the 244 participants, 64 (26.2%) reported a traumatic event; 6/234 (2.6%) had syndromal PTSD, and 14/234 (6.0%) had subthreshold PTSD. By way of regression analysis, higher PTSD symptom scores predicted poorer problem-solving skills. In addition, racial status (Caucasian vs. African American) predicted problem-solving skills; Caucasians exhibited lower levels of problem-solving skills. Individuals presenting with subsyndromal depressive symptoms may also have a history of traumatic exposure, subthreshold and syndromal PTSD. Thus, screening these individuals for PTSD symptoms is important and may inform clinical management decisions because problem-solving skills are lower in those with more severe PTSD symptoms (even after adjusting for race, age, gender, and depressive symptoms). Copyright © 2011 John Wiley & Sons, Ltd.

The extended-domain-eigenfunction method for solving elliptic boundary value problems with annular domains

Energy Technology Data Exchange (ETDEWEB)

Aarao, J; Bradshaw-Hajek, B H; Miklavcic, S J; Ward, D A, E-mail: Stan.Miklavcic@unisa.edu.a [School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095 (Australia)

2010-05-07

Standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely, if ever, obtainable. In this paper, we propose a solution technique wherein we embed the original domain into one with simple boundaries where the classical eigenfunction solution approach can be used. The solution in the larger domain, when restricted to the original domain, is then the solution of the original boundary value problem. We call this the extended-domain-eigenfunction method. To illustrate the method's strength and scope, we apply it to Laplace's equation on an annular-like domain.

Hydromagnetic boundary layer micropolar fluid flow over a stretching surface embedded in a non-darcian porous medium with radiation

Directory of Open Access Journals (Sweden)

Mostafa A. A. Mahmoud

2006-01-01

Full Text Available We have studied the effects of radiation on the boundary layer flow and heat transfer of an electrically conducting micropolar fluid over a continuously moving stretching surface embedded in a non-Darcian porous medium with a uniform magnetic field. The transformed coupled nonlinear ordinary differential equations are solved numerically. The velocity, the angular velocity, and the temperature are shown graphically. The numerical values of the skin friction coefficient, the wall couple stress, and the wall heat transfer rate are computed and discussed for various values of parameters.

A variable K - planetary boundary layer model

International Nuclear Information System (INIS)

Misra, P.K.

1976-07-01

The steady-state, homogeneous and barotropic equations of motion within the planetary boundary layer are solved with the assumption that the coefficient of eddy viscosity varies as K(Z) = K 0 (1-Z/h)sup(p), where h is the height of the boundary layer and p a parameter which depends on the atmospheric stability. The solutions are compared with the observed velocity profiles based on the Wangara data. They compare favourably. (author)

Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields

Energy Technology Data Exchange (ETDEWEB)

Li, Yuan-Yuan; Cao, Junpeng [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Yang, Wen-Li [Institute of Modern Physics, Northwest University, Xian 710069 (China); Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing, 100048 (China); Shi, Kangjie [Institute of Modern Physics, Northwest University, Xian 710069 (China); Wang, Yupeng, E-mail: yupeng@iphy.ac.cn [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China)

2014-02-15

The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector is constructed. It is shown that the second eigenvalue problem can be transformed into that of the inhomogeneous XXX spin chain with arbitrary boundary fields which can be solved via the off-diagonal Bethe ansatz method.

Stress in hard metal films

NARCIS (Netherlands)

Janssen, G.C.A.M.; Kamminga, J.D.

2004-01-01

In the absence of thermal stress, tensile stress in hard metal films is caused by grain boundary shrinkage and compressive stress is caused by ion peening. It is shown that the two contributions are additive. Moreover tensile stress generated at the grain boundaries does not relax by ion

MHD Steady/Unsteady Porous Boundary Layer of Cu–Water Nanofluid with Micropolar Effect over a Permeable Surface

Directory of Open Access Journals (Sweden)

Kamal Raslan

2018-05-01

Full Text Available This work provides a mathematical model for the cooling process of a moving surface, in the presence of a uniform external magnetic field and thermal radiation, through a porous medium by using a weak concentration micropolar nanofluid. The model—based on the conservation equations of the unsteady case in the momentum and thermal boundary layer—takes into consideration the effect of the suction process. The conservation equations were transformed into ordinary differential equations using similar transformation techniques. The equations were solved numerically for the general case and analytically for the steady case. The rate of heat transfer, couple shear stress, and surface shear stress are deduced. We discuss the impact of these physical characteristics on the mechanical properties of the surface that will be cooled.

A finite difference method for free boundary problems

KAUST Repository

Fornberg, Bengt

2010-04-01

Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems. © 2009 Elsevier B.V. All rights reserved.

Data completion problems solved as Nash games

International Nuclear Information System (INIS)

Habbal, A; Kallel, M

2012-01-01

The Cauchy problem for an elliptic operator is formulated as a two-player Nash game. Player (1) is given the known Dirichlet data, and uses as strategy variable the Neumann condition prescribed over the inaccessible part of the boundary. Player (2) is given the known Neumann data, and plays with the Dirichlet condition prescribed over the inaccessible boundary. The two players solve in parallel the associated Boundary Value Problems. Their respective objectives involve the gap between the non used Neumann/Dirichlet known data and the traces of the BVP's solutions over the accessible boundary, and are coupled through a difference term. We prove the existence of a unique Nash equilibrium, which turns out to be the reconstructed data when the Cauchy problem has a solution. We also prove that the completion algorithm is stable with respect to noise, and present two 3D experiments which illustrate the efficiency and stability of our algorithm.

A method of solution of the elastic-plastic thermal stress problem

International Nuclear Information System (INIS)

Rafalski, P.

1975-01-01

The purpose of the work is an improvement of the numerical technique for calculating the thermal stress distribution in an elastic-plastic structural element. The work consists of two parts. In the first a new method of solution of the thermal stress problem for the elastic-plastic body is presented. In the second a particular numerical technique, based on the above method, for calculating the stress and strain fields is proposed. A new mathematical approach consists in treating the stress and strain fields as mathematical objects defined in the space-time domain. The methods commonly applied use the stress and strain fields defined in the space domain and establish the relations between them at a given instant t. They reduce the problem to the system of ordinary differential equations with respect to time, which are usually solved with a step-by-step technique. The new method reduces the problem to the system of nonlinear algebraic equations. In the work the Hilbert space of admissible tensor fields is constructed. This space is the orthogonal sum of two subspaces: of statically admissible and kinematically admissible fields. Two alternative orthogonality conditions, which correspond to the equilibrium and compatibility equations with the appropriate boundary conditions, are derived. The results of the work are to be used for construction of the computer program for calculation the stress and strain fields in the elastic-plastic body with a prescribed temperature field in the interior and appropriate displacement and force conditions on the boundary

Microstructural sensitivity of 316H austenitic stainless steel: Residual stress relaxation and grain boundary fracture

Energy Technology Data Exchange (ETDEWEB)

Chen, B., E-mail: b.chen@bristol.ac.uk [Department of Mechanical Engineering, University of Bristol, Bristol BS8 1TR (United Kingdom); Flewitt, P.E.J. [Interface Analysis Centre, University of Bristol, 121 St Michael' s Hill, Bristol BS2 8BS (United Kingdom); H.H. Wills Physics Laboratory, School of Physics, University of Bristol, Tyndall Avenue, Bristol BS8 1TL (United Kingdom); Smith, D.J. [Department of Mechanical Engineering, University of Bristol, Bristol BS8 1TR (United Kingdom)

2010-10-25

Research highlights: {yields} Triaxial residual macro-stresses have been measured by neutron diffraction. {yields} Rates of stress relaxation are shown to be a function of the microstructure. {yields} Quantification of M{sub 23}C{sub 6} precipitation was undertaken by a novel approach. {yields} Intergranular M{sub 23}C{sub 6} precipitation promotes the potential to intergranular fracture. {yields} Phosphorous segregation further enhances the potential to intergranular fracture. - Abstract: The present work considers the role of thermo-mechanical history on the generation and relaxation of residual stresses, typical of those encountered in Type 316H austenitic stainless steel thick section weldments. A series of thermo-mechanical pre-treatments have been developed and applied to simulate the critical microstructures observed within the heat affected zone of the thick section parent material. The through thickness distributions of the residual macro-stresses in cylindrical specimens have been measured by neutron diffraction and then the rates of the relaxation are shown to be a function of microstructure. The susceptibility to intergranular brittle fracture at a temperature of -196 deg. C is shown to be a function of M{sub 23}C{sub 6} carbide precipitates and phosphorous segregation at the grain boundaries. Finally, the link of the present study to the understanding of the reheat cracking is briefly discussed.

Stress-deformed state of cylindrical specimens during indirect tensile strength testing

Directory of Open Access Journals (Sweden)

Levan Japaridze

2015-10-01

Full Text Available In this study, the interaction between cylindrical specimen made of homogeneous, isotropic, and linearly elastic material and loading jaws of any curvature is considered in the Brazilian test. It is assumed that the specimen is diametrically compressed by elliptic normal contact stresses. The frictional contact stresses between the specimen and platens are neglected. The analytical solution starts from the contact problem of the loading jaws of any curvature and cylindrical specimen. The contact width, corresponding loading angle (2θ0, and elliptical stresses obtained through solution of the contact problems are used as boundary conditions for a cylindrical specimen. The problem of the theory of elasticity for a cylinder is solved using Muskhelishvili's method. In this method, the displacements and stresses are represented in terms of two analytical functions of a complex variable. In the main approaches, the nonlinear interaction between the loading bearing blocks and the specimen as well as the curvature of their surfaces and the elastic parameters of their materials are taken into account. Numerical examples are solved using MATLAB to demonstrate the influence of deformability, curvature of the specimen and platens on the distribution of the normal contact stresses as well as on the tensile and compressive stresses acting across the loaded diameter. Derived equations also allow calculating the modulus of elasticity, total deformation modulus and creep parameters of the specimen material based on the experimental data of radial contraction of the specimen.

Numerical analysis of viscoelastic boundary layers : the case of plate withdrawal in a Maxwellian fluid

International Nuclear Information System (INIS)

Sadeghy, K.; Sharifi, M.

2002-01-01

The effect of a fluid's elasticity on the characteristics of its boundary layer was investigated in this work. A viscoelastic fluid of Maxwellian type was selected for this purpose and the flow induced in this fluid by a plate withdrawing at a constant velocity was studied. Conventional boundary layer assumptions were invoked to reduce the equations of motion to a simple form incorporating an elastic term in addition to the familiar inertial, viscous and pressure terms. It was shown that for elastic effects to be of an importance in a boundary layer, the fluid's relaxation time should be of an order much larger than its kinematic viscosity. By introducing a stream function, the governing equation was transformed into a nonlinear ODE with x-coordinate still appearing in the equation demonstrating that no similarity solution existed for this flow. The resulting equation was then solved numerically for Deborah numbers as large as 1.0. The results showed a marked formation of boundary layer adjacent to a moving wall for a Maxwellian fluid. The boundary layer thickness and the wall shear stress were found to scale with fluid's elasticity - both decreasing the higher the fluid's elasticity. It is thus anticipated that in free coating processes, the force required to impart a constant velocity to a withdrawing belt or plate would be lower if fluid's elasticity is significant. (author)

The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions

DEFF Research Database (Denmark)

Johannessen, Kim

2014-01-01

The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions can be expressed in terms of the Jacobi elliptic functions. The boundary conditions determine the modulus of the Jacobi elliptic functions. The boundary conditions can not be solved analytically...

A Boundary Property for Upper Domination

KAUST Repository

AbouEisha, Hassan M.

2016-08-08

An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality.The problem of finding an upper dominating set is generally NP-hard, but can be solved in polynomial time in some restricted graph classes, such as P4-free graphs or 2K2-free graphs.For classes defined by finitely many forbidden induced subgraphs, the boundary separating difficult instances of the problem from polynomially solvable ones consists of the so called boundary classes.However, none of such classes has been identified so far for the upper dominating set problem.In the present paper, we discover the first boundary class for this problem.

Boundary element methods applied to two-dimensional neutron diffusion problems

International Nuclear Information System (INIS)

Itagaki, Masafumi

1985-01-01

The Boundary element method (BEM) has been applied to two-dimensional neutron diffusion problems. The boundary integral equation and its discretized form have been derived. Some numerical techniques have been developed, which can be applied to critical and fixed-source problems including multi-region ones. Two types of test programs have been developed according to whether the 'zero-determinant search' or the 'source iteration' technique is adopted for criticality search. Both programs require only the fluxes and currents on boundaries as the unknown variables. The former allows a reduction in computing time and memory in comparison with the finite element method (FEM). The latter is not always efficient in terms of computing time due to the domain integral related to the inhomogeneous source term; however, this domain integral can be replaced by the equivalent boundary integral for a region with a non-multiplying medium or with a uniform source, resulting in a significant reduction in computing time. The BEM, as well as the FEM, is well suited for solving irregular geometrical problems for which the finite difference method (FDM) is unsuited. The BEM also solves problems with infinite domains, which cannot be solved by the ordinary FEM and FDM. Some simple test calculations are made to compare the BEM with the FEM and FDM, and discussions are made concerning the relative merits of the BEM and problems requiring future solution. (author)

Thermal stresses investigation of a gas turbine blade

Science.gov (United States)

Gowreesh, S.; Pravin, V. K.; Rajagopal, K.; Veena, P. H.

2012-06-01

The analysis of structural and thermal stress values that are produced while the turbine is operating are the key factors of study while designing the next generation gas turbines. The present study examines structural, thermal, modal analysis of the first stage rotor blade of a two stage gas turbine. The design features of the turbine segment of the gas turbine have been taken from the preliminary design of a power turbine for maximization of an existing turbojet engine with optimized dump gap of the combustion chamber, since the allowable temperature on the turbine blade dependents on the hot gas temperatures from the combustion chamber. In the present paper simplified 3-D Finite Element models are developed with governing boundary conditions and solved using the commercial FEA software ANSYS. As the temperature has a significant effect on the overall stress on the rotor blades, a detail study on mechanical and thermal stresses are estimated and evaluated with the experimental values.

On Hydromagnetic Stresses in Accretion Disk Boundary Layers

DEFF Research Database (Denmark)

Pessah, Martin Elias; Chan, Chi-kwan

2012-01-01

Detailed calculations of the physical structure of accretion disk boundary layers, and thus their inferred observational properties, rely on the assumption that angular momentum transport is opposite to the radial angular frequency gradient of the disk. The standard model for turbulent shear...... of efficient angular momentum transport in the inner disk regions. This suggests that the detailed structure of turbulent MHD accretion disk boundary layers could differ appreciably from those derived within the standard framework of turbulent shear viscosity...

Interactive problem solving using LOGO

CERN Document Server

Boecker, Heinz-Dieter; Fischer, Gerhard

2014-01-01

This book is unique in that its stress is not on the mastery of a programming language, but on the importance and value of interactive problem solving. The authors focus on several specific interest worlds: mathematics, computer science, artificial intelligence, linguistics, and games; however, their approach can serve as a model that may be applied easily to other fields as well. Those who are interested in symbolic computing will find that Interactive Problem Solving Using LOGO provides a gentle introduction from which one may move on to other, more advanced computational frameworks or more

Influence of the lithosphere-asthenosphere boundary on the stress field northwest of the Alps

Science.gov (United States)

Maury, J.; Cornet, F. H.; Cara, M.

2014-11-01

In 1356, a magnitude 6-7 earthquake occurred near Basel, in Switzerland. But recent compilations of GPS measurements reveal that measured horizontal deformation rates in northwestern continental Europe are smaller than error bars on the measurements, proving present tectonic activity, if any, is very small in this area. We propose to reconcile these apparently antinomic observations with a mechanical model of the lithosphere that takes into account the geometry of the lithosphere-asthenosphere boundary, assuming that the only loading mechanism is gravity. The lithosphere is considered to be an elastoplastic material satisfying a Von Mises plasticity criterion. The model, which is 400 km long, 360 km wide and 230 km thick, is centred near Belfort in eastern France, with its width oriented parallel to the N145°E direction. It also takes into account the real topography of both the ground surface and that of the Moho discontinuity. Not only does the model reproduce observed principal stress directions orientations, it also identifies a plastic zone that fits roughly the most seismically active domain of the region. Interestingly, a somewhat similar stress map may be produced by considering an elastic lithosphere and an ad-hoc horizontal `tectonic' stress field. However, for the latter model, examination of the plasticity criterion suggests that plastic deformation should have taken place. It is concluded that the present-day stress field in this region is likely controlled by gravity and rheology, rather than by active Alpine tectonics.

Boundary effects in quantum field theory

International Nuclear Information System (INIS)

Deutsch, D.; Candelas, P.

1979-01-01

Electromagnetic and scalar fields are quantized in the region near an arbitrary smooth boundary, and the renormalized expectation value of the stress-energy tensor is calculated. The energy density is found to diverge as the boundary is approached. For nonconformally invariant fields it varies, to leading order, as the inverse fourth power of the distance from the boundary. For conformally invariant fields the coefficient of this leading term is zero, and the energy density varies as the inverse cube of the distance. An asymptotic series for the renormalized stress-energy tensor is developed as far as the inverse-square term in powers of the distance. Some criticisms are made of the usual approach to this problem, which is via the ''renormalized mode sum energy,'' a quantity which is generically infinite. Green's-function methods are used in explicit calculations, and an iterative scheme is set up to generate asymptotic series for Green's functions near a smooth boundary. Contact is made with the theory of the asymptotic distribution of eigenvalues of the Laplacian operator. The method is extended to nonflat space-times and to an example with a nonsmooth boundary

Effects of boundary conditions on thermomechanical calculations: Spent fuel test - climax

International Nuclear Information System (INIS)

Butkovich, T.R.

1982-10-01

The effects of varying certain boundary conditions on the results of finite-element calculations were studied in relation to the Spent Fuel Test - Climax. The study employed a thermomechanical model with the ADINA structural analysis. Nodal temperature histories were generated with the compatible ADINAT heat flow codes. The boundary conditions studied included: (1) The effect of boundary loading on three progressively larger meshes. (2) Plane strain vs plane stress conditions. (3) The effect of isothermal boundaries on a small mesh and on a significantly larger mesh. The results showed that different mesh sizes had an insignificant effect on isothermal boundaries up to 5 y, while on the smallest and largest mesh, the maximum temperature difference in the mesh was 0 C. In the corresponding ADINA calculation, these different mesh sizes produce insignificant changes in the stress field and displacements in the region of interest near the heat sources and excavations. On the other hand, plane stress produces horizontal and vertical stress differences approx. 9% higher than does plane strain

Microstructure and stress corrosion cracking of the fusion boundary region in an alloy 182-A533B low alloy steel dissimilar weld joint

International Nuclear Information System (INIS)

Hou, Juan; Peng, Qunjia; Takeda, Yoichi; Kuniya, Jiro; Shoji, Tetsuo

2010-01-01

Research highlights: → High-angle misorientation at FB, type-II and type-I boundaries. → Highest residual strain and hardness in the zone between FB and type-II boundary. → Type-II and type-I boundaries had lower resistance to SCC growth than the FB. → Crack growth blunted by pitting at the FB. → Reactivation of crack growth from the pitting by oxidation along the grain boundary. - Abstract: Stress corrosion cracking (SCC) in the fusion boundary (FB) region of an Alloy 182-A533B low alloy steel (LAS) dissimilar weld joint in high temperature water doped with sulfate was studied following a microstructure characterization of the FB region. The microstructure characterization suggested the type-II and type-I boundaries in the dilution zone (DZ) adjacent to the FB had lower resistance to SCC growth than the FB. Crack propagating perpendicular to the FB in the DZ was observed to be blunted by pitting at the FB, followed by the reactivation from the pitting by localized oxidation along the grain boundary in LAS.

Identifying Phase Space Boundaries with Voronoi Tessellations

CERN Document Server

Debnath, Dipsikha; Kilic, Can; Kim, Doojin; Matchev, Konstantin T.; Yang, Yuan-Pao

2016-11-24

Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis.

[Stress analysis of femoral stems in cementless total hip arthroplasty by two-dimensional finite element method using boundary friction layer].

Science.gov (United States)

Oomori, H; Imura, S; Gesso, H

1992-04-01

To develop stem design achieving primary fixation of stems and effective load transfer to the femur, we studied stress analysis of stems in cementless total hip arthroplasty by two-dimensional finite element method using boundary friction layer in stem-bone interface. The results of analyses of stem-bone interface stresses and von Mises stresses at the cortical bones indicated that ideal stem design features would be as follows: 1) Sufficient length, with the distal end extending beyond the isthmus region. 2) Maximum possible width, to contact the cortical bones in the isthmus region. 3) No collars but a lateral shoulder at the proximal portion. 4) A distal tip, to contact the cortical bones at the distal portion.

Perturbed solutions of fixed boundary MHD equilibria

International Nuclear Information System (INIS)

Portone, A.

2004-01-01

In this study, the fixed boundary plasma MHD equilibrium problem is solved by the finite element method; then, by perturbing the flux at the plasma boundary nodes, linear formulae are derived linking the variation of several plasma parameters of interest to the variation of the currents flowing in the external circuits. On the basis of these formulae it is shown how it is possible to efficiently solve two central problems in plasma engineering, namely (1) the optimization of the currents in a given set of coils necessary to maintain a specified equilibrium configuration and (2) the derivation of a linear dynamic model describing the plasma axisymmetric displacement (n = 0 mode) about a given magnetic configuration. A case study-based on the ITER reference equilibrium magnetic configuration at burn-is analysed both in terms of equilibrium currents optimality as well as axisymmetric stability features. The results obtained by these formulae are also compared with the predictions of a non-linear free boundary code and of a linear, dynamic model. As shown, the formulae derived here are in good agreement with such predictions, confirming the validity of the present approach. (author)

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

Science.gov (United States)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

Domain decomposition method for solving elliptic problems in unbounded domains

International Nuclear Information System (INIS)

Khoromskij, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.

1991-01-01

Computational aspects of the box domain decomposition (DD) method for solving boundary value problems in an unbounded domain are discussed. A new variant of the DD-method for elliptic problems in unbounded domains is suggested. It is based on the partitioning of an unbounded domain adapted to the given asymptotic decay of an unknown function at infinity. The comparison of computational expenditures is given for boundary integral method and the suggested DD-algorithm. 29 refs.; 2 figs.; 2 tabs

Application of the method finite elements by numerical modeling stress-strain state in conveyor belts

OpenAIRE

Maras Michal; Hatala Jozef; Marasová Daniela

1997-01-01

Solving problems connected with damaging a conveyor belt at the transfer points is conditioned by knowing laws of this phenomenon. Acquiring the knowledge on this phenomen is possible to be gained either by experimental research or by the numerical model GEM 22, which enables to determine the distribution of stresses and strains in a suitably selected cross-section of a conveyor belt. The paper begins by defining the problem, determining the boundary model conditions and continues by modellin...

A Hamiltonian-based derivation of Scaled Boundary Finite Element Method for elasticity problems

International Nuclear Information System (INIS)

Hu Zhiqiang; Lin Gao; Wang Yi; Liu Jun

2010-01-01

The Scaled Boundary Finite Method (SBFEM) is a semi-analytical solution approach for solving partial differential equation. For problem in elasticity, the governing equations can be obtained by mechanically based formulation, Scaled-boundary-transformation-based formulation and principle of virtual work. The governing equations are described in the frame of Lagrange system and the unknowns are displacements. But in the solution procedure, the auxiliary variables are introduced and the equations are solved in the state space. Based on the observation that the duality system to solve elastic problem proposed by W.X. Zhong is similar to the above solution approach, the discretization of the SBFEM and the duality system are combined to derive the governing equations in the Hamilton system by introducing the dual variables in this paper. The Precise Integration Method (PIM) used in Duality system is also an efficient method for the solution of the governing equations of SBFEM in displacement and boundary stiffness matrix especially for the case which results some numerical difficulties in the usually uses the eigenvalue method. Numerical examples are used to demonstrate the validity and effectiveness of the PIM for solution of boundary static stiffness.

DEM Simulation of Biaxial Compression Experiments of Inherently Anisotropic Granular Materials and the Boundary Effects

Directory of Open Access Journals (Sweden)

Zhao-Xia Tong

2013-01-01

Full Text Available The reliability of discrete element method (DEM numerical simulations is significantly dependent on the particle-scale parameters and boundary conditions. To verify the DEM models, two series of biaxial compression tests on ellipse-shaped steel rods are used. The comparisons on the stress-strain relationship, strength, and deformation pattern of experiments and simulations indicate that the DEM models are able to capture the key macro- and micromechanical behavior of inherently anisotropic granular materials with high fidelity. By using the validated DEM models, the boundary effects on the macrodeformation, strain localization, and nonuniformity of stress distribution inside the specimens are investigated using two rigid boundaries and one flexible boundary. The results demonstrate that the boundary condition plays a significant role on the stress-strain relationship and strength of granular materials with inherent fabric anisotropy if the stresses are calculated by the force applied on the wall. However, the responses of the particle assembly measured inside the specimens are almost the same with little influence from the boundary conditions. The peak friction angle obtained from the compression tests with flexible boundary represents the real friction angle of particle assembly. Due to the weak lateral constraints, the degree of stress nonuniformity under flexible boundary is higher than that under rigid boundary.

MPFA algorithm for solving stokes-brinkman equations on quadrilateral grids

KAUST Repository

Iliev, Oleg; Kirsch, Ralf; Lakdawala, Zahra; Printsypar, Galina

2014-01-01

This work is concerned with the development of a robust and accurate numerical method for solving the Stokes-Brinkman system of equations, which describes a free fluid flow coupled with a flow in porous media. Quadrilateral boundary fitted grid

Combined conduction and radiation in a two-layer planar medium with flux boundary condition

International Nuclear Information System (INIS)

Ho, C.H.; Ozisik, M.N.

1987-01-01

The interaction of conduction and radiation is investigated under both transient and steady-state conditions for an absorbing, emitting, and isotropically scattering two-layer slab having opaque coverings at both boundaries. The slab is subjected to an externally applied constant heat flux at one boundary surface and dissipates heat by radiation into external ambients from both boundary surfaces. An analytic approach is applied to solve the radiation part of the problem, and a finite-difference scheme is used to solve the conduction part. The effects of the conduction-to-radiation parameter, the single scattering albedo, the optical thickness, and the surface emissivity on the temperature distribution are examined

An Improvement of the Differential Transformation Method and Its Application for Boundary Layer Flow of a Nanofluid

Directory of Open Access Journals (Sweden)

Abdelhalim Ebaid

2013-01-01

Full Text Available The main feature of the boundary layer flow problems of nanofluids or classical fluids is the inclusion of the boundary conditions at infinity. Such boundary conditions cause difficulties for any of the series methods when applied to solve such a kind of problems. In order to solve these difficulties, the authors usually resort to either Padé approximants or the commercial numerical codes. However, an intensive work is needed to perform the calculations using Padé technique. Due to the importance of the nanofluids flow as a growing field of research and the difficulties caused by using Padé approximants to solve such problems, a suggestion is proposed in this paper to map the semi-infinite domain into a finite one by the help of a transformation. Accordingly, the differential equations governing the fluid flow are transformed into singular differential equations with classical boundary conditions which can be directly solved by using the differential transformation method. The numerical results obtained by using the proposed technique are compared with the available exact solutions, where excellent accuracy is found. The main advantage of the present technique is the complete avoidance of using Padé approximants to treat the infinity boundary conditions.

Prediction of dislocation boundary characteristics

DEFF Research Database (Denmark)

Winther, Grethe

Plastic deformation of both fcc and bcc metals of medium to high stacking fault energy is known to result in dislocation patterning in the form of cells and extended planar dislocation boundaries. The latter align with specific crystallographic planes, which depend on the crystallographic......) and it is found that to a large extent the dislocations screen each other’s elastic stress fields [3]. The present contribution aims at advancing the previous theoretical analysis of a boundary on a known crystallographic plane to actual prediction of this plane as well as other boundary characteristics....... Crystal plasticity calculations combined with the hypothesis that these boundaries separate domains with local differences in the slip system activity are introduced to address precise prediction of the experimentally observed boundaries. The presentation will focus on two cases from fcc metals...

Stress gradients in CrN coatings

NARCIS (Netherlands)

Janssen, G.C.A.M.; Tichelaar, F.D.; Visser, C.C.G.

2006-01-01

Stress in hard films is the net sum of tensile stress generated at the grain boundaries, compressive stress due to ion peening, and thermal stress due to the difference in thermal expansion of the coating and substrate. The tensile part due to grain boundaries is thickness dependent. The other two

A study on infinite number of integrals of motion in classically integrable system with boundary: Pt.1

International Nuclear Information System (INIS)

Chen Yixin; Luo Xudong

1998-01-01

By the zero curvature condition in classically integrable system, the generating functions for integrals of motion and equations for solving K +- matrices are obtained in two-dimensional integrable systems on a finite interval with independent boundary conditions on each end. Classically integrable boundary conditions will be found by solving K +- matrices. The authors develop a Hamiltonian method in classically integrable system with independent boundary conditions on each end. The result can be applied to more integrable systems than those associated with E.K. Sklyanin's approach

Hybrid immersed interface-immersed boundary methods for AC dielectrophoresis

International Nuclear Information System (INIS)

Hossan, Mohammad Robiul; Dillon, Robert; Dutta, Prashanta

2014-01-01

Dielectrophoresis, a nonlinear electrokinetic transport mechanism, has become popular in many engineering applications including manipulation, characterization and actuation of biomaterials, particles and biological cells. In this paper, we present a hybrid immersed interface–immersed boundary method to study AC dielectrophoresis where an algorithm is developed to solve the complex Poisson equation using a real variable formulation. An immersed interface method is employed to obtain the AC electric field in a fluid media with suspended particles and an immersed boundary method is used for the fluid equations and particle transport. The convergence of the proposed algorithm as well as validation of the hybrid scheme with experimental results is presented. In this paper, the Maxwell stress tensor is used to calculate the dielectrophoretic force acting on particles by considering the physical effect of particles in the computational domain. Thus, this study eliminates the approximations used in point dipole methods for calculating dielectrophoretic force. A comparative study between Maxwell stress tensor and point dipole methods for computing dielectrophoretic forces are presented. The hybrid method is used to investigate the physics of dielectrophoresis in microfluidic devices using an AC electric field. The numerical results show that with proper design and appropriate selection of applied potential and frequency, global electric field minima can be obtained to facilitate multiple particle trapping by exploiting the mechanism of negative dielectrophoresis. Our numerical results also show that electrically neutral particles form a chain parallel to the applied electric field irrespective of their initial orientation when an AC electric field is applied. This proposed hybrid numerical scheme will help to better understand dielectrophoresis and to design and optimize microfluidic devices

Large Eddy Simulation of the ventilated wave boundary layer

DEFF Research Database (Denmark)

Lohmann, Iris P.; Fredsøe, Jørgen; Sumer, B. Mutlu

2006-01-01

A Large Eddy Simulation (LES) of (1) a fully developed turbulent wave boundary layer and (2) case 1 subject to ventilation (i.e., suction and injection varying alternately in phase) has been performed, using the Smagorinsky subgrid-scale model to express the subgrid viscosity. The model was found...... slows down the flow in the full vertical extent of the boundary layer, destabilizes the flow and decreases the mean bed shear stress significantly; whereas suction generally speeds up the flow in the full vertical extent of the boundary layer, stabilizes the flow and increases the mean bed shear stress...

Grain boundary selective oxidation and intergranular stress corrosion crack growth of high-purity nickel binary alloys in high-temperature hydrogenated water

Energy Technology Data Exchange (ETDEWEB)

Bruemmer, S. M.; Olszta, M. J.; Toloczko, M. B.; Schreiber, D. K.

2018-02-01

The effects of alloying elements in Ni-5at%X binary alloys on intergranular (IG) corrosion and stress corrosion cracking (SCC) have been assessed in 300-360°C hydrogenated water at the Ni/NiO stability line. Alloys with Cr or Al additions exhibited grain boundary oxidation and IGSCC, while localized degradation was not observed for pure Ni, Ni-Cu or Ni-Fe alloys. Environment-enhanced crack growth was determined by comparing the response in water and N2 gas. Results demonstrate that selective grain boundary oxidation of Cr and Al promoted IGSCC of these Ni alloys in hydrogenated water.

Universal equations of unsteady two-dimensional MHD boundary layer whose temperature varies with time

Directory of Open Access Journals (Sweden)

Boričić Zoran

2009-01-01

Full Text Available This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50ºC . Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation.

Boundary layer on a flat plate with suction

International Nuclear Information System (INIS)

Favre, A.; Dumas, R.; Verollet, E.

1961-01-01

This research done in wind tunnel concerns the turbulent boundary layer of a porous flat plate with suction. The porous wall is 1 m long and begins 1 m downstream of the leading edge. The Reynolds number based on the boundary layer thickness is of the order of 16.300. The suction rate defined as the ratio of the velocity perpendicular to the wall to the external flow velocity ranges from 0 to 2 per cent. The pressure gradient can be controlled. The mean velocity profiles have been determined for various positions and suction rates by means of total pressure probes together with the intensities of the turbulent velocity fluctuations components, energy spectra and correlations by means of hot wire anemometers, spectral analyser and correlator. The stream lines, the values of the viscous and turbulent shear stresses, of the local wall friction, of the turbulent energy production term, with some information on the dissipation of the energy have been derived from these measurements. For these data the integral of equation of continuity in boundary layer have been drawn. The suction effects on the boundary layer are important. The suction thoroughly alters the mean velocity profiles by increasing the viscous shear stresses near the wall and decreasing them far from the wall, it diminishes the longitudinal and transversal turbulence intensities, the turbulent shear stresses, and the production of energy of turbulence. These effects are much stressed in the inner part of the boundary layer. On the other hand the energy spectra show that the turbulence scale is little modified, the boundary layer thickness being not much diminished by the suction. The suction effects can be appreciated by comparing twice the suction rate to the wall friction coefficient (assumed airtight), quite noticeable as soon as the rate is about unity, they become very important when it reaches ten. (author) [fr

Identifying phase-space boundaries with Voronoi tessellations

International Nuclear Information System (INIS)

Debnath, Dipsikha; Matchev, Konstantin T.; Gainer, James S.; Kilic, Can; Yang, Yuan-Pao; Kim, Doojin

2016-01-01

Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase-space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis. (orig.)

Identifying phase-space boundaries with Voronoi tessellations

Energy Technology Data Exchange (ETDEWEB)

Debnath, Dipsikha; Matchev, Konstantin T. [University of Florida, Physics Department, Gainesville, FL (United States); Gainer, James S. [University of Hawaii, Department of Physics and Astronomy, Honolulu, HI (United States); Kilic, Can; Yang, Yuan-Pao [The University of Texas at Austin, Theory Group, Department of Physics and Texas Cosmology Center, Austin, TX (United States); Kim, Doojin [University of Florida, Physics Department, Gainesville, FL (United States); CERN, Theory Division, Geneva 23 (Switzerland)

2016-11-15

Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase-space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis. (orig.)

The role of prominence in determining the scope of boundary-related lengthening in Greek.

Science.gov (United States)

Katsika, Argyro

2016-03-01

This study aims at examining and accounting for the scope of the temporal effect of phrase boundaries. Previous research has indicated that there is an interaction between boundary-related lengthening and prominence such that the former extends towards the nearby prominent syllable. However, it is unclear whether this interaction is due to lexical stress and/or phrasal prominence (marked by pitch accent) and how far towards the prominent syllable the effect extends. Here, we use an electromagnetic articulography (EMA) study of Greek to examine the scope of boundary-related lengthening as a function of lexical stress and pitch accent separately. Boundaries are elicited by the means of a variety of syntactic constructions.. The results show an effect of lexical stress. Phrase-final lengthening affects the articulatory gestures of the phrase-final syllable that are immediately adjacent to the boundary in words with final stress, but is initiated earlier within phrase-final words with non-final stress. Similarly, the articulatory configurations during inter-phrasal pauses reach their point of achievement later in words with final stress than in words with non-final stress. These effects of stress hold regardless of whether the phrase-final word is accented or de-accented. Phrase-initial lengthening, on the other hand, is consistently detected on the phrase-initial constriction, independently of where the stress is within the preceding, phrase-final, word. These results indicate that the lexical aspect of prominence plays a role in determining the scope of boundary-related lengthening in Greek. Based on these results, a gestural account of prosodic boundaries in Greek is proposed in which lexical and phrasal prosody interact in a systematic and coordinated fashion. The cross-linguistic dimensions of this account and its implications for prosodic structure are discussed.

Boundary element simulation of petroleum reservoirs with hydraulically fractured wells

Science.gov (United States)

Pecher, Radek

The boundary element method is applied to solve the linear pressure-diffusion equation of fluid-flow in porous media. The governing parabolic partial differential equation is transformed into the Laplace space to obtain the elliptic modified-Helmholtz equation including the homogeneous initial condition. The free- space Green's functions, satisfying this equation for anisotropic media in two and three dimensions, are combined with the generalized form of the Green's second identity. The resulting boundary integral equation is solved by following the collocation technique and applying the given time-dependent boundary conditions of the Dirichlet or Neumann type. The boundary integrals are approximated by the Gaussian quadrature along each element of the discretized domain boundary. Heterogeneous regions are represented by the sectionally-homogeneous zones of different rock and fluid properties. The final values of the interior pressure and velocity fields and of their time-derivatives are found by numerically inverting the solutions from the Laplace space by using the Stehfest's algorithm. The main extension of the mostly standard BEM-procedure is achieved in the modelling of the production and injection wells represented by internal sources and sinks. They are treated as part of the boundary by means of special single-node and both-sided elements, corresponding to the line and plane sources respectively. The wellbore skin and storage effects are considered for the line and cylindrical sources. Hydraulically fractured wells of infinite conductivity are handled directly according to the specified constraint type, out of the four alternatives. Fractures of finite conductivity are simulated by coupling the finite element model of their 1D-interior with the boundary element model of their 2D- exterior. Variable fracture width, fractures crossing zone boundaries, ``networking'' of fractures, fracture-tip singularity handling, or the 3D-description are additional advanced

Application of the perturbation iteration method to boundary layer type problems.

Science.gov (United States)

Pakdemirli, Mehmet

2016-01-01

The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution technique. The inner and outer solutions are determined with the iteration algorithm and matched to construct a composite expansion valid within all parts of the domain. The solutions are contrasted with the available exact or numerical solutions. It is shown that the perturbation-iteration algorithm can be effectively used for solving boundary layer type problems.

Development of a Positive Youth Development Program: Promoting the Mental Health of Stressful Adolescents Using Principles of Problem Solving Therapy

Directory of Open Access Journals (Sweden)

Daniel T.L. Shek

2006-01-01

Full Text Available This paper outlines the proposal for the development, implementation, and evaluation of a positive youth development program that attempts to promote the mental health of stressful Chinese adolescents using principles of Problem Solving Therapy (PST. There are two general aims of PST: to help clients identify life difficulties and resolve them, as well as to teach them skills on how to deal with future problems. The proposed project will utilize the principles of PST as the guiding framework to run two mental health promotion courses for adolescents who are experiencing disturbing stressful responses and students who want to improve their stress management style. Both objective and subjective outcome evaluation strategies will be carried out to assess the effectiveness of the intervention to promote the psychological well-being in adolescents who are experiencing stress. A related sample proposal is described that can give social workers some insight on how to prepare a proposal for developing the Tier 2 Program of the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programs.

An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

Directory of Open Access Journals (Sweden)

A. H. Bhrawy

2014-01-01

Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

Investigation of slip transfer across HCP grain boundaries with application to cold dwell facet fatigue

International Nuclear Information System (INIS)

Zheng, Zebang; Balint, Daniel S.; Dunne, Fionn P.E.

2017-01-01

This paper addresses the role of grain boundary slip transfer and thermally-activated discrete dislocation plasticity in the redistribution of grain boundary stresses during cold dwell fatigue in titanium alloys. Atomistic simulations have been utilised to calculate the grain boundary energies for titanium with respect to the misorientation angles. The grain boundary energies are utilised within a thermally-activated discrete dislocation plasticity model incorporating slip transfer controlled by energetic and grain boundary geometrical criteria. The model predicts the grain size effect on the flow strength in Ti alloys. Cold dwell fatigue behaviour in Ti-6242 alloy is investigated and it is shown that significant stress redistribution from soft to hard grains occurs during the stress dwell, which is observed both for grain boundaries for which slip transfer is permitted and inhibited. However, the grain boundary slip penetration is shown to lead to significantly higher hard-grain basal stresses near the grain boundary after dwell, thus exacerbating the load shedding stress compared to an impenetrable grain boundary. The key property controlling the dwell fatigue response is argued to remain the time constant associated with the thermal activation process for dislocation escape, but the slip penetrability is also important and exacerbates the load shedding. The inclusion of a macrozone does not significantly change the conclusions but does potentially lead to the possibility of a larger initial facet.

APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS

Directory of Open Access Journals (Sweden)

Vorona Yu.V.

2015-12-01

Full Text Available Boundary Integral Equation Method is used for solving analytically the problems of coupled thermoelastic spherical wave propagation. The resulting mathematical expressions coincide with the solutions obtained in a conventional manner.

A finite volume procedure for fluid flow, heat transfer and solid-body stress analysis

KAUST Repository

Jagad, P. I.

2018-04-12

A unified cell-centered unstructured mesh finite volume procedure is presented for fluid flow, heat transfer and solid-body stress analysis. An in-house procedure (A. W. Date, Solution of Transport Equations on Unstructured Meshes with Cell-Centered Colocated Variables. Part I: Discretization, International Journal of Heat and Mass Transfer, vol. 48 (6), 1117-1127, 2005) is extended to include the solid-body stress analysis. The transport terms for a cell-face are evaluated in a structured grid-like manner. The Cartesian gradients at the center of each cell-face are evaluated using the coordinate transformation relations. The accuracy of the procedure is demonstrated by solving several benchmark problems involving different boundary conditions, source terms, and types of loading.

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.)

An axisymmetric boundary element formulation of sound wave propagation in fluids including viscous and thermal losses

DEFF Research Database (Denmark)

Cutanda Henriquez, Vicente; Juhl, Peter Møller

2013-01-01

are solved using extended boundary conditions that account for: i) negligible temperature fluctuations at the boundary, and ii) normal and tangential matching of the boundary’s particle velocity. The proposed model does not require constructing a special mesh for the viscous and thermal boundary layers...

Mode solutions for a Klein-Gordon field in anti-de Sitter spacetime with dynamical boundary conditions of Wentzell type

Science.gov (United States)

Dappiaggi, Claudio; Ferreira, Hugo R. C.; Juárez-Aubry, Benito A.

2018-04-01

We study a real, massive Klein-Gordon field in the Poincaré fundamental domain of the (d +1 )-dimensional anti-de Sitter (AdS) spacetime, subject to a particular choice of dynamical boundary conditions of generalized Wentzell type, whereby the boundary data solves a nonhomogeneous, boundary Klein-Gordon equation, with the source term fixed by the normal derivative of the scalar field at the boundary. This naturally defines a field in the conformal boundary of the Poincaré fundamental domain of AdS. We completely solve the equations for the bulk and boundary fields and investigate the existence of bound state solutions, motivated by the analogous problem with Robin boundary conditions, which are recovered as a limiting case. Finally, we argue that both Robin and generalized Wentzell boundary conditions are distinguished in the sense that they are invariant under the action of the isometry group of the AdS conformal boundary, a condition which ensures in addition that the total flux of energy across the boundary vanishes.

Effects of microscopic boundary conditions on plastic deformations of small-sized single crystals

DEFF Research Database (Denmark)

Kuroda, Mitsutoshi; Tvergaard, Viggo

2009-01-01

The finite deformation version of the higher-order gradient crystal plasticity model proposed by the authors is applied to solve plane strain boundary value problems, in order to obtain an understanding of the effect of the higher-order boundary conditions. Numerical solutions are carried out...

Efficient modelling of aerodynamic flows in the boundary layer for high performance computing

CSIR Research Space (South Africa)

Smith, L

2011-01-01

Full Text Available A unique technique to couple boundary-layer solutions with an inviscid solver is introduced. The boundary-layer solution is obtained using the two-integral method to solve displacement thickness with Newton’s method, at a fraction of the cost of a...

Stress Transfer Processes during Great Plate Boundary Thrusting Events: A Study from the Andaman and Nicobar Segments

Science.gov (United States)

Andrade, V.; Rajendran, K.

2010-12-01

The response of subduction zones to large earthquakes varies along their strike, both during the interseismic and post-seismic periods. The December 26, 2004 earthquake nucleated at 3° N latitude and its rupture propagated northward, along the Andaman-Sumatra subduction zone, terminating at 15°N. Rupture speed was estimated at about 2.0 km per second in the northern part under the Andaman region and 2.5 - 2.7 km per second under southern Nicobar and North Sumatra. We have examined the pre and post-2004 seismicity to understand the stress transfer processes within the subducting plate, in the Andaman (10° - 15° N ) and Nicobar (5° - 10° N) segments. The seismicity pattern in these segments shows distinctive characteristics associated with the outer rise, accretionary prism and the spreading ridge, all of which are relatively better developed in the Andaman segment. The Ninety East ridge and the Sumatra Fault System are significant tectonic features in the Nicobar segment. The pre-2004 seismicity in both these segments conform to the steady-state conditions wherein large earthquakes are fewer and compressive stresses dominate along the plate interface. Among the pre-2004 great earthquakes are the 1881 Nicobar and 1941 Andaman events. The former is considered to be a shallow thrust event that generated a small tsunami. Studies in other subduction zones suggest that large outer-rise tensional events follow great plate boundary breaking earthquakes due to the the up-dip transfer of stresses within the subducting plate. The seismicity of the Andaman segment (1977-2004) concurs with the steady-state stress conditions where earthquakes occur dominantly by thrust faulting. The post-2004 seismicity shows up-dip migration along the plate interface, with dominance of shallow normal faulting, including a few outer rise events and some deeper (> 100 km) strike-slip faulting events within the subducting plate. The September 13, 2002, Mw 6.5 thrust faulting earthquake at

Discretization of the induced-charge boundary integral equation.

Science.gov (United States)

Bardhan, Jaydeep P; Eisenberg, Robert S; Gillespie, Dirk

2009-07-01

Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.

Discretization of the induced-charge boundary integral equation.

Energy Technology Data Exchange (ETDEWEB)

Bardhan, J. P.; Eisenberg, R. S.; Gillespie, D.; Rush Univ. Medical Center

2009-07-01

Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch et al. [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.

Real-time simulation of thermal stresses and creep in plates subjected to transient heat input

DEFF Research Database (Denmark)

Hattel, Jesper Henri; Jacobsen, Torben Krogsdal; Hansen, P.N.

1997-01-01

-difference approach. It applies a general formulation which takes into account nonconstant material properties (e.g. temperature, material, or time dependency), heat-transfer coefficients, and creep. The temperature calculation applies a one-dimensional numerical model, whereas the stress analysis is semi......This paper presents a novel numerical technique for solving the temperature and stress fields in a plate subjected to arbitrarily varying transient boundary conditions (transient temperature and heat-flux variations) on a surface. The numerical method is based on the control-volume finite......-two-dimensional. Both plane stress and plane strain conditions are considered as extreme cases. It is shown that, by using the developed numerical technique, very fast real-time simulations can be performed. The method has proved its applicability in e.g. high-pressure die-casting, and applications to this industrial...

Quasicontinuum analysis of dislocation-coherent twin boundary interaction to provide local rules to discrete dislocation dynamics

Science.gov (United States)

Tran, H.-S.; Tummala, H.; Duchene, L.; Pardoen, T.; Fivel, M.; Habraken, A. M.

2017-10-01

The interaction of a pure screw dislocation with a Coherent Twin Boundary Σ3 in copper was studied using the Quasicontinuum method. Coherent Twin Boundary behaves as a strong barrier to dislocation glide and prohibits slip transmission across the boundary. Dislocation pileup modifies the stress field at its intersection with the Grain Boundary (GB). A methodology to estimate the strength of the barrier for a dislocation to slip across CTB is proposed. A screw dislocation approaching the boundary from one side either propagates into the adjacent twin grain by cutting through the twin boundary or is stopped and increases the dislocation pileup amplitude at the GB. Quantitative estimation of the critical stress for transmission was performed using the virial stress computed by Quasicontinuum method. The transmission mechanism and critical stress are in line with the literature. Such information can be used as input for dislocation dynamic simulations for a better modeling of grain boundaries.

MHD Boundary Layer Slip Flow and Heat Transfer over a Flat Plate

International Nuclear Information System (INIS)

Bhattacharyya, Krishnendu; Mukhopadhyay, Swati; Layek, G. C.

2011-01-01

An analysis of magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with slip condition at the boundary is presented. A complete self-similar set of equations are obtained from the governing equations using similarity transformations and are solved by a shooting method. In the boundary slip condition no local similarity occurs. Velocity and temperature distributions within the boundary layer are presented. Our analysis reveals that the increase of magnetic and slip parameters reduce the boundary layer thickness and also enhance the heat transfer from the plate. (fundamental areas of phenomenology(including applications))

Functional geometric method for solving free boundary problems for harmonic functions

Energy Technology Data Exchange (ETDEWEB)

Demidov, Aleksander S [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)

2010-01-01

A survey is given of results and approaches for a broad spectrum of free boundary problems for harmonic functions of two variables. The main results are obtained by the functional geometric method. The core of these methods is an interrelated analysis of the functional and geometric characteristics of the problems under consideration and of the corresponding non-linear Riemann-Hilbert problems. An extensive list of open questions is presented. Bibliography: 124 titles.

Boundaries immersed in a scalar quantum field

International Nuclear Information System (INIS)

Actor, A.A.; Bender, I.

1996-01-01

We study the interaction between a scalar quantum field φ(x), and many different boundary configurations constructed from (parallel and orthogonal) thin planar surfaces on which φ(x) is constrained to vanish, or to satisfy Neumann conditions. For most of these boundaries the Casimir problem has not previously been investigated. We calculate the canonical and improved vacuum stress tensors left angle T μv (x) right angle and left angle direct difference μv (x) right angle of φ(x) for each example. From these we obtain the local Casimir forces on all boundary planes. For massless fields, both vacuum stress tensors yield identical attractive local Casimir forces in all Dirichlet examples considered. This desirable outcome is not a priori obvious, given the quite different features of left angle T μv (x) right angle and left angle direct difference μv (x) right angle. For Neumann conditions, left angle T μv (x) right angle and left angle direct difference μv (x) right angle lead to attractive Casimir stresses which are not always the same. We also consider Dirichlet and Neumann boundaries immersed in a common scalar quantum field, and find that these repel. The extensive catalogue of worked examples presented here belongs to a large class of completely solvable Casimir problems. Casimir forces previously unknown are predicted, among them ones which might be measurable. (orig.)

Sinc-collocation method for solving the Blasius equation

International Nuclear Information System (INIS)

Parand, K.; Dehghan, Mehdi; Pirkhedri, A.

2009-01-01

Sinc-collocation method is applied for solving Blasius equation which comes from boundary layer equations. It is well known that sinc procedure converges to the solution at an exponential rate. Comparison with Howarth and Asaithambi's numerical solutions reveals that the proposed method is of high accuracy and reduces the solution of Blasius' equation to the solution of a system of algebraic equations.

Determination of free boundary problem of flow through porous media

International Nuclear Information System (INIS)

Tavares Junior, H.M.; Souza, A.J. de

1989-01-01

This paper deals with a free boundary problem of flow through porous media, which is solved by simplicial method conbined with mesh refinement. Variational method on fixed domain is utilized. (author)

Stress analysis of fuel claddings with axial fins including creep effects

International Nuclear Information System (INIS)

Krieg, R.

1977-01-01

For LMFBR fuel claddings with axial fins the stress and strain fields are calculated which may be caused by internal pressure, differential thermal expansion and irradiation induced differential swelling. To provide an appropriate description of the cladding material it is assumed that the total strain is the sum of a linear elastic and a creep term, where the latter one includes the thermal as well as the irradiation induced creep. First the linear elastic problem is treated by a semi-analytical method leading to a bipotential equation for Airys' stress function. Solving this equation analytically means that the field equations valid within the cladding are satisfied exactly. By applying a combined point matching- least square-method the boundary conditions could be satisfied approximately such that in most cases the remaining error is within the uncertainty range of the loading conditions. Then the nonlinear problem which includes creep is approximated by a sequence of linear elastic solutions with time as parameter. The accumulated creep strain is treated here as an imposed strain field. To study the influence of different effects such as fin shape, temperature region, irradiation induced creep and swelling or internal pressure, a total of eleven cases with various parameter variations are investigated. The results are presented graphically in the following forms: stress and strain distributions over the cladding cross section for end of life conditions and boundary stresses and strains versus time. (Auth.)

Theoretical Analysis of Stress Distribution in Bonded Single Strap and Stiffened Joints

Directory of Open Access Journals (Sweden)

Behnam Ghoddous

Full Text Available Abstract In this paper, distribution of peeling stress in two types of adhesively-bonded joints is investigated. The joints are a single strap and a stiffened joint. Theses joints are under uniform tensile load and materials are assumed orthotropic. Layers can be identical or different in mechanical or geometrical properties. A two-dimensional elasticity theory that includes the complete stress-strain and the complete strain-displacement relations for adhesive and adherends is used in this analysis. The displacement is assumed to be linear in the adhesive layer. A set of differential equations was derived and solved by using appropriate boundary conditions. Results revealed that the peak peeling stress developed within the adhesive layer is a function of geometrical and mechanical properties. FEM solution is used as the second method to verify the analytical results. A good agreement is observed between analytical and FEM solutions.

Heat transfer, velocity-temperature correlation, and turbulent shear stress from Navier-Stokes computations of shock wave/turbulent boundary layer interaction flows

Science.gov (United States)

Wang, C. R.; Hingst, W. R.; Porro, A. R.

1991-01-01

The properties of 2-D shock wave/turbulent boundary layer interaction flows were calculated by using a compressible turbulent Navier-Stokes numerical computational code. Interaction flows caused by oblique shock wave impingement on the turbulent boundary layer flow were considered. The oblique shock waves were induced with shock generators at angles of attack less than 10 degs in supersonic flows. The surface temperatures were kept at near-adiabatic (ratio of wall static temperature to free stream total temperature) and cold wall (ratio of wall static temperature to free stream total temperature) conditions. The computational results were studied for the surface heat transfer, velocity temperature correlation, and turbulent shear stress in the interaction flow fields. Comparisons of the computational results with existing measurements indicated that (1) the surface heat transfer rates and surface pressures could be correlated with Holden's relationship, (2) the mean flow streamwise velocity components and static temperatures could be correlated with Crocco's relationship if flow separation did not occur, and (3) the Baldwin-Lomax turbulence model should be modified for turbulent shear stress computations in the interaction flows.

Boundary stress tensor and asymptotically AdS3 non-Einstein spaces at the chiral point

International Nuclear Information System (INIS)

Giribet, Gaston; Goya, Andres; Leston, Mauricio

2011-01-01

Chiral gravity admits asymptotically AdS 3 solutions that are not locally equivalent to AdS 3 ; meaning that solutions do exist which, while obeying the strong boundary conditions usually imposed in general relativity, happen not to be Einstein spaces. In topologically massive gravity (TMG), the existence of non-Einstein solutions is particularly connected to the question about the role played by complex saddle points in the Euclidean path integral. Consequently, studying (the existence of) nonlocally AdS 3 solutions to chiral gravity is relevant to understanding the quantum theory. Here, we discuss a special family of nonlocally AdS 3 solutions to chiral gravity. In particular, we show that such solutions persist when one deforms the theory by adding the higher-curvature terms of the so-called new massive gravity. Moreover, the addition of higher-curvature terms to the gravity action introduces new nonlocally AdS 3 solutions that have no analogues in TMG. Both stationary and time-dependent, axially symmetric solutions that asymptote AdS 3 space without being locally equivalent to it appear. Defining the boundary stress tensor for the full theory, we show that these non-Einstein geometries have associated vanishing conserved charges.

The causal boundary of wave-type spacetimes

International Nuclear Information System (INIS)

Flores, J.L.; Sanchez, M.

2008-01-01

A complete and systematic approach to compute the causal boundary of wave-type spacetimes is carried out. The case of a 1-dimensional boundary is specially analyzed and its critical appearance in pp-wave type spacetimes is emphasized. In particular, the corresponding results obtained in the framework of the AdS/CFT correspondence for holography on the boundary, are reinterpreted and very widely generalized. Technically, a recent new definition of causal boundary is used and stressed. Moreover, a set of mathematical tools is introduced (analytical functional approach, Sturm-Liouville theory, Fermat-type arrival time, Busemann-type functions)

Magnetohydrodynamic boundary layer on a wedge

International Nuclear Information System (INIS)

Rao, B.N.; Mittal, M.L.

1981-01-01

The effects of the Hall and ionslip currents on the gas-dynamic boundary layer are investigated in view of the increasing prospects for using the MHD principle in electric power generation. The currents are included in the analysis using the generalized Ohm's law (Sherman and Sutton, 1964), and the resulting two nonlinear coupled equations are solved using a modification in the method suggested by Nachtsheim and Swigert (1965), Dewey and Gross (1967), and Steinheuer (1968). Solutions are presented for the incompressible laminar boundary-layer equations in the absence and the presence of the load parameter, and for the pressure gradient parameter for flow separation

About potential of double layer and boundary value problems for Laplace equation

International Nuclear Information System (INIS)

Aleshin, M.V.

1991-01-01

An integral operator raisen by a kernel of the double layer's potential is investigated. The kernel is defined on S (S - two-digit variety of C 2 class presented by a boundary of the finite domain in R 3 ). The operator is considered on C(S). Following results are received: the operator's spectrum belongs to [-1,1]; it's eigenvalues and eigenfunctions may be found by Kellog's method; knowledge of the operator's spectrum is enough to construct it's resolvent. These properties permit to point out the determined interation processes, solving boundary value problems for Laplace equation. One of such processes - solving of Roben problem - is generalized on electrostatic problems. 6 refs

Effect of thermal exposure on the residual stress relaxation in a hardened cylindrical sample under creep conditions

Science.gov (United States)

Radchenko, V. P.; Saushkin, M. N.; Tsvetkov, V. V.

2016-05-01

This paper describes the effect of thermal exposure (high-temperature exposure) ( T = 675°C) on the residual creep stress relaxation in a surface hardened solid cylindrical sample made of ZhS6UVI alloy. The analysis is carried out with the use of experimental data for residual stresses after micro-shot peening and exposures to temperatures equal to T = 675°C during 50, 150, and 300 h. The paper presents the technique for solving the boundary-value creep problem for the hardened cylindrical sample with the initial stress-strain state under the condition of thermal exposure. The uniaxial experimental creep curves obtained under constant stresses of 500, 530, 570, and 600 MPa are used to construct the models describing the primary and secondary stages of creep. The calculated and experimental data for the longitudinal (axial) tensor components of residual stresses are compared, and their satisfactory agreement is determined.

Casimir stress in an inhomogeneous medium

International Nuclear Information System (INIS)

Philbin, T.G.; Xiong, C.; Leonhardt, U.

2010-01-01

The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz's theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wise homogeneous dielectrics with planar boundaries. A Casimir force per unit volume can be extracted from the infinite stress but it diverges on the boundaries between the inhomogeneous medium and the homogeneous dielectrics. An alternative regularization of the vacuum stress is considered that removes the contribution of the inhomogeneity over small distances, where macroscopic electromagnetism is invalid. The alternative regularization yields a finite Casimir stress inside the inhomogeneous region, but the stress and force per unit volume diverge on the boundaries with the homogeneous dielectrics. The case of inhomogeneous dielectrics with planar boundaries thus falls outside the current understanding of the Casimir effect.

Natural convection flow between moving boundaries | Chepkwony ...

African Journals Online (AJOL)

The two-point boundary value problem governing the flow is characterized by a non-dimensional parameter K. It is solved numerically using shooting method and the Newton-Raphson method to locate the missing initial conditions. The numerical results reveal that no solution exists beyond a critical value of K and that dual ...

Introducing the Boundary Element Method with MATLAB

Science.gov (United States)

Ang, Keng-Cheng

2008-01-01

The boundary element method provides an excellent platform for learning and teaching a computational method for solving problems in physical and engineering science. However, it is often left out in many undergraduate courses as its implementation is deemed to be difficult. This is partly due to the perception that coding the method requires…

On nonlinear statistical thermodynamics of boundary plasma with postactions

International Nuclear Information System (INIS)

Temko, S.W.; Temko, K.W.; Kuz'min, S.K.

1992-01-01

The authors use the statistical thermodynamics of small systems proposed before their publications for boundary weakly ionized plasma with postaction. Boundary properties of the plasma is taken into account by two ways: (1) suppose that only small number of very quick particles are able to leave the cloud having done entrance into outer medium work; (2) take into account the interaction between particles and inner surface of the cloud. Interactions in the boundary plasma are described by corresponding potential functions. The potential functions are mathematical models of real interactions in boundary plasma. Choosing of potential functions, their numerical parameters, geometrical form and dimensions of the cloud is made by using the methods of optimal experiment planning, maximum likelihood and computer experiment. Free energy of the cloud is a likelihood function. State of boundary plasma with admixtures is described by vector-density of particles distribution. Term ''distribution'' is used here in Sobolev-Schwartc sense. The authors obtain the vector-density of particles distribution in cloud which gives the condition minimum of free energy for every time moment under quasistatistical equilibrium. The system of conditions for free energy conditional minimizing for every time moment includes integral equilibrium equations, ''non-hard normalization'' and additional conditions taken as a result of analyzing physical and physical-chemical nature of boundary plasma. To obtain conditional minimum of free energy it is necessary to solve the system of conditions. First of all they solve equilibrium problem by the authors method. They obtain vector-density of particles distribution in the cloud. Then using method of random walk with postaction between sets of random walk process they build distribution function of random vector-density

Cumulative effects in strategic environmental assessment: The influence of plan boundaries

Energy Technology Data Exchange (ETDEWEB)

Bidstrup, Morten, E-mail: bidstrup@plan.aau.dk [Aalborg University (Denmark); Kørnøv, Lone, E-mail: lonek@plan.aau.dk [Aalborg University (Denmark); Partidário, Maria Rosário, E-mail: mariapartidario@tecnico.ulisboa.pt [CEG-IST, Instituto Superior Técnico, Universidade de Lisboa (Portugal)

2016-02-15

Cumulative effects (CE) assessment is lacking quality in impact assessment (IA) worldwide. It has been argued that the strategic environmental assessment (SEA) provides a suitable IA framework for addressing CE because it is applied to developments with broad boundaries, but few have tested this claim. Through a case study on the Danish mining sector, this article explores how plan boundaries influence the analytical boundaries applied for assessing CE in SEA. The case was studied through document analysis in combination with semi-structured group interviews of the responsible planners, who also serve as SEA practitioners. It was found that CE are to some extent assessed and managed implicitly throughout the planning process. However, this is through a focus on lowering the cumulative stress of mining rather than the cumulative stress on and capacity of the receiving environment. Plan boundaries do influence CE assessment, though all boundaries are not equally influential. The geographical and time boundaries of the Danish mining plans are broad or flexible enough to accommodate a meaningful assessment of CE, but the topical boundary is restrictive. The study indicates that collaboration among planning authorities and legally appointed CE leadership may facilitate better practice on CE assessment in sector-specific SEA contexts. However, most pressing is the need for relating assessment to the receiving environment as opposed to solely the stress of a proposed plan.

Cumulative effects in strategic environmental assessment: The influence of plan boundaries

International Nuclear Information System (INIS)

Bidstrup, Morten; Kørnøv, Lone; Partidário, Maria Rosário

2016-01-01

Cumulative effects (CE) assessment is lacking quality in impact assessment (IA) worldwide. It has been argued that the strategic environmental assessment (SEA) provides a suitable IA framework for addressing CE because it is applied to developments with broad boundaries, but few have tested this claim. Through a case study on the Danish mining sector, this article explores how plan boundaries influence the analytical boundaries applied for assessing CE in SEA. The case was studied through document analysis in combination with semi-structured group interviews of the responsible planners, who also serve as SEA practitioners. It was found that CE are to some extent assessed and managed implicitly throughout the planning process. However, this is through a focus on lowering the cumulative stress of mining rather than the cumulative stress on and capacity of the receiving environment. Plan boundaries do influence CE assessment, though all boundaries are not equally influential. The geographical and time boundaries of the Danish mining plans are broad or flexible enough to accommodate a meaningful assessment of CE, but the topical boundary is restrictive. The study indicates that collaboration among planning authorities and legally appointed CE leadership may facilitate better practice on CE assessment in sector-specific SEA contexts. However, most pressing is the need for relating assessment to the receiving environment as opposed to solely the stress of a proposed plan.

Sustainable knowledge development across cultural boundaries: Experiences from the EU-project SILMAS (Toolbox for conflict solving instruments in Alpine Lake Management)

Science.gov (United States)

Fegerl, Michael; Wieden, Wilfried

2013-04-01

Increasingly people have to communicate knowledge across cultural and language boundaries. Even though recent technologies offer powerful communication facilities people often feel confronted with barriers which clearly reduce their chances of making their interaction a success. Concrete evidence concerning such problems derives from a number of projects, where generated knowledge often results in dead-end products. In the Alpine Space-project SILMAS (Sustainable Instruments for Lake Management in Alpine Space), in which both authors were involved, a special approach (syneris® ) was taken to avoid this problem and to manage project knowledge in sustainable form. Under this approach knowledge input and output are handled interactively: Relevant knowledge can be developed continuously and users can always access the latest state of expertise. Resort to the respective tools and procedures can also assist in closing knowledge gaps and in developing innovative responses to familiar or novel problems. This contribution intends to describe possible ways and means which have been found to increase the chances of success of knowledge communication across cultural boundaries. The process of trans-cultural discussions of experts to find a standardized solution is highlighted as well as the problem of dissemination of expert knowledge to variant stakeholders. Finally lessons learned are made accessible, where a main task lies in the creation of a tool box for conflict solving instruments, as a demonstrable result of the project and for the time thereafter. The interactive web-based toolbox enables lake managers to access best practice instruments in standardized, explicit and cross-linguistic form.

Heat conduction in a plate-type fuel element with time-dependent boundary conditions

International Nuclear Information System (INIS)

Faya, A.J.G.; Maiorino, J.R.

1981-01-01

A method for the solution of boundary-value problems with variable boundary conditions is applied to solve a heat conduction problem in a plate-type fuel element with time dependent film coefficient. The numerical results show the feasibility of the method in the solution of this class of problems. (Author) [pt

Boundary integral method for torsion of composite shafts

International Nuclear Information System (INIS)

Chou, S.I.; Mohr, J.A.

1987-01-01

The Saint-Venant torsion problem for homogeneous shafts with simply or multiply-connected regions has received a great deal of attention in the past. However, because of the mathematical difficulties inherent in the problem, very few problems of torsion of shafts with composite cross sections have been solved analytically. Muskhelishvili (1963) studied the torsion problem for shafts with cross sections having several solid inclusions surrounded by an elastic material. The problem of a circular shaft reinforced by a non-concentric round inclusion, a rectangular shaft composed of two rectangular parts made of different materials were solved. In this paper, a boundary integral equation method, which can be used to solve problems more complex than those considered by Katsikadelis et. al., is developed. Square shaft with two dissimilar rectangular parts, square shaft with a square inclusion are solved and the results compared with those given in the reference cited above. Finally, a square shaft composed of two rectangular parts with circular inclusion is solved. (orig./GL)

Existence of solutions to boundary value problem of fractional differential equations with impulsive

Directory of Open Access Journals (Sweden)

Weihua JIANG

2016-12-01

Full Text Available In order to solve the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line, the existence of solutions to the boundary problem is specifically studied. By defining suitable Banach spaces, norms and operators, using the properties of fractional calculus and applying the contraction mapping principle and Krasnoselskii's fixed point theorem, the existence of solutions for the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line is proved, and examples are given to illustrate the existence of solutions to this kind of equation boundary value problems.

Coherent structures in wave boundary layers. Part 1. Oscillatory motion

DEFF Research Database (Denmark)

Carstensen, Stefan; Sumer, B. Mutlu; Fredsøe, Jørgen

2010-01-01

This work concerns oscillatory boundary layers over smooth beds. It comprises combined visual and quantitative techniques including bed shear stress measurements. The experiments were carried out in an oscillating water tunnel. The experiments reveal two significant coherent flow structures: (i......) Vortex tubes, essentially two-dimensional vortices close to the bed extending across the width of the boundary-layer flow, caused by an inflectional-point shear layer instability. The imprint of these vortices in the bed shear stress is a series of small, insignificant kinks and dips. (ii) Turbulent...... spots, isolated arrowhead-shaped areas close to the bed in an otherwise laminar boundary layer where the flow ‘bursts’ with violent oscillations. The emergence of the turbulent spots marks the onset of turbulence. Turbulent spots cause single or multiple violent spikes in the bed shear stress signal...

Inverse boundary element calculations based on structural modes

DEFF Research Database (Denmark)

Juhl, Peter Møller

2007-01-01

The inverse problem of calculating the flexural velocity of a radiating structure of a general shape from measurements in the field is often solved by combining a Boundary Element Method with the Singular Value Decomposition and a regularization technique. In their standard form these methods sol...

Mixed convection boundary layer flow over a moving vertical flat plate in an external fluid flow with viscous dissipation effect.

Directory of Open Access Journals (Sweden)

Norfifah Bachok

Full Text Available The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.

The effect of couple-stresses on the stress concentration around a moving crack

Directory of Open Access Journals (Sweden)

S. Itou

1981-01-01

Full Text Available The problem of a uniformly propagating finite crack in an infinite medium is solved within the linearized couple-stress theory. The self-equilibrated system of pressure is applied to the crack surfaces. The problem is reduced to dual integral equations and solved by a series-expansion method. The dynamic stress-intensity factor is computed numerically.

Modeling of Airfoil Trailing Edge Flap with Immersed Boundary Method

DEFF Research Database (Denmark)

Zhu, Wei Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær

2011-01-01

The present work considers incompressible flow over a 2D airfoil with a deformable trailing edge. The aerodynamic characteristics of an airfoil with a trailing edge flap is numerically investigated using computational fluid dynamics. A novel hybrid immersed boundary (IB) technique is applied...... to simulate the moving part of the trailing edge. Over the main fixed part of the airfoil the Navier-Stokes (NS) equations are solved using a standard body-fitted finite volume technique whereas the moving trailing edge flap is simulated with the immersed boundary method on a curvilinear mesh. The obtained...... results show that the hybrid approach is an efficient and accurate method for solving turbulent flows past airfoils with a trailing edge flap and flow control using trailing edge flap is an efficient way to regulate the aerodynamic loading on airfoils....

Couple stresses and the fracture of rock.

Science.gov (United States)

Atkinson, Colin; Coman, Ciprian D; Aldazabal, Javier

2015-03-28

An assessment is made here of the role played by the micropolar continuum theory on the cracked Brazilian disc test used for determining rock fracture toughness. By analytically solving the corresponding mixed boundary-value problems and employing singular-perturbation arguments, we provide closed-form expressions for the energy release rate and the corresponding stress-intensity factors for both mode I and mode II loading. These theoretical results are augmented by a set of fracture toughness experiments on both sandstone and marble rocks. It is further shown that the morphology of the fracturing process in our centrally pre-cracked circular samples correlates very well with discrete element simulations. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Study on the relationship between stress intensity factor and J integral for mixed mode crack with arbitrary inclination based on SBFEM

International Nuclear Information System (INIS)

Zhu, C L; Li, J B; Lin, G; Zhong, H

2010-01-01

The J integral and the stress intensity factor (SIF) K are both important research objects of fracture mechanics, and are often employed to establish criteria for crackpropagation. The relationship between them has always been a research hotspot. In this paper, the SIF can be obtained conveniently by the scaled boundary finite element method (SBFEM) due to the fact that analytical solution can be obtained along the radial direction for stress singularity problems. The J integral can be solved analytically using the formulae between J and K for mixed mode crack with arbitrary inclination in elastic materials. Moreover, the J integral values obtained by this method are more accurate and convenient than by its definition. Factors that affect the accuracy of SIF and J integral, such as the distance between the crack and outer boundary, size of the discretized elements and partition of the domain into super-elements, are examined.

A coupled boundary element-finite difference solution of the elliptic modified mild slope equation

DEFF Research Database (Denmark)

Naserizadeh, R.; Bingham, Harry B.; Noorzad, A.

2011-01-01

The modified mild slope equation of [5] is solved using a combination of the boundary element method (BEM) and the finite difference method (FDM). The exterior domain of constant depth and infinite horizontal extent is solved by a BEM using linear or quadratic elements. The interior domain...

Eigenstates of a particle in an array of hexagons with periodic boundary condition

Directory of Open Access Journals (Sweden)

A Nemati

2013-10-01

Full Text Available In this paper the problem of a particle in an array of hexagons with periodic boundary condition is solved. Using the projection operators, we categorize eigenfunctions corresponding to each of the irreducible representations of the symmetry group . Based on these results, the Dirichlet and Neumann boundary conditions are discussed.

Transpiration and film cooling boundary layer computer program. Volume 1: Numerical solutions of the turbulent boundary layer equations with equilibrium chemistry

Science.gov (United States)

Levine, J. N.

1971-01-01

A finite difference turbulent boundary layer computer program has been developed. The program is primarily oriented towards the calculation of boundary layer performance losses in rocket engines; however, the solution is general, and has much broader applicability. The effects of transpiration and film cooling as well as the effect of equilibrium chemical reactions (currently restricted to the H2-O2 system) can be calculated. The turbulent transport terms are evaluated using the phenomenological mixing length - eddy viscosity concept. The equations of motion are solved using the Crank-Nicolson implicit finite difference technique. The analysis and computer program have been checked out by solving a series of both laminar and turbulent test cases and comparing the results to data or other solutions. These comparisons have shown that the program is capable of producing very satisfactory results for a wide range of flows. Further refinements to the analysis and program, especially as applied to film cooling solutions, would be aided by the acquisition of a firm data base.

Solving PDEs in Python the FEniCS tutorial I

CERN Document Server

Langtangen, Hans Petter

2016-01-01

This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license.

Calculation of eddy viscosity in a compressible turbulent boundary layer with mass injection and chemical reaction, volume 1. [theoretical analysis

Science.gov (United States)

Omori, S.

1973-01-01

The turbulent kinetic energy equation is coupled with boundary layer equations to solve the characteristics of compressible turbulent boundary layers with mass injection and combustion. The Reynolds stress is related to the turbulent kinetic energy using the Prandtl-Wieghardt formulation. When a lean mixture of hydrogen and nitrogen is injected through a porous plate into the subsonic turbulent boundary layer of air flow and ignited by external means, the turbulent kinetic energy increases twice as much as that of noncombusting flow with the same mass injection rate of nitrogen. The magnitudes of eddy viscosity between combusting and noncombusting flows with injection, however, are almost the same due to temperature effects, while the distributions are different. The velocity profiles are significantly affected by combustion; that is, combustion alters the velocity profile as if the mass injection rate is increased, reducing the skin-friction as a result of a smaller velocity gradient at the wall. If pure hydrogen as a transpiration coolant is injected into a rocket nozzle boundary layer flow of combustion products, the temperature drops significantly across the boundary layer due to the high heat capacity of hydrogen. At a certain distance from the wall, hydrogen reacts with the combustion products, liberating an extensive amount of heat. The resulting large increase in temperature reduces the eddy viscosity in this region.

An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments

Science.gov (United States)

Tian, Fang-Bao; Luo, Haoxiang; Zhu, Luoding; Liao, James C.; Lu, Xi-Yun

2012-01-01

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish. PMID:23564971

An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments

Science.gov (United States)

Tian, Fang-Bao; Luo, Haoxiang; Zhu, Luoding; Liao, James C.; Lu, Xi-Yun

2011-08-01

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish.

RECTC/RECTCF, 2. Order Elliptical Partial Differential Equation, Arbitrary Boundary Conditions

International Nuclear Information System (INIS)

Hackbusch, W.

1983-01-01

1 - Description of problem or function: A general linear elliptical second order partial differential equation on a rectangle with arbitrary boundary conditions is solved. 2 - Method of solution: Multi-grid iteration

Deformation by grain boundary sliding and slip creep versus diffusional creep

International Nuclear Information System (INIS)

Ruano, O A; Sherby, O D; Wadsworth, J.

1998-01-01

A review is presented of the debates between the present authors and other investigators regarding the possible role of diffusional creep in the plastic flow of polycrystalline metals at low stresses. These debates are recorded in eleven papers over the past seventeen years. ln these papers it has been shown that the creep rates of materials in the so-called diffusional creep region are almost always higher than those predicted by the diffusional creep theory. Additionally, the predictions of grain size effects and stress exponents from diffusional creep theory are often not found in the experimental data. Finally, denuded zones have been universally considered to be direct evidence for diffusional creep; but, those reported in the literature are shown to be found only under conditions where a high stress exponent is observed. Also, the locations of the denuded zones do not match those predicted. Alternative mechanisms are described in which diffusion-controlled dislocation creep and/or grain boundary sliding are the dominant deformation processes in low-stress creep. It is proposed that denuded zones are formed by stress-directed grain boundary migration with the precipitates dissolving in the moving grain boundaries. The above observations have led us to the conclusion that grain boundary sliding and slip creep are in fact the principal mechanisms for observations of plastic flow in the so-called diffusional creep regions

Boundary conditions on the Jointed Block Test: A two-dimensional and three-dimensional finite element analysis of stresses and temperatures

International Nuclear Information System (INIS)

Hardy, M.P.; Mitchell, S.J.

1983-12-01

This report presents the results from a numerical modeling study which was performed in support of the analysis of data from the Near-Surface Test Facility Block Test. The objective of the work was to investigate the potential for features of the test geometry and construction to influence the uniformity of the stress distribution across the test block and generate anomalous deformational response characteristics during loading. The analysis results indicated that the components of the test set-up can modify the imposed boundary conditions and affect the stress distribution in the block. However, the influence of these conditions was not sufficient to generate the anomalous conditions observed in actual field data. 5 refs

Coping with organizational stress among hospital nurses in Southern Ontario.

Science.gov (United States)

Tyson, Paul D; Pongruengphant, Rana; Aggarwal, Bela

2002-05-01

Government cutbacks and anticipated staff reductions were hypothesized to be a unique source of organizational stress. The study focused on how nurses coped with stress and whether any strategy effectively reduced occupational stress. A sample of 107 nurses were asked to rate their occupational stress, job satisfaction, and coping strategies. Avoidance and social support were found to be significantly correlated with stress, but neither of these coping strategies appeared to reduce nurses' level of organizational stress. However, an interaction between problem solving and job satisfaction was found to be highly significant and it added 42% to predicting stress levels. Supporting the stress-buffering hypothesis, nurses with lower intrinsic job satisfaction seemed to benefit from employing problem solving as a coping strategy whereas dissatisfied nurses who infrequently use problem solving reported the highest levels of organizational stress. Paradoxically, intrinsically satisfied nurses who most frequently utilize problem solving experienced heightened organizational stress.

Stress field models from Maxwell stress functions: southern California

Science.gov (United States)

Bird, Peter

2017-08-01

The lithospheric stress field is formally divided into three components: a standard pressure which is a function of elevation (only), a topographic stress anomaly (3-D tensor field) and a tectonic stress anomaly (3-D tensor field). The boundary between topographic and tectonic stress anomalies is somewhat arbitrary, and here is based on the modeling tools available. The topographic stress anomaly is computed by numerical convolution of density anomalies with three tensor Green's functions provided by Boussinesq, Cerruti and Mindlin. By assuming either a seismically estimated or isostatic Moho depth, and by using Poisson ratio of either 0.25 or 0.5, I obtain four alternative topographic stress models. The tectonic stress field, which satisfies the homogeneous quasi-static momentum equation, is obtained from particular second derivatives of Maxwell vector potential fields which are weighted sums of basis functions representing constant tectonic stress components, linearly varying tectonic stress components and tectonic stress components that vary harmonically in one, two and three dimensions. Boundary conditions include zero traction due to tectonic stress anomaly at sea level, and zero traction due to the total stress anomaly on model boundaries at depths within the asthenosphere. The total stress anomaly is fit by least squares to both World Stress Map data and to a previous faulted-lithosphere, realistic-rheology dynamic model of the region computed with finite-element program Shells. No conflict is seen between the two target data sets, and the best-fitting model (using an isostatic Moho and Poisson ratio 0.5) gives minimum directional misfits relative to both targets. Constraints of computer memory, execution time and ill-conditioning of the linear system (which requires damping) limit harmonically varying tectonic stress to no more than six cycles along each axis of the model. The primary limitation on close fitting is that the Shells model predicts very sharp

Parallel algorithms for boundary value problems

Science.gov (United States)

Lin, Avi

1991-01-01

A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are twofold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.

Integral methods of solving boundary-value problems of nonstationary heat conduction and their comparative analysis

Science.gov (United States)

Kot, V. A.

2017-11-01

The modern state of approximate integral methods used in applications, where the processes of heat conduction and heat and mass transfer are of first importance, is considered. Integral methods have found a wide utility in different fields of knowledge: problems of heat conduction with different heat-exchange conditions, simulation of thermal protection, Stefantype problems, microwave heating of a substance, problems on a boundary layer, simulation of a fluid flow in a channel, thermal explosion, laser and plasma treatment of materials, simulation of the formation and melting of ice, inverse heat problems, temperature and thermal definition of nanoparticles and nanoliquids, and others. Moreover, polynomial solutions are of interest because the determination of a temperature (concentration) field is an intermediate stage in the mathematical description of any other process. The following main methods were investigated on the basis of the error norms: the Tsoi and Postol’nik methods, the method of integral relations, the Gudman integral method of heat balance, the improved Volkov integral method, the matched integral method, the modified Hristov method, the Mayer integral method, the Kudinov method of additional boundary conditions, the Fedorov boundary method, the method of weighted temperature function, the integral method of boundary characteristics. It was established that the two last-mentioned methods are characterized by high convergence and frequently give solutions whose accuracy is not worse that the accuracy of numerical solutions.

Granular rheology: measuring boundary forces with laser-cut leaf springs

Science.gov (United States)

Tang, Zhu; Brzinski, Theodore A.; Daniels, Karen E.

2017-06-01

In granular physics experiments, it is a persistent challenge to obtain the boundary stress measurements necessary to provide full a rheological characterization of the dynamics. Here, we describe a new technique by which the outer boundary of a 2D Couette cell both confines the granular material and provides spatially- and temporally- resolved stress measurements. This key advance is enabled by desktop laser-cutting technology, which allows us to design and cut linearly-deformable walls with a specified spring constant. By tracking the position of each segment of the wall, we measure both the normal and tangential stress throughout the experiment. This permits us to calculate the amount of shear stress provided by basal friction, and thereby determine accurate values of μ(I).

On the Role of Situational Stressors in the Disruption of Global Neural Network Stability during Problem Solving.

Science.gov (United States)

Liu, Mengting; Amey, Rachel C; Forbes, Chad E

2017-12-01

When individuals are placed in stressful situations, they are likely to exhibit deficits in cognitive capacity over and above situational demands. Despite this, individuals may still persevere and ultimately succeed in these situations. Little is known, however, about neural network properties that instantiate success or failure in both neutral and stressful situations, particularly with respect to regions integral for problem-solving processes that are necessary for optimal performance on more complex tasks. In this study, we outline how hidden Markov modeling based on multivoxel pattern analysis can be used to quantify unique brain states underlying complex network interactions that yield either successful or unsuccessful problem solving in more neutral or stressful situations. We provide evidence that brain network stability and states underlying synchronous interactions in regions integral for problem-solving processes are key predictors of whether individuals succeed or fail in stressful situations. Findings also suggested that individuals utilize discriminate neural patterns in successfully solving problems in stressful or neutral situations. Findings overall highlight how hidden Markov modeling can provide myriad possibilities for quantifying and better understanding the role of global network interactions in the problem-solving process and how the said interactions predict success or failure in different contexts.

A Contingency View of Problem Solving in Schools: A Case Analysis.

Science.gov (United States)

Hanson, E. Mark; Brown, Michael E.

Patterns of problem-solving activity in one middle-class urban high school are examined and a problem solving model rooted in a conceptual framework of contingency theory is presented. Contingency theory stresses that as political, economic, and social conditions in an organization's environment become problematic, the internal structures of the…

Numerical Treatment of Degenerate Diffusion Equations via Feller's Boundary Classification, and Applications

Science.gov (United States)

Cacio, Emanuela; Cohn, Stephen E.; Spigler, Renato

2011-01-01

A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.

Immersed boundary-simplified lattice Boltzmann method for incompressible viscous flows

Science.gov (United States)

Chen, Z.; Shu, C.; Tan, D.

2018-05-01

An immersed boundary-simplified lattice Boltzmann method is developed in this paper for simulations of two-dimensional incompressible viscous flows with immersed objects. Assisted by the fractional step technique, the problem is resolved in a predictor-corrector scheme. The predictor step solves the flow field without considering immersed objects, and the corrector step imposes the effect of immersed boundaries on the velocity field. Different from the previous immersed boundary-lattice Boltzmann method which adopts the standard lattice Boltzmann method (LBM) as the flow solver in the predictor step, a recently developed simplified lattice Boltzmann method (SLBM) is applied in the present method to evaluate intermediate flow variables. Compared to the standard LBM, SLBM requires lower virtual memories, facilitates the implementation of physical boundary conditions, and shows better numerical stability. The boundary condition-enforced immersed boundary method, which accurately ensures no-slip boundary conditions, is implemented as the boundary solver in the corrector step. Four typical numerical examples are presented to demonstrate the stability, the flexibility, and the accuracy of the present method.

Solution of Moving Boundary Space-Time Fractional Burger’s Equation

Directory of Open Access Journals (Sweden)

E. A.-B. Abdel-Salam

2014-01-01

Full Text Available The fractional Riccati expansion method is used to solve fractional differential equations with variable coefficients. To illustrate the effectiveness of the method, the moving boundary space-time fractional Burger’s equation is studied. The obtained solutions include generalized trigonometric and hyperbolic function solutions. Among these solutions, some are found for the first time. The linear and periodic moving boundaries for the kink solution of the Burger’s equation are presented graphically and discussed.

Acoustic scattering on spheroidal shapes near boundaries

Science.gov (United States)

Miloh, Touvia

2016-11-01

A new expression for the Lamé product of prolate spheroidal wave functions is presented in terms of a distribution of multipoles along the axis of the spheroid between its foci (generalizing a corresponding theorem for spheroidal harmonics). Such an "ultimate" singularity system can be effectively used for solving various linear boundary-value problems governed by the Helmholtz equation involving prolate spheroidal bodies near planar or other boundaries. The general methodology is formally demonstrated for the axisymmetric acoustic scattering problem of a rigid (hard) spheroid placed near a hard/soft wall or inside a cylindrical duct under an axial incidence of a plane acoustic wave.

Receptivity and Forced Response to Acoustic Disturbances in High-Speed Boundary Layers

Science.gov (United States)

Balakumar, P.; King, Rudolph A.; Chou, Amanda; Owens, Lewis R.; Kegerise, Michael A.

2016-01-01

Supersonic boundary-layer receptivity to freestream acoustic disturbances is investigated by solving the Navier-Stokes equations for Mach 3.5 flow over a sharp flat plate and a 7-deg half-angle cone. The freestream disturbances are generated from a wavy wall placed at the nozzle wall. The freestream acoustic disturbances radiated by the wavy wall are obtained by solving the linearized Euler equations. The results for the flat plate show that instability modes are generated at all the incident angles ranging from zero to highly oblique. However, the receptivity coefficient decreases by about 20 times when the incident angle increases from zero to a highly oblique angle of 68 degrees. The results for the cone show that no instability modes are generated when the acoustic disturbances impinge the cone obliquely. The results show that the perturbations generated inside the boundary layer by the acoustic disturbances are the response of the boundary layer to the external forcing. The amplitude of the forced disturbances inside the boundary layer are about 2.5 times larger than the incoming field for zero azimuthal wavenumber and they are about 1.5 times for large azimuthal wavenumbers.

Twin and grain boundary in InP: A synchrotron radiation study

International Nuclear Information System (INIS)

Han, Y.; Liu, X.; Jiao, J.; Lin, L.; Jiang, J.; Wang, Z.; Tian, Y.

1998-01-01

Experimentally observed X-ray reflectivity curves show bi-crystal(twin) characteristics. The study revealed that there was defect segregation at the twin boundary. Stress was relaxed at the edge of the boundary. Relaxation of the stress resulted in formation of twin and other defects. As a result of formation of such defects, a defect-free and stress-free zone or low defect density and small stress zone is created around the defects. So a twin model was proposed to explain the experimental results. Stress(mainly thermal stress), chemical stoichiometry deviation and impurities nonhomogeneous distributions are the key factors that cause twins in LEC InP crystal growth. Twins on (111) face in LEC InP crystal were studied. Experimental evidence of above mentioned twin model and suggestions on how to get twin-free LEC InP single crystals will be discussed

The kinetic boundary layer around an absorbing sphere and the growth of small droplets

International Nuclear Information System (INIS)

Widder, M.E.; Titulaer, U.M.

1989-01-01

Deviations from the classical Smoluchowski expression for the growth rate of a droplet in a supersaturated vapor can be expected when the droplet radius is not large compared to the mean free path of a vapor molecule. The growth rate then depends significantly on the structure of the kinetic boundary layer around a sphere. The authors consider this kinetic boundary layer for a dilute system of Brownian particles. For this system a large class of boundary layer problems for a planar wall have been solved. They show how the spherical boundary layer can be treated by a perturbation expansion in the reciprocal droplet radius. In each order one has to solve a finite number of planar boundary layer problems. The first two corrections to the planar problem are calculated explicitly. For radii down to about two velocity persistence lengths (the analog of the mean free path for a Brownian particle) the successive approximations for the growth rate agree to within a few percent. A reasonable estimate of the growth rate for all radii can be obtained by extrapolating toward the exactly known value at zero radius. Kinetic boundary layer effects increase the time needed for growth from 0 to 10 (or 2 1/2) velocity persistence lengths by roughly 35% (or 175%)

Diffuse interface immersed boundary method for multi-fluid flows with arbitrarily moving rigid bodies

Science.gov (United States)

Patel, Jitendra Kumar; Natarajan, Ganesh

2018-05-01

We present an interpolation-free diffuse interface immersed boundary method for multiphase flows with moving bodies. A single fluid formalism using the volume-of-fluid approach is adopted to handle multiple immiscible fluids which are distinguished using the volume fractions, while the rigid bodies are tracked using an analogous volume-of-solid approach that solves for the solid fractions. The solution to the fluid flow equations are carried out using a finite volume-immersed boundary method, with the latter based on a diffuse interface philosophy. In the present work, we assume that the solids are filled with a "virtual" fluid with density and viscosity equal to the largest among all fluids in the domain. The solids are assumed to be rigid and their motion is solved using Newton's second law of motion. The immersed boundary methodology constructs a modified momentum equation that reduces to the Navier-Stokes equations in the fully fluid region and recovers the no-slip boundary condition inside the solids. An implicit incremental fractional-step methodology in conjunction with a novel hybrid staggered/non-staggered approach is employed, wherein a single equation for normal momentum at the cell faces is solved everywhere in the domain, independent of the number of spatial dimensions. The scalars are all solved for at the cell centres, with the transport equations for solid and fluid volume fractions solved using a high-resolution scheme. The pressure is determined everywhere in the domain (including inside the solids) using a variable coefficient Poisson equation. The solution to momentum, pressure, solid and fluid volume fraction equations everywhere in the domain circumvents the issue of pressure and velocity interpolation, which is a source of spurious oscillations in sharp interface immersed boundary methods. A well-balanced algorithm with consistent mass/momentum transport ensures robust simulations of high density ratio flows with strong body forces. The

The effects of external conditions in turbulent boundary layers

Science.gov (United States)

Brzek, Brian G.

The effects of multiple external conditions on turbulent boundary layers were studied in detail. These external conditions include: surface roughness, upstream turbulence intensity, and pressure gradient. Furthermore, the combined effects of these conditions show the complicated nature of many realistic flow conditions. It was found that the effects of surface roughness are difficult to generalize, given the importance of so many parameters. These parameters include: roughness geometry, roughness regime, roughness height to boundary layer thickness, (k/delta), roughness parameter, ( k+), Reynolds number, and roughness function (Delta B+). A further complication, is the difficulty in computing the wall shear stress, tauw/rho. For the sand grain type roughness, the mean velocity and Reynolds stresses were studied in inner and outer variables, as well as, boundary layer parameters, anisotropy tensor, production term, and viscous stress and form drag contributions. To explore the effects of roughness and Reynolds number dependence in the boundary layer, a new experiment was carefully designed to properly capture the x-dependence of the single-point statistics. It was found that roughness destroys the viscous layer near the wall, thus, reducing the contribution of the viscous stress in the wall region. As a result, the contribution in the skin friction due to form drag increases, while the viscous stress decreases. This yields Reynolds number invariance in the skin friction, near-wall roughness parameters, and inner velocity profiles as k + increases into the fully rough regime. However, in the transitionally rough regime, (i.e., 5 component shows the largest influence of roughness, where the high peak near the wall was decreased and became nearly flat for the fully rough regime profiles. In addition, the Reynolds stresses in outer variables show self-similarity for fixed experimental conditions. However, as the roughness parameter, k +, increases, all Reynolds stress

Analysis and measurement of residual stress distribution of vanadium/ceramics joints for fusion reactor applications

International Nuclear Information System (INIS)

Nemoto, Y.; Ueda, K.

1998-01-01

Vanadium alloys are considered as candidate structural materials for fusion reactor system. When vanadium alloys are used in fusion reactor system, joining with ceramics for insulating is one of material issues to be solved to make component of fusion reactor. In the application of ceramics/metal jointing and coating, residual stress caused by difference of thermal expansion rate between ceramics and metals is an important factor in obtaining good bonding strength and soundness of coating. In this work, residual stress distribution in direct diffusion bonded vanadium/alumina joint (jointing temperature: 1400 C) was measured by small area X-ray diffraction method. And the comparison of finite element method (FEM) analysis and actual stress distribution was carried out. Tensile stress concentration at the edge of the boundary of the joint in alumina was observed. The residual stress concentration may cause cracks in alumina, or failure of bonding. Actually, cracks in alumina caused by thermal stress after bonding at 1500 C was observed. The stress concentration of the joint must be reduced to obtain good bonded joint. Lower bonding temperature or to devise the shape of the outer surface of the joint will reduce the stress concentration. (orig.)

A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

Science.gov (United States)

Liska, Sebastian; Colonius, Tim

2017-02-01

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3700 are used to verify the accuracy and physical fidelity of the formulation.

A Monotone, Higher-Order Accurate, Fixed-Grid Finite-Volume Method for Advection Problems with Moving Boundaries

NARCIS (Netherlands)

Y.J. Hassen (Yunus); B. Koren (Barry)

2008-01-01

textabstractIn this paper, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed Cartesian grid. The essence of the present method is

New deformation model of grain boundary strengthening in polycrystalline metals

International Nuclear Information System (INIS)

Trefilov, V.I.; Moiseev, V.F.; Pechkovskij, Eh.P.

1988-01-01

A new model explaining grain boundary strengthening in polycrystalline metals and alloys by strain hardening due to localization of plastic deformation in narrow bands near grain boundaries is suggested. Occurrence of localized deformation is caused by different flow stresses in grains of different orientation. A new model takes into account the active role of stress concentrator, independence of the strengthening coefficient on deformation, influence of segregations. Successful use of the model suggested for explanation of rhenium effect in molybdenum and tungsten is alloys pointed out

Boundary conditions in rational conformal field theories

International Nuclear Information System (INIS)

Behrend, Roger E.; Pearce, Paul A.; Petkova, Valentina B.; Zuber, Jean-Bernard

2000-01-01

We develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that solving Cardy's equation, expressing consistency of a RCFT on a cylinder, is equivalent to finding integer valued matrix representations of the Verlinde algebra. These matrices allow us to naturally associate a graph G to each RCFT such that the conformal boundary conditions are labelled by the nodes of G. This approach is carried to completion for sl(2) theories leading to complete sets of conformal boundary conditions, their associated cylinder partition functions and the A-D-E classification. We also review the current status for WZW sl(3) theories. Finally, a systematic generalisation of the formalism of Cardy-Lewellen is developed to allow for multiplicities arising from more general representations of the Verlinde algebra. We obtain information on the bulk-boundary coefficients and reproduce the relevant algebraic structures from the sewing constraints

Efficient method of solving the problems of steady-state oscillations of symmetric rectangular domains of general type

Directory of Open Access Journals (Sweden)

Олена Валентинівна Лупаренко

2015-03-01

Full Text Available When the wave processes in bounded elastic bodies are examined, we are faced with a significant complication of the structure of the wave field compared to the case of infinite bodies. This is due to the complex nature of the reflection of elastic waves from the boundaries of the body because the direction of the general flow of energy is changed. Even more complicated the structure of the wave field is, if there are inner boundaries between fields with different elastic properties. This entails the emergence of new wave effects associated with the dynamic stress concentration in the vicinity of the internal and external boundaries of the field. The nature of edge effects is changed too. They will depend not only from the size of the field but also from the geometric and elastic parameters defining the nature of heterogeneity. At the forefront are the questions of systematization of the results for the purpose of extradition of practical recommendations for optimal design of heterogeneous section details in particular conditions of its operation. Urgent enough is the question of the possibility of neglecting of structural heterogeneity and anisotropy of the section of the body in strengthening calculations and evaluation of possible errors. The mathematical basis for the study will be the expressions for particular solutions of equations of motion, constructed for infinite layers, which are sets of plane standing waves. When choosing the form of partial solutions, we must take into account not only the opportunity to satisfy the boundary conditions at the exterior boundary of the field, but also the mechanical properties at the interface of the sphere. This entails the complication of numerical-analytical algorithm of solving the problem

Requisite for Honing the Problem Solving Skill of Early Adolescents in the Digital Era

Science.gov (United States)

Sumitha, S.; Jose, Rexlin

2016-01-01

Problems can be the cause of stress, tension, emotional instability and physical strain. Especially, adolescents should have the skill of solving a problem in order to reach his/her desired ambitions in life. The problem solving skill requires some abstract thinking to arrive at a clear solution. Problem solving ability helps them to meet their…

Boundary element analysis of stress due to thermal shock loading or reactor pressure vessel nozzle; Napetostna analiza pri nestacionarni termicni obremenitvi cevnega prikljucka reaktorske tlacne posode z metodo robnih elementov

Energy Technology Data Exchange (ETDEWEB)

Kramberger, J; Potrc, I [Tehniska fakulteta, Maribor (Yugoslavia)

1989-07-01

Apart from being exposed to the primary loading of internal pressure and steady temperature field, the reactor pressure vessel is also subject to various thermal transients (thermal shocks). Theoretical and experimental stress analyses show that severe material stresses occur in the nozzle area of the pressure vessel which may lead to defects (cracks). It has been our aim to evaluate these stresses by the use of the Boundary Element method. (author)

Detection of Cavities by Inverse Heat Conduction Boundary Element Method Using Minimal Energy Technique

International Nuclear Information System (INIS)

Choi, C. Y.

1997-01-01

A geometrical inverse heat conduction problem is solved for the infrared scanning cavity detection by the boundary element method using minimal energy technique. By minimizing the kinetic energy of temperature field, boundary element equations are converted to the quadratic programming problem. A hypothetical inner boundary is defined such that the actual cavity is located interior to the domain. Temperatures at hypothetical inner boundary are determined to meet the constraints of measurement error of surface temperature obtained by infrared scanning, and then boundary element analysis is performed for the position of an unknown boundary (cavity). Cavity detection algorithm is provided, and the effects of minimal energy technique on the inverse solution method are investigated by means of numerical analysis

An interactive boundary layer modeling methodology for aerodynamic flows[Presentation

CSIR Research Space (South Africa)

Smith, L

2011-11-01

Full Text Available the Goldstein singularity without the need to solve the entire flow domain simultaneously. In this work the incompressible Navier- Stokes equations will be used for the outer flow. In the majority of previous studies the boundary layer thickness is simulated...

General quantitative analysis of stress partitioning and boundary conditions in undrained biphasic porous media via a purely macroscopic and purely variational approach

Science.gov (United States)

Serpieri, Roberto; Travascio, Francesco

2016-03-01

In poroelasticity, the effective stress law relates the external stress applied to the medium to the macroscopic strain of the solid phase and the interstitial pressure of the fluid saturating the mixture. Such relationship has been formerly introduced by Terzaghi in form of a principle. To date, no poroelastic theory is capable of recovering a stress partitioning law in agreement with Terzaghi's postulated one in the absence of ad hoc constitutive assumptions on the medium. We recently proposed a variational macroscopic continuum description of two-phase poroelasticity to derive a general biphasic formulation at finite deformations, termed variational macroscopic theory of porous media (VMTPM). Such approach proceeds from the inclusion of the intrinsic volumetric strain among the kinematic descriptors aside to macroscopic displacements, and as a variational theory, uses the Hamilton least-action principle as the unique primitive concept of mechanics invoked to derive momentum balance equations. In a previous related work it was shown that, for the subclass of undrained problems, VMTPM predicts that stress is partitioned in the two phases in strict compliance with Terzaghi's law, irrespective of the microstructural and constitutive features of a given medium. In the present contribution, we further develop the linearized framework of VMTPM to arrive at a general operative formula that allows the quantitative determination of stress partitioning in a jacketed test over a generic isotropic biphasic specimen. This formula is quantitative and general, in that it relates the partial phase stresses to the externally applied stress as function of partitioning coefficients that are all derived by strictly following a purely variational and purely macroscopic approach, and in the absence of any specific hypothesis on the microstructural or constitutive features of a given medium. To achieve this result, the stiffness coefficients of the theory are derived by using

Explicit formulation for natural frequencies of double-beam system with arbitrary boundary conditions

Energy Technology Data Exchange (ETDEWEB)

Mirzabeigy, Alborz; Madoliat, Reza [Iran University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of); Dabbagh, Vahid [University of Malaya, Kuala Lumpur (Malaysia)

2017-02-15

In this paper, free transverse vibration of two parallel beams connected through Winkler type elastic layer is investigated. Euler- Bernoulli beam hypothesis has been applied and it is assumed that boundary conditions of upper and lower beams are similar while arbitrary without any limitation even for non-ideal boundary conditions. Material properties and cross-section geometry of beams could be different from each other. The motion of the system is described by a homogeneous set of two partial differential equations, which is solved by using the classical Bernoulli-Fourier method. Explicit expressions are derived for the natural frequencies. In order to verify accuracy of results, the problem once again solved using modified Adomian decomposition method. Comparison between results indicates excellent accuracy of proposed formulation for any arbitrary boundary conditions. Derived explicit formulation is simplest method to determine natural frequencies of double-beam systems with high level of accuracy in comparison with other methods in literature.

Implicit constitutive models with a thermodynamic basis: a study of stress concentration

Science.gov (United States)

Bridges, C.; Rajagopal, K. R.

2015-02-01

Motivated by the recent generalization of the class of elastic bodies by Rajagopal (Appl Math 48:279-319, 2003), there have been several recent studies that have been carried out within the context of this new class. Rajagopal and Srinivasa (Proc R Soc Ser A 463:357-367, 2007, Proc R Soc Ser A: Math Phys Eng Sci 465:493-500, 2009) provided a thermodynamic basis for such models and appealing to the idea that rate of entropy production ought to be maximized they developed nonlinear rate equations of the form where T is the Cauchy stress and D is the stretching tensor as well as , where S is the Piola-Kirchhoff stress tensor and E is the Green-St. Venant strain tensor. We follow a similar procedure by utilizing the Gibb's potential and the left stretch tensor V from the Polar Decomposition of the deformation gradient, and we show that when the displacement gradient is small one arrives at constitutive relations of the form . This is, of course, in stark contrast to traditional elasticity wherein one obtains a single model, Hooke's law, when the displacement gradient is small. By solving a classical boundary value problem, with a particular form for f( T), we show that when the stresses are small, the strains are also small which is in agreement with traditional elasticity. However, within the context of our model, when the stress blows up the strains remain small, unlike the implications of Hooke's law. We use this model to study boundary value problems in annular domains to illustrate its efficacy.

Vibration analysis of rotating functionally graded Timoshenko microbeam based on modified couple stress theory under different temperature distributions

Science.gov (United States)

Ghadiri, Majid; Shafiei, Navvab

2016-04-01

In this study, thermal vibration of rotary functionally graded Timoshenko microbeam has been analyzed based on modified couple stress theory considering temperature change in four types of temperature distribution on thermal environment. Material properties of FG microbeam are supposed to be temperature dependent and vary continuously along the thickness according to the power-law form. The axial forces are also included in the model as the thermal and true spatial variation due to the rotation. Governing equations and boundary conditions have been derived by employing Hamiltonian's principle. The differential quadrature method is employed to solve the governing equations for cantilever and propped cantilever boundary conditions. Validations are done by comparing available literatures and obtained results which indicate accuracy of applied method. Results represent effects of temperature changes, different boundary conditions, nondimensional angular velocity, length scale parameter, different boundary conditions, FG index and beam thickness on fundamental, second and third nondimensional frequencies. Results determine critical values of temperature changes and other essential parameters which can be applicable to design micromachines like micromotor and microturbine.

Grain boundary composition and irradiation-assisted stress corrosion cracking resistance in Type 348 stainless steel

International Nuclear Information System (INIS)

Jacobs, A.J.; Wozadlo, G.P.; Nakata, K.

1994-01-01

Scanning transmission electron microscopy (STEM) analyses, in-reactor swelling mandrel tests, and laboratory constant extension rate tensile (CERT) tests were conducted on nine custom type 348 (UNS S34800) stainless steel (SS) alloys in an attempt to correlate grain boundary composition with irradiation-assisted stress corrosion cracking (IASCC) resistance. Phosphorus (P) enrichment showed the best correlation with in-reactor test results, and chromium (Cr) depletion showed the best correlation with laboratory results. Silicon (Si) and P enrichment were found to depend quantitatively on the bulk concentrations of these elements. The amount of Cr depletion seemed dependent at least partially on the amounts of Si and/or P enrichment. Si and P enrichment and Cr depletion were suppressed by higher carbon (C) contents, such as that present in commercial-purity type 348 SS

Analysis of the Slab Temperature, Thermal Stresses and Fractures Computed with the Implementation of Local and Average Boundary Conditions in the Secondary Cooling Zones

Directory of Open Access Journals (Sweden)

Hadała B.

2016-12-01

Full Text Available The numerical simulations of the temperature fields have been accomplished for slab casting made of a low carbon steel. The casting process of slab of 1500 mm in width and 225 mm in height has been modeled. Two types of boundary condition models of heat transfer have been employed in numerical simulations. The heat transfer coefficient in the first boundary condition model was calculated from the formula which takes into account the slab surface temperature and water flow rate in each secondary cooling zone. The second boundary condition model defines the heat transfer coefficient around each water spray nozzle. The temperature fields resulting from the average in zones water flow rate and from the nozzles arrangement have been compared. The thermal stresses and deformations resulted from such temperature field have given higher values of fracture criterion at slab corners.

Stress dependence of microstructures in experimentally deformed calcite

Science.gov (United States)

Platt, John P.; De Bresser, J. H. P.

2017-12-01

Optical measurements of microstructural features in experimentally deformed Carrara marble help define their dependence on stress. These features include dynamically recrystallized grain size (Dr), subgrain size (Sg), minimum bulge size (Lρ), and the maximum scale length for surface-energy driven grain-boundary migration (Lγ). Taken together with previously published data Dr defines a paleopiezometer over the range 15-291 MPa and temperature over the range 500-1000 °C, with a stress exponent of -1.09 (CI -1.27 to -0.95), showing no detectable dependence on temperature. Sg and Dr measured in the same samples are closely similar in size, suggesting that the new grains did not grow significantly after nucleation. Lρ and Lγ measured on each sample define a relationship to stress with an exponent of approximately -1.6, which helps define the boundary between a region of dominant strain-energy-driven grain-boundary migration at high stress, from a region of dominant surface-energy-driven grain-boundary migration at low stress.

Slip patterns and preferred dislocation boundary planes

DEFF Research Database (Denmark)

Winther, G.

2003-01-01

The planes of deformation induced extended planar dislocation boundaries are analysed in two different co-ordinate systems, namely the macroscopic system defined by the deformation axes and the crystallographic system given by the crystallographic lattice. The analysis covers single and polycryst......The planes of deformation induced extended planar dislocation boundaries are analysed in two different co-ordinate systems, namely the macroscopic system defined by the deformation axes and the crystallographic system given by the crystallographic lattice. The analysis covers single...... and polycrystals of fcc metals in three deformation modes (rolling, tension and torsion). In the macroscopic system, boundaries lie close to the macroscopically most stressed planes. In the crystallographic system, the boundary plane depends on the grain/crystal orientation. The boundary planes in both co......-ordinate systems are rationalised based on the slip. The more the slip is concentrated on a slip plane, the closer the boundaries lie to this. The macroscopic preference arises from the macroscopic directionality of the slip. The established relations are applied to (a) prediction of boundary planes from slip...

A "feasible direction" search for Lineal Programming problem solving

Directory of Open Access Journals (Sweden)

Jaime U Malpica Angarita

2003-07-01

Full Text Available The study presents an approach to solve linear programming problems with no artificial variables. A primal linear minimization problem is standard form and its associated dual linear maximization problem are used. Initially, the dual (or a partial dual program is solved by a "feasible direction" search, where the Karush-Kuhn-Tucker conditions help to verify its optimality and then its feasibility. The "feasible direction" search exploits the characteristics of the convex polyhedron (or prototype formed by the dual program constraints to find a starting point and then follows line segments, whose directions are found in afine subspaces defined by boundary hyperplanes of polyhedral faces, to find next points up to the (an optimal one. Them, the remaining dual constraints not satisfaced at that optimal dual point, if there are any, are handled as nonbasic variables of the primal program, which is to be solved by such "feasible direction" search.

Change of Surface Roughness and Planetary Boundary Layer

DEFF Research Database (Denmark)

Jensen, Niels Otto

1978-01-01

The ratio between upstream and far downstream surface friction velocities relative to a change in surface roughness is given on the basis of results from surface Rossby number similarity theory. By simple theories for the internal boundary layer, which are found to compare quite well with recent...... numerical results from higher-order closure models, it is found that, even at a downwind distance such that the internal boundary layer has grown to the full height of the planetary boundary layers, the surface stress still considerably exceeds the equilibrium value...

Analytical and numerical analyses for a penny-shaped crack embedded in an infinite transversely isotropic multi-ferroic composite medium: semi-permeable electro-magnetic boundary condition

Science.gov (United States)

Zheng, R.-F.; Wu, T.-H.; Li, X.-Y.; Chen, W.-Q.

2018-06-01

The problem of a penny-shaped crack embedded in an infinite space of transversely isotropic multi-ferroic composite medium is investigated. The crack is assumed to be subjected to uniformly distributed mechanical, electric and magnetic loads applied symmetrically on the upper and lower crack surfaces. The semi-permeable (limited-permeable) electro-magnetic boundary condition is adopted. By virtue of the generalized method of potential theory and the general solutions, the boundary integro-differential equations governing the mode I crack problem, which are of nonlinear nature, are established and solved analytically. Exact and complete coupling magneto-electro-elastic field is obtained in terms of elementary functions. Important parameters in fracture mechanics on the crack plane, e.g., the generalized crack surface displacements, the distributions of generalized stresses at the crack tip, the generalized stress intensity factors and the energy release rate, are explicitly presented. To validate the present solutions, a numerical code by virtue of finite element method is established for 3D crack problems in the framework of magneto-electro-elasticity. To evaluate conveniently the effect of the medium inside the crack, several empirical formulae are developed, based on the numerical results.

Improved algorithm for solving nonlinear parabolized stability equations

International Nuclear Information System (INIS)

Zhao Lei; Zhang Cun-bo; Liu Jian-xin; Luo Ji-sheng

2016-01-01

Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. (paper)

The effect of guide-field and boundary conditions on collisionless magnetic reconnection in a stressed X-point collapse

Energy Technology Data Exchange (ETDEWEB)

Graf von der Pahlen, J.; Tsiklauri, D. [School of Physics and Astronomy, Queen Mary University of London, London E1 4NS (United Kingdom)

2014-01-15

Works of Tsiklauri and Haruki [Phys. Plasmas 15, 102902 (2008); 14, 112905 (2007)] are extended by inclusion of the out-of-plane magnetic (guide) field. In particular, magnetic reconnection during collisionless, stressed X-point collapse for varying out-of-plane guide-fields is studied using a kinetic, 2.5D, fully electromagnetic, relativistic particle-in-cell numerical code. For zero guide-field, cases for both open and closed boundary conditions are investigated, where magnetic flux and particles are lost and conserved, respectively. It is found that reconnection rates, out-of-plane currents and density in the X-point increase more rapidly and peak sooner in the closed boundary case, but higher values are reached in the open boundary case. The normalized reconnection rate is fast: 0.10-0.25. In the open boundary case it is shown that an increase of guide-field yields later onsets in the reconnection peak rates, while in the closed boundary case initial peak rates occur sooner but are suppressed. The reconnection current changes similarly with increasing guide-field; however for low guide-fields the reconnection current increases, giving an optimal value for the guide-field between 0.1 and 0.2 times the in-plane field in both cases. Also, in the open boundary case, it is found that for guide-fields of the order of the in-plane magnetic field, the generation of electron vortices occurs. Possible causes of the vortex generation, based on the flow of decoupled particles in the diffusion region and localized plasma heating, are discussed. Before peak reconnection onset, oscillations in the out-of-plane electric field at the X-point are found, ranging in frequency from approximately 1 to 2 ω{sub pe} and coinciding with oscillatory reconnection. These oscillations are found to be part of a larger wave pattern in the simulation domain. Mapping the out-of-plane electric field along the central lines of the domain over time and applying a 2D Fourier transform reveal that

Improvement of creep-rupture properties by serrated grain boundaries in high-tungsten cobalt-base superalloys

International Nuclear Information System (INIS)

Tanaka, Manabu

1993-01-01

The improvement of creep-rupture properties by serrated grain boundaries was investigated using cobalt-base superalloys containing about 14 to 20 wt.% tungsten at 1089 and 1311 K. Serrated grain boundaries improved both the rupture life and the ductility, especially under lower stresses at 1089 K. The increase in rupture life was larger in the alloys containing a larger amount of W. Ductile grain boundary fracture surfaces, which involved dimple patterns and grain boundary ledges, were observed in the specimens with serrated grain boundaries whereas brittle grain boundary facets were observed in the specimens with normal straight grain boundaries ruptured at 1089 K. The strengthening by serrated grain boundaries was also effective at 1311 K, but there was little difference in rupture life between the specimens with serrated grain boundaries and those with straight grain boundaries under lower stresses, since serrated grain boundaries developed also in the specimens with straight grain boundaries according to grain boundary precipitates forming during creep at 1311 K. The increase in W content of the alloys led to the increase in rupture life of the specimens with serrated grain boundaries at 1089 and 1311 K. (orig.) [de

Buckling of Nonprismatic Column on Varying Elastic Foundation with Arbitrary Boundary Conditions

Directory of Open Access Journals (Sweden)

Ahmad A. Ghadban

2017-01-01

Full Text Available Buckling of nonprismatic single columns with arbitrary boundary conditions resting on a nonuniform elastic foundation may be considered as the most generalized treatment of the subject. The buckling differential equation for such columns is extremely difficult to solve analytically. Thus, the authors propose a numerical approach by discretizing the column into a finite number of segments. Each segment has constants E (modulus of elasticity, I (moment of inertia, and β (subgrade stiffness. Next, an exact analytical solution is derived for each prismatic segment resting on uniform elastic foundation. These segments are then assembled in a matrix from which the critical buckling load is obtained. The derived formulation accounts for different end boundary conditions. Validation is performed by benchmarking the present results against analytical solutions found in the literature, showing excellent agreement. After validation, more examples are solved to illustrate the power and flexibility of the proposed method. Overall, the proposed method provides reasonable results, and the examples solved demonstrate the versatility of the developed approach and some of its many possible applications.

Two transparent boundary conditions for the electromagnetic scattering from two-dimensional overfilled cavities

Science.gov (United States)

Du, Kui

2011-07-01

We consider electromagnetic scattering from two-dimensional (2D) overfilled cavities embedded in an infinite ground plane. The unbounded computational domain is truncated to a bounded one by using a transparent boundary condition (TBC) proposed on a semi-ellipse. For overfilled rectangular cavities with homogeneous media, another TBC is introduced on the cavity apertures, which produces a smaller computational domain. The existence and uniqueness of the solutions of the variational formulations for the transverse magnetic and transverse electric polarizations are established. In the exterior domain, the 2D scattering problem is solved in the elliptic coordinate system using the Mathieu functions. In the interior domain, the problem is solved by a finite element method. Numerical experiments show the efficiency and accuracy of the new boundary conditions.

Review on solving the forward problem in EEG source analysis

Directory of Open Access Journals (Sweden)

Vergult Anneleen

2007-11-01

Full Text Available Abstract Background The aim of electroencephalogram (EEG source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes. Methods While other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field. Results It starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poisson's differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter. In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poisson's equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM, the finite element method (FEM and the finite difference method (FDM. In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poisson's equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative

The γ-ε martensitic transformation: a model for stress induced variant and its interaction with grain boundary

International Nuclear Information System (INIS)

Guenin, G.

1995-01-01

The γ (f.c.c.) to ε (h.c.p.) martensitic transformation occurs through the Shockley a/6 left angle 211 right angle faulting every second {111} plane of the f.c.c. structure. A stress induced thin single variant corresponds to a single a/6 left angle 211 right angle faulting vector and leads to a large homogeneous shear (0.35) in amplitude. The tip of such a plate is composed of a set of identical Shockley partial dislocations with large mutual interactions. This work is a presentation of a model which describes the martensite morphology of stress induced ε martensite in shape memory Fe-Mn-Si based alloys. The model includes the formation mechanism of the plate (Seeger's like) and its growth inside a limited grain. The mutual interaction of Shockley dislocations and their interaction with the grain boundary is semi quantitatively described; it leads to a lenticular shape of ε martensite thin plates. The model is able to explain the behaviour of this kind of alloys concerning the superelastic effect and the shape memory. (orig.)

Locality at the boundary implies gap in the bulk for 2D PEPS

DEFF Research Database (Denmark)

Kastoryano, Michael J.; Lucia, Angelo; Perez-Garcia, David

2018-01-01

Proving that the parent Hamiltonian of a Projected Entangled Pair State (PEPS) is gapped remains an important open problem. We take a step forward in solving this problem by showing that if the boundary state of any rectangular subregion is a quasi-local Gibbs state of the virtual indices, then t...... boundary theories and dynamical properties in an interacting many body system. We show that the proof can be extended to MPO-injective PEPS, and speculate that the assumption on the locality of the boundary Hamiltonian follows from exponential decay of correlations in the bulk....

Boundary Plasma Turbulence Simulations for Tokamaks

International Nuclear Information System (INIS)

Xu, X.; Umansky, M.; Dudson, B.; Snyder, P.

2008-05-01

The boundary plasma turbulence code BOUT models tokamak boundary-plasma turbulence in a realistic divertor geometry using modified Braginskii equations for plasma vorticity, density (ni), electron and ion temperature (T e ; T i ) and parallel momenta. The BOUT code solves for the plasma fluid equations in a three dimensional (3D) toroidal segment (or a toroidal wedge), including the region somewhat inside the separatrix and extending into the scrape-off layer; the private flux region is also included. In this paper, a description is given of the sophisticated physical models, innovative numerical algorithms, and modern software design used to simulate edge-plasmas in magnetic fusion energy devices. The BOUT code's unique capabilities and functionality are exemplified via simulations of the impact of plasma density on tokamak edge turbulence and blob dynamics

On a stochastic Burgers equation with Dirichlet boundary conditions

Directory of Open Access Journals (Sweden)

Ekaterina T. Kolkovska

2003-01-01

Full Text Available We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

Prediction of the Stress-Strain Behavior of Open-Cell Aluminum Foam under Compressive Loading and the Effects of Various RVE Boundary Conditions

Science.gov (United States)

Hamidi Ghaleh Jigh, Behrang; Farsi, Mohammad Ali; Hosseini Toudeshky, Hossein

2018-04-01

The prediction of the mechanical behavior of metallic foams with realistic microstructure and the effects of various boundary conditions on the mechanical behavior is an important and challenging issue in modeling representative volume elements (RVEs). A numerical investigation is conducted to determine the effects of various boundary conditions and cell wall cross sections on the compressive mechanical properties of aluminum foam, including the stiffness, plateau stress and onset strain of densification. The open-cell AA6101-T6 aluminum foam Duocel is used in the analyses in this study. Geometrical characteristics including the cell size, foam relative density, and cross-sectional shape and thickness of the cell walls are extracted from images of the foam. Then, the obtained foam microstructure is analyzed as a 2D model. The ligaments are modeled as shear deformable beams with elastic-plastic material behavior. To prevent interpenetration of the nodes and walls inside the cells with large deformations, self-contact-type frictionless interaction is stipulated between the internal surfaces. Sensitivity analyses are performed using several boundary conditions and cells wall cross-sectional shapes. The predicted results from the finite element analyses are compared with the experimental results. Finally, the most appropriate boundary conditions, leading to more consistent results with the experimental data, are introduced.

Prediction of the Stress-Strain Behavior of Open-Cell Aluminum Foam under Compressive Loading and the Effects of Various RVE Boundary Conditions

Science.gov (United States)

Hamidi Ghaleh Jigh, Behrang; Farsi, Mohammad Ali; Hosseini Toudeshky, Hossein

2018-05-01

The prediction of the mechanical behavior of metallic foams with realistic microstructure and the effects of various boundary conditions on the mechanical behavior is an important and challenging issue in modeling representative volume elements (RVEs). A numerical investigation is conducted to determine the effects of various boundary conditions and cell wall cross sections on the compressive mechanical properties of aluminum foam, including the stiffness, plateau stress and onset strain of densification. The open-cell AA6101-T6 aluminum foam Duocel is used in the analyses in this study. Geometrical characteristics including the cell size, foam relative density, and cross-sectional shape and thickness of the cell walls are extracted from images of the foam. Then, the obtained foam microstructure is analyzed as a 2D model. The ligaments are modeled as shear deformable beams with elastic-plastic material behavior. To prevent interpenetration of the nodes and walls inside the cells with large deformations, self-contact-type frictionless interaction is stipulated between the internal surfaces. Sensitivity analyses are performed using several boundary conditions and cells wall cross-sectional shapes. The predicted results from the finite element analyses are compared with the experimental results. Finally, the most appropriate boundary conditions, leading to more consistent results with the experimental data, are introduced.

Sewing constraints for conformal field theories on surfaces with boundaries

International Nuclear Information System (INIS)

Lewellen, D.C.

1992-01-01

In a conformal field theory, correlation functions on any Riemann surface are in principle unambiguously defined by sewing together three-point functions on the sphere, provided that the four-point functions on the sphere are crossing symmetric, and the one-point functions on the torus are modular covariant. In this work we extend Sonoda's proof of this result to conformal field theories defined on surfaces with boundaries. Four additional sewing constraints arise; three on the half-plane and one on the cylinder. These relate the various OPE coefficients in the theory (bulk, boundary, and bulk-boundary) to one another. In rational theories these relations can be expressed in terms of data arising solely within the bulk theory: The matrix S which implements modular transformations on the characters, and the matrices implementing duality transformations on the four-point conformal-block functions. As an example we solve these relations for the boundary and bulk-boundary structure constants in the Ising model with all possible conformally invariant boundary conditions. The role of the basic sewing constraints in the construction of open string theories is discussed. (orig.)

FEAST: a two-dimensional non-linear finite element code for calculating stresses

International Nuclear Information System (INIS)

Tayal, M.

1986-06-01

The computer code FEAST calculates stresses, strains, and displacements. The code is two-dimensional. That is, either plane or axisymmetric calculations can be done. The code models elastic, plastic, creep, and thermal strains and stresses. Cracking can also be simulated. The finite element method is used to solve equations describing the following fundamental laws of mechanics: equilibrium; compatibility; constitutive relations; yield criterion; and flow rule. FEAST combines several unique features that permit large time-steps in even severely non-linear situations. The features include a special formulation for permitting many finite elements to simultaneously cross the boundary from elastic to plastic behaviour; accomodation of large drops in yield-strength due to changes in local temperature and a three-step predictor-corrector method for plastic analyses. These features reduce computing costs. Comparisons against twenty analytical solutions and against experimental measurements show that predictions of FEAST are generally accurate to ± 5%

[Stress analysis on the acetabular side of bipolar hemiarthroplasty by the two-dimensional finite element method incorporating the boundary friction layer].

Science.gov (United States)

Ichihashi, K; Imura, S; Oomori, H; Gesso, H

1994-11-01

We compared the biomechanical characteristics of bipolar and unipolar hemiarthroplasty on the proximal migration of the outer head by determining the von Mises stress distribution and acetabular (outer head) displacement with clinical assessment of hemiarthroplasty in 75 patients. This analysis used the two-dimensional finite element method, which incorporated boundary friction layers on both the inner and outer bearings of the prosthesis. Acetabular reaming increased stress within the pelvic bone and migration of the outer head. A combination of the acetabular reaming and bone transplantation increased the stress within the pelvic bone and grafted bone, and caused outer head migration. These findings were supported by clinical results. Although the bipolar endoprosthesis was biomechanically superior to the unipolar endoprosthesis, migration of the outer head still occurred. The bipolar endoprosthesis appeared to be indicated in cases of a femoral neck fracture or of avascular necrosis in the femoral head, but its use in cases of osteoarthritis in the hip required caution.

Discretization errors at free boundaries of the Grad-Schlueter-Shafranov equation

International Nuclear Information System (INIS)

Meyer-Spasche, R.; Fornberg, B.

1990-10-01

The numerical error of standard finite-difference schemes is analyzed at free boundaries of the Grad-Schlueter-Shafranov equation of plasma physics. A simple correction strategy is devised to eliminate (to leading order) the errors which arise as the free boundary crosses the rectangular grid at irregular locations. The resulting scheme can be solved by Gauss-Newton or Inverse iterations, or by multigrid iterations. Extrapolation (from 2nd to 3rd order of accuracy) is possible for the new scheme. (orig.)

Infinite-Dimensional Boundary Observer for Lithium-Ion Battery State Estimation

DEFF Research Database (Denmark)

Hasan, Agus; Jouffroy, Jerome

2017-01-01

This paper presents boundary observer design for state-of-charge (SOC) estimation of lithium-ion batteries. The lithium-ion battery dynamics are governed by thermal-electrochemical principles, which mathematically modeled by partial differential equations (PDEs). In general, the model is a reaction......-diffusion equation with time-dependent coefficients. A Luenberger observer is developed using infinite-dimensional backstepping method and uses only a single measurement at the boundary of the battery. The observer gains are computed by solving the observer kernel equation. A numerical example is performed to show...

A highly accurate spectral method for the Navier–Stokes equations in a semi-infinite domain with flexible boundary conditions

Energy Technology Data Exchange (ETDEWEB)

Matsushima, Toshiki; Ishioka, Keiichi, E-mail: matsushima@kugi.kyoto-u.ac.jp, E-mail: ishioka@gfd-dennou.org [Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502 (Japan)

2017-04-15

This paper presents a spectral method for numerically solving the Navier–Stokes equations in a semi-infinite domain bounded by a flat plane: the aim is to obtain high accuracy with flexible boundary conditions. The proposed use is for numerical simulations of small-scale atmospheric phenomena near the ground. We introduce basis functions that fit the semi-infinite domain, and an integral condition for vorticity is used to reduce the computational cost when solving the partial differential equations that appear when the viscosity term is treated implicitly. Furthermore, in order to ensure high accuracy, two iteration techniques are applied when solving the system of linear equations and in determining boundary values. This significantly reduces numerical errors, and the proposed method enables high-resolution numerical experiments. This is demonstrated by numerical experiments showing the collision of a vortex ring into a wall; these were performed using numerical models based on the proposed method. It is shown that the time evolution of the flow field is successfully obtained not only near the boundary, but also in a region far from the boundary. The applicability of the proposed method and the integral condition is discussed. (paper)

Recursive solution for dynamic response of one-dimensional structures with time-dependent boundary conditions

Energy Technology Data Exchange (ETDEWEB)

Abadi, Mohammad Tahaye [Aerospace Research Institute, Tehran (Iran, Islamic Republic of)

2015-10-15

A recursive solution method is derived for the transient response of one-dimensional structures subjected to the general form of time dependent boundary conditions. Unlike previous solution methods that assumed the separation of variables, the present method involves formulating and solving the dynamic problems using the summation of two single-argument functions satisfying the motion equation. Based on boundary and initial conditions, a recursive procedure is derived to determine the single-argument functions. Such a procedure is applied to the general form of boundary conditions, and an analytical solution is derived by solving the recursive equation. The present solution method is implemented for base excitation problems, and the results are compared with those of the previous analytical solution and the Finite element (FE) analysis. The FE results converge to the present analytical solution, although considerable error is found in predicting a solution method on the basis of the separation of variables. The present analytical solution predicts the transient response for wave propagation problems in broadband excitation frequencies.

Recursive solution for dynamic response of one-dimensional structures with time-dependent boundary conditions

International Nuclear Information System (INIS)

Abadi, Mohammad Tahaye

2015-01-01

A recursive solution method is derived for the transient response of one-dimensional structures subjected to the general form of time dependent boundary conditions. Unlike previous solution methods that assumed the separation of variables, the present method involves formulating and solving the dynamic problems using the summation of two single-argument functions satisfying the motion equation. Based on boundary and initial conditions, a recursive procedure is derived to determine the single-argument functions. Such a procedure is applied to the general form of boundary conditions, and an analytical solution is derived by solving the recursive equation. The present solution method is implemented for base excitation problems, and the results are compared with those of the previous analytical solution and the Finite element (FE) analysis. The FE results converge to the present analytical solution, although considerable error is found in predicting a solution method on the basis of the separation of variables. The present analytical solution predicts the transient response for wave propagation problems in broadband excitation frequencies.

Stress intensity evaluation for surface crack with use of boundary element method and influence function method and the surface crack extension analysis

International Nuclear Information System (INIS)

Yuuki, R.; Ejima, K.

1991-01-01

In this study, three-dimensional boundary element elastostatic analysis is carried out on various surface crack problems. The present BEM uses a Mindlin's solution as well as a Kelvin's solution as a fundamental solution. So we can obtain accurate solutions for a surface crack just before or after a penetration. The obtained solutions for various shapes of surface cracks are stored as the data base, based on the influence function method. We develop the surface crack extension analysis system using the stress intensity factor data base and also the fatigue crack growth law. Our system seems to be useful especially for the analysis of the surface crack just before or after the penetration and also under the residual stresses

The Impacts of Control Mechanism in Strategic Alliance on Alliance Performance: From the Perspective of Boundary Dilemma

Institute of Scientific and Technical Information of China (English)

SHEN Hao; XIE En; WANG Dong

2016-01-01

In order to solve the problem of boundary dilemma in the strategic alliance,this paper firstly examines the impact of the control mechanism in the strategic alliance on the coordinative efficiency and opportunistic risks of the alliance,and then it tests the different impacts of coordinative efficiency and opportunistic risks on the performances of the alliance members.The empirical results indicate that the formal contract control can efficiently resolve the problem of opportunistic risks in the boundary dilemma,so as to improve the performance of the alliance members;whereas the informal social control including relation control and information technology control can efficiently solve the problem of coordinative efficiency in the boundary dilemma,so as to improve the performance of the alliance members.These findings can enrich and extend existing literature in strategic alliance management and provide significant empirical evidences and theoretical supports for the strategic alliance members to resolve boundary dilemma and further enhance alliance cooperative performance.

Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm

Directory of Open Access Journals (Sweden)

Omar Abu Arqub

2012-01-01

Full Text Available In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. This novel approach possesses main advantages; it can be applied without any limitation on the nature of the problem, the type of singularity, and the number of mesh points. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the presented technique. The results reveal that the algorithm is very effective, straightforward, and simple.

Recursive recovery of Markov transition probabilities from boundary value data

Energy Technology Data Exchange (ETDEWEB)

Patch, Sarah Kathyrn [Univ. of California, Berkeley, CA (United States)

1994-04-01

In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requires finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.

An efficient strongly coupled immersed boundary method for deforming bodies

Science.gov (United States)

Goza, Andres; Colonius, Tim

2016-11-01

Immersed boundary methods treat the fluid and immersed solid with separate domains. As a result, a nonlinear interface constraint must be satisfied when these methods are applied to flow-structure interaction problems. This typically results in a large nonlinear system of equations that is difficult to solve efficiently. Often, this system is solved with a block Gauss-Seidel procedure, which is easy to implement but can require many iterations to converge for small solid-to-fluid mass ratios. Alternatively, a Newton-Raphson procedure can be used to solve the nonlinear system. This typically leads to convergence in a small number of iterations for arbitrary mass ratios, but involves the use of large Jacobian matrices. We present an immersed boundary formulation that, like the Newton-Raphson approach, uses a linearization of the system to perform iterations. It therefore inherits the same favorable convergence behavior. However, we avoid large Jacobian matrices by using a block LU factorization of the linearized system. We derive our method for general deforming surfaces and perform verification on 2D test problems of flow past beams. These test problems involve large amplitude flapping and a wide range of mass ratios. This work was partially supported by the Jet Propulsion Laboratory and Air Force Office of Scientific Research.

RACORO Extended-Term Aircraft Observations of Boundary-Layer Clouds

Science.gov (United States)

Vogelmann, Andrew M.; McFarquhar, Greg M.; Ogren, John A.; Turner, David D.; Comstock, Jennifer M.; Feingold, Graham; Long, Charles N.; Jonsson, Haflidi H.; Bucholtz, Anthony; Collins, Don R.;

A New View of the Dynamics of Reynolds Stress Generation in Turbulent Boundary Layers

Science.gov (United States)

Cantwell, Brian J.; Chacin, Juan M.

1998-01-01

The structure of a numerically simulated turbulent boundary layer over a flat plate at Re(theta) = 670 was studied using the invariants of the velocity gradient tensor (Q and R) and a related scalar quantity, the cubic discriminant (D = 27R(exp 2)/4 + Q(exp 3)). These invariants have previously been used to study the properties of the small-scale motions responsible for the dissipation of turbulent kinetic energy. In addition, these scalar quantities allow the local flow patterns to be unambiguously classified according to the terminology proposed by Chong et al. The use of the discriminant as a marker of coherent motions reveals complex, large-scale flow structures that are shown to be associated with the generation of Reynolds shear stress -u'v'(bar). These motions are characterized by high spatial gradients of the discriminant and are believed to be an important part of the mechanism that sustains turbulence in the near-wall region.

Analysis of stress wave propagation in an elasto-viscoplastic plate

International Nuclear Information System (INIS)

Nakagawa, Noritoshi; Kawai, Ryoji; Urushi, Norio.

1986-01-01

Stress waves which propagate in the body are reflected at the boundary, and due to the interaction of the reflected stress waves, the focussing of stress waves will take place and a high stress level can be caused. The focussing of stress waves due to the reflection from the boundary may bring about fracture of the body, so that this is an important problem from a viewpoint of dynamic strength of structures. In this paper the process of stress wave focussing and the strain-rate dependence of constitutive equation in elastic and plastic regions are investigated. In the case where an in-plane step load uniformly acts on the straight edge of the plate with a semi-circular boundary, the propagation of stress waves in the plate was numerically analyzed by the finite element method, applying viscoelastic, elasto-plastic and elasto-viscoplastic constitutive equations. As the result, the process of focussing of stress waves due to reflection from the semi-circular boundary was observed and the difference in propagation behaviour of stress waves was discussed in materials represented by some kinds of constitutive equations. (author)

Problem solving skills for schizophrenia.

Science.gov (United States)

Xia, J; Li, Chunbo

2007-04-18

The severe and long-lasting symptoms of schizophrenia are often the cause of severe disability. Environmental stress such as life events and the practical problems people face in their daily can worsen the symptoms of schizophrenia. Deficits in problem solving skills in people with schizophrenia affect their independent and interpersonal functioning and impair their quality of life. As a result, therapies such as problem solving therapy have been developed to improve problem solving skills for people with schizophrenia. To review the effectiveness of problem solving therapy compared with other comparable therapies or routine care for those with schizophrenia. We searched the Cochrane Schizophrenia Group's Register (September 2006), which is based on regular searches of BIOSIS, CENTRAL, CINAHL, EMBASE, MEDLINE and PsycINFO. We inspected references of all identified studies for further trials. We included all clinical randomised trials comparing problem solving therapy with other comparable therapies or routine care. We extracted data independently. For homogenous dichotomous data we calculated random effects, relative risk (RR), 95% confidence intervals (CI) and, where appropriate, numbers needed to treat (NNT) on an intention-to-treat basis. For continuous data, we calculated weighted mean differences (WMD) using a random effects statistical model. We included only three small trials (n=52) that evaluated problem solving versus routine care, coping skills training or non-specific interaction. Inadequate reporting of data rendered many outcomes unusable. We were unable to undertake meta-analysis. Overall results were limited and inconclusive with no significant differences between treatment groups for hospital admission, mental state, behaviour, social skills or leaving the study early. No data were presented for global state, quality of life or satisfaction. We found insufficient evidence to confirm or refute the benefits of problem solving therapy as an additional

Versions of the Collocation and Least Residuals Method for Solving Problems of Mathematical Physics in the Convex Quadrangular Domains

Directory of Open Access Journals (Sweden)

Vasily A. Belyaev

2017-01-01

Full Text Available The new versions of the collocations and least residuals (CLR method of high-order accuracy are proposed and implemented for the numerical solution of the boundary value problems for PDE in the convex quadrangular domains. Their implementation and numerical experiments are performed by the examples of solving the biharmonic and Poisson equations. The solution of the biharmonic equation is used for simulation of the stress-strain state of an isotropic plate under the action of the transverse load. Differential problems are projected into the space of fourth-degree polynomials by the CLR method. The boundary conditions for the approximate solution are put down exactly on the boundary of the computational domain. The versions of the CLR method are implemented on the grids, which are constructed by two different ways. In the first version, a “quasiregular” grid is constructed in the domain, the extreme lines of this grid coincide with the boundaries of the domain. In the second version, the domain is initially covered by a regular grid with rectangular cells. Herewith, the collocation and matching points that are situated outside the domain are used for approximation of the differential equations in the boundary cells that had been crossed by the boundary. In addition the “small” irregular triangular cells that had been cut off by the domain boundary from rectangular cells of the initial regular grid are joined to adjacent quadrangular cells. This technique allowed to essentially reduce the conditionality of the system of linear algebraic equations of the approximate problem in comparison with the case when small irregular cells together with other cells were used as independent ones for constructing an approximate solution of the problem. It is shown that the approximate solution of problems converges with high order and matches with high accuracy with the analytical solution of the test problems in the case of the known solution in

An outgoing energy flux boundary condition for finite difference ICRP antenna models

International Nuclear Information System (INIS)

Batchelor, D.B.; Carter, M.D.

1992-11-01

For antennas at the ion cyclotron range of frequencies (ICRF) modeling in vacuum can now be carried out to a high level of detail such that shaping of the current straps, isolating septa, and discrete Faraday shield structures can be included. An efficient approach would be to solve for the fields in the vacuum region near the antenna in three dimensions by finite methods and to match this solution at the plasma-vacuum interface to a solution obtained in the plasma region in one dimension by Fourier methods. This approach has been difficult to carry out because boundary conditions must be imposed at the edge of the finite difference grid on a point-by-point basis, whereas the condition for outgoing energy flux into the plasma is known only in terms of the Fourier transform of the plasma fields. A technique is presented by which a boundary condition can be imposed on the computational grid of a three-dimensional finite difference, or finite element, code by constraining the discrete Fourier transform of the fields at the boundary points to satisfy an outgoing energy flux condition appropriate for the plasma. The boundary condition at a specific grid point appears as a coupling to other grid points on the boundary, with weighting determined by a kemel calctdated from the plasma surface impedance matrix for the various plasma Fourier modes. This boundary condition has been implemented in a finite difference solution of a simple problem in two dimensions, which can also be solved directly by Fourier transformation. Results are presented, and it is shown that the proposed boundary condition does enforce outgoing energy flux and yields the same solution as is obtained by Fourier methods

Problem-Solving and Mental Health Outcomes of Women and Children in the Wake of Intimate Partner Violence

Directory of Open Access Journals (Sweden)

John Maddoux

2014-01-01

Full Text Available The environmental stress of intimate partner violence is common and often results in mental health problems of depression, anxiety, and PTSD for women and behavioral dysfunctions for their children. Problem-solving skills can serve to mitigate or accentuate the environmental stress of violence and associated impact on mental health. To better understand the relationship between problem-solving skills and mental health of abused women with children, a cross-sectional predictive analysis of 285 abused women who used justice or shelter services was completed. The women were asked about social problem-solving, and mental health symptoms of depression, anxiety, and PTSD as well as behavioral functioning of their children. Higher negative problem-solving scores were associated with significantly P<0.001 greater odds of having clinically significant levels of PTSD, anxiety, depression, and somatization for the woman and significantly P<0.001 greater odds of her child having borderline or clinically significant levels of both internalizing and externalizing behaviors. A predominately negative problem-solving approach was strongly associated with poorer outcomes for both mothers and children in the aftermath of the environmental stress of abuse. Interventions addressing problem-solving ability may be beneficial in increasing abused women’s abilities to navigate the daily stressors of life following abuse.

Forced Response Analysis of a Fan with Boundary Layer Inlet Distortion

Science.gov (United States)

Bakhle, Milind A.; Reddy, T. S. R.; Coroneos, Rula M.

2014-01-01

Boundary layer ingesting propulsion systems have the potential to significantly reduce fuel burn for future generations of commercial aircraft, but these systems must be designed to overcome the challenge of high dynamic stresses in fan blades due to forced response. High dynamic stresses can lead to high cycle fatigue failures. High-fidelity computational analysis of the fan aeromechanics is integral to an ongoing effort to design a boundary layer ingesting inlet and fan for a wind-tunnel test. An unsteady flow solution from a Reynoldsaveraged Navier Stokes analysis of a coupled inlet-fan system is used to calculate blade unsteady loading and assess forced response of the fan to distorted inflow. Conducted prior to the mechanical design of a fan, the initial forced response analyses performed in this study provide an early look at the levels of dynamic stresses that are likely to be encountered. For the boundary layer ingesting inlet, the distortion contains strong engine order excitations that act simultaneously. The combined effect of these harmonics was considered in the calculation of the forced response stresses. Together, static and dynamic stresses can provide the information necessary to evaluate whether the blades are likely to fail due to high cycle fatigue. Based on the analyses done, the overspeed condition is likely to result in the smallest stress margin in terms of the mean and alternating stresses. Additional work is ongoing to expand the analyses to off-design conditions, on-resonance conditions, and to include more detailed modeling of the blade structure.

A fast direct solver for boundary value problems on locally perturbed geometries

Science.gov (United States)

Zhang, Yabin; Gillman, Adrianna

2018-03-01

Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.

Monotone methods for solving a boundary value problem of second order discrete system

Directory of Open Access Journals (Sweden)

Wang Yuan-Ming

1999-01-01

Full Text Available A new concept of a pair of upper and lower solutions is introduced for a boundary value problem of second order discrete system. A comparison result is given. An existence theorem for a solution is established in terms of upper and lower solutions. A monotone iterative scheme is proposed, and the monotone convergence rate of the iteration is compared and analyzed. The numerical results are given.

Study of Boundary Layer Convective Heat Transfer with Low Pressure Gradient Over a Flat Plate Via He's Homotopy Perturbation Method

International Nuclear Information System (INIS)

Fathizadeh, M.; Aroujalian, A.

2012-01-01

The boundary layer convective heat transfer equations with low pressure gradient over a flat plate are solved using Homotopy Perturbation Method, which is one of the semi-exact methods. The nonlinear equations of momentum and energy solved simultaneously via Homotopy Perturbation Method are in good agreement with results obtained from numerical methods. Using this method, a general equation in terms of Pr number and pressure gradient (λ) is derived which can be used to investigate velocity and temperature profiles in the boundary layer.

An efficient realization of frequency dependent boundary conditions in an acoustic finite-difference time-domain model

DEFF Research Database (Denmark)

Escolano-Carrasco, José; Jacobsen, Finn; López, J.J.

2008-01-01

The finite-difference time-domain (FDTD) method provides a simple and accurate way of solving initial boundary value problems. However, most acoustic problems involve frequency dependent boundary conditions, and it is not easy to include such boundary conditions in an FDTD model. Although solutions...... to this problem exist, most of them have high computational costs, and stability cannot always be ensured. In this work, a solution is proposed based on "mixing modelling strategies"; this involves separating the FDTD mesh and the boundary conditions (a digital filter representation of the impedance...

A creep rupture model accounting for cavitation at sliding grain boundaries

NARCIS (Netherlands)

Giessen, Erik van der; Tvergaard, Viggo

1991-01-01

An axisymmetric cell model analysis is used to study creep failure by grain boundary cavitation at facets normal to the maximum principal tensile stress, taking into account the influence of cavitation and sliding at adjacent inclined grain boundaries. It is found that the interaction between the

A mixed Fourier–Galerkin–finite-volume method to solve the fluid dynamics equations in cylindrical geometries

International Nuclear Information System (INIS)

Núñez, Jóse; Ramos, Eduardo; Lopez, Juan M

2012-01-01

We describe a hybrid method based on the combined use of the Fourier Galerkin and finite-volume techniques to solve the fluid dynamics equations in cylindrical geometries. A Fourier expansion is used in the angular direction, partially translating the problem to the Fourier space and then solving the resulting equations using a finite-volume technique. We also describe an algorithm required to solve the coupled mass and momentum conservation equations similar to a pressure-correction SIMPLE method that is adapted for the present formulation. Using the Fourier–Galerkin method for the azimuthal direction has two advantages. Firstly, it has a high-order approximation of the partial derivatives in the angular direction, and secondly, it naturally satisfies the azimuthal periodic boundary conditions. Also, using the finite-volume method in the r and z directions allows one to handle boundary conditions with discontinuities in those directions. It is important to remark that with this method, the resulting linear system of equations are band-diagonal, leading to fast and efficient solvers. The benefits of the mixed method are illustrated with example problems. (paper)

How do Economic Crises Impact Firm Boundaries?

DEFF Research Database (Denmark)

Foss, Kirsten

2010-01-01

How economic crises impact the boundaries of firms has been offered virtually no attention in the literature on the theory of the firm. I review the best-known theories of the firm and identify the variables that matter for the explanation of firm boundaries. I then examine how an economic crisis...... may impact these variables and change efficient firm boundaries. The various theories of the firm have difficulties explaining how firms efficiently adapt their boundaries to such prominent characteristics of economic crisis as declining demand and increased costs of external finance. However, all...... these theories stress uncertainty as an antecedent of firm organization, and as uncertainty is also an important characteristic of an economic crisis I examine how uncertainty is allowed to play out in the various theories in order to identify what predictions we can derive from the theory regarding changes...

Student Solutions Manual to Boundary Value Problems and Partial Differential Equations

CERN Document Server

Powers, David L

2005-01-01

This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e. The SSM is available in print via PDF or electronically, and provides the student with the detailed solutions of the odd-numbered problems contained throughout the book.Provides students with exercises that skillfully illustrate the techniques used in the text to solve science and engineering problemsNearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercisesMany exercises based on current engineering applications

Effect of externally generated turbulence on wave boundary layer

DEFF Research Database (Denmark)

Fredsøe, Jørgen; Sumer, B. Mutlu; Kozakiewicz, A.

2003-01-01

This experimental study deals with the effect of externally generated turbulence on the oscillatory boundary layer to simulate the turbulence in the wave boundary layer under broken waves in the swash zone. The subject has been investigated experimentally in a U-shaped, oscillating water tunnel...... results. The mean and turbulence quantities in the outer flow region are increased substantially with the introduction of the grids. It is shown that the externally generated turbulence is able to penetrate the bed boundary layer, resulting in an increase in the bed shear stress, and therefore...

Three-dimensional wake field analysis by boundary element method

International Nuclear Information System (INIS)

Miyata, K.

1987-01-01

A computer code HERTPIA was developed for the calculation of electromagnetic wake fields excited by charged particles travelling through arbitrarily shaped accelerating cavities. This code solves transient wave problems for a Hertz vector. The numerical analysis is based on the boundary element method. This program is validated by comparing its results with analytical solutions in a pill-box cavity

Boundary value problems for multi-term fractional differential equations

Science.gov (United States)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.

RANS Modeling of Benchmark Shockwave / Boundary Layer Interaction Experiments

Science.gov (United States)

Georgiadis, Nick; Vyas, Manan; Yoder, Dennis

2010-01-01

This presentation summarizes the computations of a set of shock wave / turbulent boundary layer interaction (SWTBLI) test cases using the Wind-US code, as part of the 2010 American Institute of Aeronautics and Astronautics (AIAA) shock / boundary layer interaction workshop. The experiments involve supersonic flows in wind tunnels with a shock generator that directs an oblique shock wave toward the boundary layer along one of the walls of the wind tunnel. The Wind-US calculations utilized structured grid computations performed in Reynolds-averaged Navier-Stokes mode. Three turbulence models were investigated: the Spalart-Allmaras one-equation model, the Menter Shear Stress Transport wavenumber-angular frequency two-equation model, and an explicit algebraic stress wavenumber-angular frequency formulation. Effects of grid resolution and upwinding scheme were also considered. The results from the CFD calculations are compared to particle image velocimetry (PIV) data from the experiments. As expected, turbulence model effects dominated the accuracy of the solutions with upwinding scheme selection indicating minimal effects.!

A controlled trial of trauma-focused therapy versus problem-solving in Islamic children affected by civil conflict and disaster in Aceh, Indonesia.

Science.gov (United States)

Dawson, Katie; Joscelyne, Amy; Meijer, Catherine; Steel, Zachary; Silove, Derrick; Bryant, Richard A

2018-03-01

To evaluate the relative efficacies of trauma-focused cognitive behavior therapy and problem-solving therapy in treating post-traumatic stress disorder in children affected by civil conflict in Aceh, Indonesia. A controlled trial of children with post-traumatic stress disorder ( N = 64) randomized children to either five individual weekly sessions of trauma-focused cognitive behavior therapy or problem-solving therapy provided by lay-counselors who were provided with brief training. Children were assessed by blind independent assessors at pretreatment, posttreatment and 3-month follow-up on post-traumatic stress disorder, depression and anger, as well as caregiver ratings of the child's post-traumatic stress disorder levels. Intent-to-treat analyses indicated no significant linear time × treatment condition interaction effects for post-traumatic stress disorder at follow-up ( t(129.05) = -0.55, p = 0.58), indicating the two conditions did not differ. Across both conditions, there were significant reductions in post-traumatic stress disorder on self-reported ( t(131.26) = -9.26, p solving: 2.68, 95% confidence interval = [2.07, 3.29]). These findings suggest that trauma-focused cognitive behavior therapy and problem-solving approaches are comparably successful in reducing post-traumatic stress disorder and anger in treating mental health in children in a post-conflict setting. This pattern may reflect the benefits of non-specific therapy effects or gains associated with trauma-focused or problem-solving approaches.

Separable boundary-value problems in physics

CERN Document Server

Willatzen, Morten

2011-01-01

Innovative developments in science and technology require a thorough knowledge of applied mathematics, particularly in the field of differential equations and special functions. These are relevant in modeling and computing applications of electromagnetic theory and quantum theory, e.g. in photonics and nanotechnology. The problem of solving partial differential equations remains an important topic that is taught at both the undergraduate and graduate level. Separable Boundary-Value Problems in Physics is an accessible and comprehensive treatment of partial differential equations i

Temperature field conduction solution by incomplete boundary condition

Energy Technology Data Exchange (ETDEWEB)

Novakovic, M; Petrasinovic, Lj; Djuric, M [Tehnoloski fakultet, Novi Sad (Yugoslavia); Perovic, N [Institut za Nuklearne Nauke Boris Kidric, Belgrade (Yugoslavia)

1977-01-01

The problem of determination of one part boundary conditions temperatures for Fourier partial differential equation when the other part of boundary condition and derivates (heat fluxes) are known is a practical interest as it enables one to determine and accessible temperature by measuring temperatures on other side, of the wall. Method developed and applied here consist of transforming the Fourier partial differential equation by time discretisation in sets of pairs of ordinary differential equations for temperature and heat flux. Such pair of differential equations of first order was solved by Runge-Kutta method. The integration proceeds along space interval simultaneosly for all time intervals. It is interesting to note that this procedure does not require the initial condition.

A nearly orthogonal 2D grid system in solving the shallow water equations in the head bay of Bengal

International Nuclear Information System (INIS)

Roy, G.D. . E.mail: roy_gd@hotmail.com; Hussain, Farzana . E.mail: farzana@sust.edu

2001-11-01

A typical nearly orthogonal grid system is considered to solve the shallow water equations along the head bay of Bengal. A pencil of straight lines at uniform angular distance through a suitable origin, O at the mean sea level (MSL), are considered as a system of grid lines. A system of concentric and uniformly distributed ellipses with center at O is considered as the other system of grid lines. In order to solve the shallow water equations numerically, a system of transformations is applied so that the grid system in the transformed domain becomes a rectangular one. Shallow water equations are solved using appropriate initial and boundary conditions to estimate the water level due to tide and surge. The typical grid system is found to be suitable in incorporating the bending of the coastline and the island boundaries accurately in the numerical scheme along the coast of Bangladesh. (author)

Influence of Variable Thermal Conductivity on MHD Boundary Layer Slip Flow of Ethylene-Glycol Based Cu Nanofluids over a Stretching Sheet with Convective Boundary Condition

Directory of Open Access Journals (Sweden)

N. Bhaskar Reddy

2014-01-01

Full Text Available An analysis is carried out to investigate the influence of variable thermal conductivity and partial velocity slip on hydromagnetic two-dimensional boundary layer flow of a nanofluid with Cu nanoparticles over a stretching sheet with convective boundary condition. Using similarity transformation, the governing boundary layer equations along with the appropriate boundary conditions are transformed to a set of ordinary differential equations. Employing Runge-kutta fourth-order method along with shooting technique, the resultant system of equations is solved. The influence of various pertinent parameters such as nanofluid volume fraction parameter, the magnetic parameter, radiation parameter, thermal conductivity parameter, velocity slip parameter, Biot number, and suction or injection parameter on the velocity of the flow field and heat transfer characteristics is computed numerically and illustrated graphically. The present results are compared with the existing results for the case of regular fluid and found an excellent agreement.

Improved algorithm for solving nonlinear parabolized stability equations

Science.gov (United States)

Zhao, Lei; Zhang, Cun-bo; Liu, Jian-xin; Luo, Ji-sheng

2016-08-01

Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. Project supported by the National Natural Science Foundation of China (Grant Nos. 11332007 and 11402167).

Boundary-layer effects in droplet splashing

Science.gov (United States)

Riboux, Guillaume; Gordillo, Jose Manuel

2017-11-01

A drop falling onto a solid substrate will disintegrate into smaller parts when its impact velocity exceeds the so called critical velocity for splashing. Under these circumstances, the very thin liquid sheet ejected tangentially to the solid after the drop touches the substrate, lifts off as a consequence of the aerodynamic forces exerted on it and finally breaks into smaller droplets, violently ejected radially outwards, provoking the splash. Here, the tangential deceleration experienced by the fluid entering the thin liquid sheet is investigated making use of boundary layer theory. The velocity component tangent to the solid, computed using potential flow theory provides the far field boundary condition as well as the pressure gradient for the boundary layer equations. The structure of the flow permits to find a self similar solution of the boundary layer equations. This solution is then used to calculate the boundary layer thickness at the root of the lamella as well as the shear stress at the wall. The splash model presented in, which is slightly modified to account for the results obtained from the boundary layer analysis, provides a very good agreement between the measurements and the predicted values of the critical velocity for the splash.

Evaluation of local stress for stress corrosion crack initiation by three-dimensional polycrystal model

International Nuclear Information System (INIS)

Kamaya, Masayuki; Kitamura, Takayuki

2006-01-01

In order to understand the initiation behavior of microstructurally small cracks in a stress corrosion cracking condition, it is important to know the tensile normal stress acting on the grain boundary (normal G.B. stress). The local stress in a polycrystalline body is greatly influenced by deformation constraint which is caused by anisotropic and/or inhomogeneous property of each grain. In present study, the local normal G.B. stress on bi- and tri-crystal bodies and a three-dimensional polycrystalline body consisting of 100 grains were evaluated by the finite element method under a remote uniform tensile stress condition. The polycrystalline body was generated by using a Monte Carlo procedure and random orientations were assigned to each grain. It was revealed that the local normal G.B. stress on the polycrystalline body is inhomogeneous under uniform applied stress. The stress tends to be large near the triple points due to the deformation constraint caused by adjacent grains, even though the grain boundary inclination to the load axis has large influence. It was also shown that particular high stress was not observed at corners of the polycrystalline body. (author)

Local Stress States and Microstructural Damage Response Associated with Deformation Twins in Hexagonal Close Packed Metals

Directory of Open Access Journals (Sweden)

Indranil Basu

2017-12-01

Full Text Available The current work implements a correlative microscopy method utilizing electron back scatter diffraction, focused ion beam and digital image correlation to accurately determine spatially resolved stress profiles in the vicinity of grain/twin boundaries and tensile deformation twin tips in commercially pure titanium. Measured local stress gradients were in good agreement with local misorientation values. The role of dislocation-boundary interactions on the buildup of local stress gradients is elucidated. Stress gradients across the twin-parent interface were compressive in nature with a maximum stress magnitude at the twin boundary. Stress profiles near certain grain boundaries initially display a local stress minimum, followed by a typically observed “one over square root of distance” variation, as was first postulated by Eshelby, Frank and Nabarro. The observed trends allude to local stress relaxation mechanisms very close to the grain boundaries. Stress states in front of twin tips showed tensile stress gradients, whereas the stress state inside the twin underwent a sign reversal. The findings highlight the important role of deformation twins and their corresponding interaction with grain boundaries on damage nucleation in metals.

An efficient implicit direct forcing immersed boundary method for incompressible flows

International Nuclear Information System (INIS)

Cai, S-G; Ouahsine, A; Smaoui, H; Favier, J; Hoarau, Y

2015-01-01

A novel efficient implicit direct forcing immersed boundary method for incompressible flows with complex boundaries is presented. In the previous work [1], the calculation is performed on the Cartesian grid regardless of the immersed object, with a fictitious force evaluated on the Lagrangian points to mimic the presence of the physical boundaries. However the explicit direct forcing method [1] fails to accurately impose the non-slip boundary condition on the immersed interface. In the present work, the calculation is based on the implicit treatment of the artificial force while in an effective way of system iteration. The accuracy is also improved by solving the Navier-Stokes equation with the rotational incremental pressure- correction projection method of Guermond and Shen [2]. Numerical simulations performed with the proposed method are in good agreement with those in the literature

Implicit Boundary Integral Methods for the Helmholtz Equation in Exterior Domains

Science.gov (United States)

2016-06-01

solve the Helmholtz equation as ∂Ω goes through significant change in its shape and topology — applications for which implicit representation of the...boundary-value problems for the wave equation and maxwell’s equations. Russian Math . Surv., 1965. [16] S. Reutskiy. The method of fundamental

An optimal iterative algorithm to solve Cauchy problem for Laplace equation

KAUST Repository

Majeed, Muhammad Usman

2015-05-25

An optimal mean square error minimizer algorithm is developed to solve severely ill-posed Cauchy problem for Laplace equation on an annulus domain. The mathematical problem is presented as a first order state space-like system and an optimal iterative algorithm is developed that minimizes the mean square error in states. Finite difference discretization schemes are used to discretize first order system. After numerical discretization algorithm equations are derived taking inspiration from Kalman filter however using one of the space variables as a time-like variable. Given Dirichlet and Neumann boundary conditions are used on the Cauchy data boundary and fictitious points are introduced on the unknown solution boundary. The algorithm is run for a number of iterations using the solution of previous iteration as a guess for the next one. The method developed happens to be highly robust to noise in Cauchy data and numerically efficient results are illustrated.

Structure measurements in a synthetic turbulent boundary layer

Science.gov (United States)

Arakeri, Jaywant H.

1987-09-01

Extensive hot-wire measurements have been made to determine the structure of the large eddy in a synthejc turbulent boundary layer on a flat-plate model. The experiments were carried out in a wind tunnel at a nominal free-stream velocity of 12 m/s. The synthetic turbulent boundary layer had a hexagonal pattern of eddies and a ratio of streamwise scale to spanwise scale of 3.2:1. The measured celerity of the large eddy was 84.2 percent of the free-stream velocity. There was some loss of coherence, but very little distortion, as the eddies moved downstream. Several mean properties of the synthetic boundary layer were found to agree quite well with the mean properties of a natural turbulent boundary layer at the same Reynolds number. The large eddy is composed of a pair of primary counter-rotating vortices about five [...] long in the streamwise direction and about one [...] apart in the spanwise direction, where [...] is the mean boundary-layer thickness. The sense of the primary pair is such as to pump fluid away from the wall in the region between the vortices. A secondary pair of counter-rotating streamwise vortices, having a sense opposite to that of the primary pair, is observed outside of and slightly downstream from the primary vortices. Both pairs of vortices extend across the full thickness of the boundary layer and are inclined at a shallow angle to the surface of the flat plate. The data show that the mean vorticity vectors are not tangential to the large-eddy vortices. In fact, the streamwise and normal vorticity components that signal the presence of the eddy are of the same order of magnitude. Definite signatures are obtained in terms of the mean skin-friction coefficient and the mean wake parameter averaged at constant phase. Velocities induced by the vortices are partly responsible for entrainment of irrotational fluid, for transport of momentum, for generation of Reynolds stresses, and for maintenance of streamwise and normal vorticity in the outer

Contribution to the analytical and numerical evaluation of oil well equilibrium for any cross section under a uniform pressure and an anisotropic stress field

Energy Technology Data Exchange (ETDEWEB)

Bouziane, A.

1989-09-01

The integral equation, the finite element and an analytical method are used and compared to compute the state of equilibrium of an oil well. This well is of whatever cross section and is subjected to a uniform pressure and an anisotropic stress field at the infinity. In the first part, the equations of the Mechanics of deformable solids are recalled using dual vectorial spaces theory. These equations are briefly introduced by using a four spaces diagram. In the second part, an analytical method using the complex potentials developed by Muskhelishvili is used to solve the problem. In the third part, three methods of integral equations are developed (direct and indirect). The stress boundary conditions at infinity are taken into account by superimposing a particular solution to the fundamental solution. With such a method, both displacements and stresses are correctly represented as well on the boundary as inside the domain. The finite element method is developed in the fourth part. For complicate shapes of well cross section the used automatic mesh generator does not seem well adapted. In conclusion, the integral equation method gives the results which are in the best agreement with the analytical solutions.

Intergranular and inter-phased boundaries in the materials

International Nuclear Information System (INIS)

Aslanides, A.; Backhaus-Ricoult, M.; Bayle-Guillemaud, P.

2000-01-01

This document collects the abstracts of the talks presented during the colloquium J2IM on the intergranular and inter-phased boundaries in the materials. Around the themes of the interfaces behaviour and grain boundaries defects in materials, these days dealt with the microstructure behaviour in many domains such as the interfaces in batteries, the irradiation damages and the special case of the fuel-cladding interactions, the stressed interfaces, the alumina or silicon carbides substrates. (A.L.B.)

Mathematical Model of Stress-Strain State of Curved Tube of Non-Circular Cross-Section with Account of Technological Wall Thickness Variation

Science.gov (United States)

Pirogov, S. P.; Ustinov, N. N.; Smolin, N. I.

2018-05-01

A mathematical model of the stress-strain state of a curved tube of a non-circular cross-section is presented, taking into account the technological wall thickness variation. On the basis of the semi-membrane shell theory, a system of linear differential equations describing the deformation of a tube under the effect of pressure is obtained. To solve the boundary value problem, the method of shooting is applied. The adequacy of the proposed mathematical model is verified by comparison with the experimental data and the results of the calculation of tubes by the energy method.

A Fortran program (RELAX3D) to solve the 3 dimensional Poisson (Laplace) equation

International Nuclear Information System (INIS)

Houtman, H.; Kost, C.J.

1983-09-01

RELAX3D is an efficient, user friendly, interactive FORTRAN program which solves the Poisson (Laplace) equation Λ 2 =p for a general 3 dimensional geometry consisting of Dirichlet and Neumann boundaries approximated to lie on a regular 3 dimensional mesh. The finite difference equations at these nodes are solved using a successive point-iterative over-relaxation method. A menu of commands, supplemented by HELP facility, controls the dynamic loading of the subroutine describing the problem case, the iterations to converge to a solution, and the contour plotting of any desired slices, etc

Stress analysis on a PWR pressure vessel support structure

International Nuclear Information System (INIS)

Cruz, J.R.B.; Mattar Neto, M.; Jesus Miranda, C.A. de.

1992-01-01

The paper presents the stress analysis of a research PWR vessel support structure. Different geometries and thermal boundary conditions are evaluated. The finite element analysis is performed using ANSYS program. The ASME Section III criteria are applied for the stress verification and the following points are discussed: stress classification and linearization; jurisdictional boundary between ASME Subsection NB (Class 1 Components) and Subsection NF (Component Supports). (author)

Abraham Pais Prize Lecture: Shifting Problems and Boundaries in the History of Modern Physics

Science.gov (United States)

Nye, Mary-Jo

A long established category of study in the history of science is the ``history of physical sciences.'' It is a category that immediately begs the question of disciplinary boundaries for the problems and subjects addressed in historical inquiry. As a historian of the physical sciences, I often have puzzled over disciplinary boundaries and the means used to create or justify them. Scientists most often have been professionally identified with specific institutionalized fields since the late 19th century, but the questions they ask and the problems they solve are not neatly carved up by disciplinary perimeters. Like institutional departments or professorships, the Nobel Prizes in the 20th century often have delineated the scope of ``Physics'' or ``Chemistry'' (and ``Physiology or Medicine''), but the Prizes do not reflect disciplinary rigidity, despite some standard core subjects. In this paper I examine trends in Nobel Prize awards that indicate shifts in problem solving and in boundaries in twentieth century physics, tying those developments to changing themes in the history of physics and physical science in recent decades.

Solving the Stokes problem on a massively parallel computer

DEFF Research Database (Denmark)

Axelsson, Owe; Barker, Vincent A.; Neytcheva, Maya

2001-01-01

boundary value problem for each velocity component, are solved by the conjugate gradient method with a preconditioning based on the algebraic multi‐level iteration (AMLI) technique. The velocity is found from the computed pressure. The method is optimal in the sense that the computational work...... is proportional to the number of unknowns. Further, it is designed to exploit a massively parallel computer with distributed memory architecture. Numerical experiments on a Cray T3E computer illustrate the parallel performance of the method....

Oblique radiation lateral open boundary conditions for a regional climate atmospheric model

Science.gov (United States)

Cabos Narvaez, William; De Frutos Redondo, Jose Antonio; Perez Sanz, Juan Ignacio; Sein, Dmitry

2013-04-01

The prescription of lateral boundary conditions in regional atmospheric models represent a very important issue for limited area models. The ill-posed nature of the open boundary conditions makes it necessary to devise schemes in order to filter spurious wave reflections at boundaries, being desirable to have one boundary condition per variable. On the other side, due to the essentially hyperbolic nature of the equations solved in state of the art atmospheric models, external data is required only for inward boundary fluxes. These circumstances make radiation lateral boundary conditions a good choice for the filtering of spurious wave reflections. Here we apply the adaptive oblique radiation modification proposed by Mikoyada and Roseti to each of the prognostic variables of the REMO regional atmospheric model and compare it to the more common normal radiation condition used in REMO. In the proposed scheme, special attention is paid to the estimation of the radiation phase speed, essential to detecting the direction of boundary fluxes. One of the differences with the classical scheme is that in case of outward propagation, the adaptive nudging imposed in the boundaries allows to minimize under and over specifications problems, adequately incorporating the external information.

An updated stress map of the continental United States reveals heterogeneous intraplate stress

Science.gov (United States)

Levandowski, Will; Herrmann, Robert B.; Briggs, Rich; Boyd, Oliver; Gold, Ryan

2018-06-01

Knowledge of the state of stress in Earth's crust is key to understanding the forces and processes responsible for earthquakes. Historically, low rates of natural seismicity in the central and eastern United States have complicated efforts to understand intraplate stress, but recent improvements in seismic networks and the spread of human-induced seismicity have greatly improved data coverage. Here, we compile a nationwide stress map based on formal inversions of focal mechanisms that challenges the idea that deformation in continental interiors is driven primarily by broad, uniform stress fields derived from distant plate boundaries. Despite plate-boundary compression, extension dominates roughly half of the continent, and second-order forces related to lithospheric structure appear to control extension directions. We also show that the states of stress in several active eastern United States seismic zones differ significantly from those of surrounding areas and that these anomalies cannot be explained by transient processes, suggesting that earthquakes are focused by persistent, locally derived sources of stress. Such spatially variable intraplate stress appears to justify the current, spatially variable estimates of seismic hazard. Future work to quantify sources of stress, stressing-rate magnitudes and their relationship with strain and earthquake rates could allow prospective mapping of intraplate hazard.

Problem-solving and mental health outcomes of women and children in the wake of intimate partner violence.

Science.gov (United States)

Maddoux, John; Symes, Lene; McFarlane, Judith; Koci, Anne; Gilroy, Heidi; Fredland, Nina

2014-01-01

The environmental stress of intimate partner violence is common and often results in mental health problems of depression, anxiety, and PTSD for women and behavioral dysfunctions for their children. Problem-solving skills can serve to mitigate or accentuate the environmental stress of violence and associated impact on mental health. To better understand the relationship between problem-solving skills and mental health of abused women with children, a cross-sectional predictive analysis of 285 abused women who used justice or shelter services was completed. The women were asked about social problem-solving, and mental health symptoms of depression, anxiety, and PTSD as well as behavioral functioning of their children. Higher negative problem-solving scores were associated with significantly (P women's abilities to navigate the daily stressors of life following abuse.

Stretching the stress boundary: Linking air pollution health effects to a neurohormonal stress response.

Science.gov (United States)

Kodavanti, Urmila P

2016-12-01

Inhaled pollutants produce effects in virtually all organ systems in our body and have been linked to chronic diseases including hypertension, atherosclerosis, Alzheimer's and diabetes. A neurohormonal stress response (referred to here as a systemic response produced by activation of the sympathetic nervous system and hypothalamus-pituitary-adrenal (HPA)-axis) has been implicated in a variety of psychological and physical stresses, which involves immune and metabolic homeostatic mechanisms affecting all organs in the body. In this review, we provide new evidence for the involvement of this well-characterized neurohormonal stress response in mediating systemic and pulmonary effects of a prototypic air pollutant - ozone. A plethora of systemic metabolic and immune effects are induced in animals exposed to inhaled pollutants, which could result from increased circulating stress hormones. The release of adrenal-derived stress hormones in response to ozone exposure not only mediates systemic immune and metabolic responses, but by doing so, also modulates pulmonary injury and inflammation. With recurring pollutant exposures, these effects can contribute to multi-organ chronic conditions associated with air pollution. This review will cover, 1) the potential mechanisms by which air pollutants can initiate the relay of signals from respiratory tract to brain through trigeminal and vagus nerves, and activate stress responsive regions including hypothalamus; and 2) the contribution of sympathetic and HPA-axis activation in mediating systemic homeostatic metabolic and immune effects of ozone in various organs. The potential contribution of chronic environmental stress in cardiovascular, neurological, reproductive and metabolic diseases, and the knowledge gaps are also discussed. This article is part of a Special Issue entitled Air Pollution, edited by Wenjun Ding, Andrew J. Ghio and Weidong Wu. Published by Elsevier B.V.

Experimental validation of a boundary element solver for exterior acoustic radiation problems

NARCIS (Netherlands)

Visser, Rene; Nilsson, A.; Boden, H.

2003-01-01

The relation between harmonic structural vibrations and the corresponding acoustic radiation is given by the Helmholtz integral equation (HIE). To solve this integral equation a new solver (BEMSYS) based on the boundary element method (BEM) has been implemented. This numerical tool can be used for

Micro Ramps in Supersonic Turbulent Boundary Layers : An experimental and numerical study

NARCIS (Netherlands)

Sun, Z.

2014-01-01

The micro vortex generator (MVG) is used extensively in low speed aerodynamic problems and is now extended into the supersonic flow regime to solve undesired flow features that are associated with shock wave boundary layer interactions (SWBLI) such as flow separation and associated unsteadiness of

Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with initial stresses.

Science.gov (United States)

Guo, Xiao; Wei, Peijun

2016-03-01

The dispersion relations of elastic waves in a one-dimensional phononic crystal formed by periodically repeating of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are studied in this paper. The influences of initial stress on the dispersive relation are considered based on the incremental stress theory. First, the incremental stress theory of elastic solid is extended to the magneto-electro-elasto solid. The governing equations, constitutive equations, and boundary conditions of the incremental stresses in a magneto-electro-elasto solid are derived with consideration of the existence of initial stresses. Then, the transfer matrices of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are formulated, respectively. The total transfer matrix of a single cell in the phononic crystal is obtained by the multiplication of two transfer matrixes related with two adjacent slabs. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. The oblique propagation and the normal propagation situations are both considered. In the case of normal propagation of elastic waves, the analytical expressions of the dispersion equation are derived and compared with other literatures. The influences of initial stresses, including the normal initial stresses and shear initial stresses, on the dispersive relations are both discussed based on the numerical results. Copyright © 2015 Elsevier B.V. All rights reserved.

Discrete maximum principle for Poisson equation with mixed boundary conditions solved by hp-FEM

Czech Academy of Sciences Publication Activity Database

Vejchodský, Tomáš; Šolín, P.

2009-01-01

Roč. 1, č. 2 (2009), s. 201-214 ISSN 2070-0733 R&D Projects: GA AV ČR IAA100760702; GA ČR(CZ) GA102/07/0496; GA ČR GA102/05/0629 Institutional research plan: CEZ:AV0Z10190503 Keywords : discrete maximum principle * hp-FEM * Poisson equation * mixed boundary conditions Subject RIV: BA - General Mathematics

Structure of reconnection boundary layers in incompressible MHD

International Nuclear Information System (INIS)

Sonnerup, B.U.Oe.; Wang, D.J.

1987-01-01

The incompressible MHD equations with nonvanishing viscosity and resistivity are simplified by use of the boundary layer approximation to describe the flow and magnetic field in the exit flow regions of magnetic field reconnection configurations when the reconnection rate is small. The conditions are derived under which self-similar solutions exist of the resulting boundary layer equations. For the case of zero viscosity and resistivity, the equations describing such self-similar layers are then solved in terms of quadratures, and the resulting flow and field configurations are described. Symmetric solutions, relevant, for example, to reconnection in the geomagnetic tail, as well as asymmetric solutions, relevant to reconnection at the earth's magnetopause, are found to exist. The nature of the external solutions to which the boundary layer solutions should be matched is discussed briefly, but the actual matching, which is to occur at Alfven-wave characteristic curves in the boundary layer solutions, is not carried out. Finally, it is argued that the solutions obtained may also be used to describe the structure of the intense vortex layers observed to occur at magnetic separatrices in computer simulations and in certain analytical models of the reconnection process

Calculation code NIRVANA for free boundary MHD equilibrium

International Nuclear Information System (INIS)

Ninomiya, Hiromasa; Suzuki, Yasuo; Kameari, Akihisa

1975-03-01

The calculation method and code of solving the free boundary problem for MHD equilibrium has been developed. Usage of the code ''NIRVANA'' is described. The toroidal plasma current density determined as a function of the flux function PSI is substituted by a group of the ring currents, whereby the equation of MHD equilibrium is transformed into an integral equation. Either of the two iterative methods is chosen to solve the integral equation, depending on the assumptions made of the plasma surface points. Calculation of the magnetic field configurations is possible when the plasma surface coincides self-consistently with the magnetic flux including the separatrix points. The code is usable in calculation of the circular or non-circular shell-less Tokamak equilibrium. (auth.)

Discrete Lattice effect of various forcing methods of body force on immersed Boundary-Lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Son, Sung Wan; Ha, Man Yeong; Yoon, Hyun Sik [Pusan National University, Busan (Korea, Republic of); Jeong, Hae Kwon [POSCO, Pohang (Korea, Republic of); Balachandar, S. [University of Florida, Florida (United States)

2013-02-15

We investigate the discrete lattice effect of various forcing methods in the lattice Boltzmann method (LBM) to include the body force obtained from the immersed boundary method (IBM). In the immersed boundary lattice Boltzmann method (IB-LBM), the LBM needs a forcing method to involve the body force on a forcing point near the immersed boundary that is calculated by IBM. The proper forcing method in LBM is derived to include the body force, which appears to resolve problems such as multiphase flow, non-ideal gas behavior, etc. Many researchers have adopted different forcing methods in LBM to involve the body force from IBM, even when they solved similar problems. However, it is necessary to evaluate the discrete lattice effect, which originates from different forcing methods in LBM, to include the effect of the body force from IBM on the results. Consequently, in this study, a rigorous analysis of the discrete lattice effect for different forcing methods in IB-LBM is performed by solving various problems.

Discrete Lattice effect of various forcing methods of body force on immersed Boundary-Lattice Boltzmann method

International Nuclear Information System (INIS)

Son, Sung Wan; Ha, Man Yeong; Yoon, Hyun Sik; Jeong, Hae Kwon; Balachandar, S.

2013-01-01

We investigate the discrete lattice effect of various forcing methods in the lattice Boltzmann method (LBM) to include the body force obtained from the immersed boundary method (IBM). In the immersed boundary lattice Boltzmann method (IB-LBM), the LBM needs a forcing method to involve the body force on a forcing point near the immersed boundary that is calculated by IBM. The proper forcing method in LBM is derived to include the body force, which appears to resolve problems such as multiphase flow, non-ideal gas behavior, etc. Many researchers have adopted different forcing methods in LBM to involve the body force from IBM, even when they solved similar problems. However, it is necessary to evaluate the discrete lattice effect, which originates from different forcing methods in LBM, to include the effect of the body force from IBM on the results. Consequently, in this study, a rigorous analysis of the discrete lattice effect for different forcing methods in IB-LBM is performed by solving various problems.

A Viscous Fluid Flow through a Thin Channel with Mixed Rigid-Elastic Boundary: Variational and Asymptotic Analysis

Directory of Open Access Journals (Sweden)

R. Fares

2012-01-01

Full Text Available We study the nonsteady Stokes flow in a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results, and some a priori estimates, we construct an asymptotic solution. The existence of a junction region between the two rectangles imposes to consider, as part of the asymptotic solution, some boundary layer correctors that correspond to this region. We present and solve the problems for all the terms of the asymptotic expansion. For two different cases, we describe the order of steps of the algorithm of solving the problem and we construct the main term of the asymptotic expansion. By means of the a priori estimates, we justify our asymptotic construction, by obtaining a small error between the exact and the asymptotic solutions.

Boundary Layer Fluid Flow in a Channel with Heat Source, Soret ...

African Journals Online (AJOL)

The boundary layer fluid flow in a channel with heat source, soret effects and slip condition was studied. The governing equations were solved using perturbation technique. The effects of different parameters such Prandtl number Pr , Hartmann number M, Schmidt number Sc, suction parameter ƒÜ , soret number Sr and the ...

Coherent structures in wave boundary layers. Part 2. Solitary motion

DEFF Research Database (Denmark)

Sumer, B. Mutlu; Jensen, Palle Martin; Sørensen, Lone B.

2010-01-01

This study continues the investigation of wave boundary layers reported by Carstensen, Sumer & Fredsøe (J. Fluid Mech., 2010, part 1 of this paper). The present paper summarizes the results of an experimental investigation of turbulent solitary wave boundary layers, simulated by solitary motion...... the boundary-layer flow experiences a regular array of vortex tubes near the bed over a short period of time during the deceleration stage; and (iii) transitional regime characterized with turbulent spots, revealed by single/multiple, or, sometimes, quite dense spikes in the bed shear stress traces...

Year-Long Vertical Velocity Statistics Derived from Doppler Lidar Data for the Continental Convective Boundary Layer

Energy Technology Data Exchange (ETDEWEB)

Berg, Larry K. [Pacific Northwest National Laboratory, Richland, Washington; Newsom, Rob K. [Pacific Northwest National Laboratory, Richland, Washington; Turner, David D. [Global Systems Division, NOAA/Earth System Research Laboratory, Boulder, Colorado

2017-09-01

One year of Coherent Doppler Lidar (CDL) data collected at the U.S. Department of Energy’s Atmospheric Radiation Measurement (ARM) site in Oklahoma is analyzed to provide profiles of vertical velocity variance, skewness, and kurtosis for cases of cloud-free convective boundary layers. The variance was scaled by the Deardorff convective velocity scale, which was successful when the boundary layer depth was stationary but failed in situations when the layer was changing rapidly. In this study the data are sorted according to time of day, season, wind direction, surface shear stress, degree of instability, and wind shear across the boundary-layer top. The normalized variance was found to have its peak value near a normalized height of 0.25. The magnitude of the variance changes with season, shear stress, and degree of instability, but was not impacted by wind shear across the boundary-layer top. The skewness was largest in the top half of the boundary layer (with the exception of wintertime conditions). The skewness was found to be a function of the season, shear stress, wind shear across the boundary-layer top, with larger amounts of shear leading to smaller values. Like skewness, the vertical profile of kurtosis followed a consistent pattern, with peak values near the boundary-layer top (also with the exception of wintertime data). The altitude of the peak values of kurtosis was found to be lower when there was a large amount of wind shear at the boundary-layer top.

Web-Based Problem-Solving Assignment and Grading System

Science.gov (United States)

Brereton, Giles; Rosenberg, Ronald

2014-11-01

In engineering courses with very specific learning objectives, such as fluid mechanics and thermodynamics, it is conventional to reinforce concepts and principles with problem-solving assignments and to measure success in problem solving as an indicator of student achievement. While the modern-day ease of copying and searching for online solutions can undermine the value of traditional assignments, web-based technologies also provide opportunities to generate individualized well-posed problems with an infinite number of different combinations of initial/final/boundary conditions, so that the probability of any two students being assigned identical problems in a course is vanishingly small. Such problems can be designed and programmed to be: single or multiple-step, self-grading, allow students single or multiple attempts; provide feedback when incorrect; selectable according to difficulty; incorporated within gaming packages; etc. In this talk, we discuss the use of a homework/exam generating program of this kind in a single-semester course, within a web-based client-server system that ensures secure operation.

Coping as a mediator of the relationship between stress mindset and psychological stress response: a pilot study.

Science.gov (United States)

Horiuchi, Satoshi; Tsuda, Akira; Aoki, Shuntaro; Yoneda, Kenichiro; Sawaguchi, Yusuke

2018-01-01

Coping, the cognitive and behavioral effort required to manage the effects of stressors, is important in determining psychological stress responses (ie, the emotional, behavioral, and cognitive responses to stressors). Coping was classified into categories of emotional expression (eg, negative feelings and thoughts), emotional support seeking (eg, approaching loved ones to request encouragement), cognitive reinterpretation (eg, reframing a problem positively), and problem solving (eg, working to solve the problem). Stress mindset refers to the belief that stress has enhancing (stress-is-enhancing mindset) or debilitating consequences (stress-is-debilitating mindset). This study examined whether coping mediated the relationship between stress mindset and psychological stress responses. Psychological stress responses were conceptualized as depression-anxiety, irritability-anger, and helplessness. The following two hypotheses were tested: 1) a stronger stress-is-enhancing mindset is associated with less frequent use of emotional expression, emotional support seeking, and problem solving, which in turn is associated with lower levels of depression-anxiety, irritability-anger, and helplessness; 2) a stronger stress-is-debilitating mindset is associated with more frequent use of these coping strategies, which in turn is associated with higher levels of these psychological stress responses. The participants were 30 male and 94 female undergraduate and graduate students (mean age =20.4 years). Stress mindset, coping, and psychological stress responses were measured using self-report questionnaires. Six mediation analyses were performed with stress-is-enhancing mindset or stress-is-debilitating mindset as the independent variable, one of the psychological stress responses as the dependent variable, and the four coping strategies as mediators. Emotional expression partially mediated the relationship between a strong stress-is-debilitating mindset and higher irritability

Boundary element methods for electrical engineers

CERN Document Server

POLJAK, D

2005-01-01

In the last couple of decades the Boundary Element Method (BEM) has become a well-established technique that is widely used for solving various problems in electrical engineering and electromagnetics. Although there are many excellent research papers published in the relevant literature that describe various BEM applications in electrical engineering and electromagnetics, there has been a lack of suitable textbooks and monographs on the subject. This book presents BEM in a simple fashion in order to help the beginner to understand the very basic principles of the method. It initially derives B

Solving Two -Dimensional Diffusion Equations with Nonlocal Boundary Conditions by a Special Class of Padé Approximants

Directory of Open Access Journals (Sweden)

Mohammad Siddique

2010-08-01

Full Text Available Parabolic partial differential equations with nonlocal boundary conditions arise in modeling of a wide range of important application areas such as chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. In this paper, we present the implementation of positivity- preserving Padé numerical schemes to the two-dimensional diffusion equation with nonlocal time dependent boundary condition. We successfully implemented these numerical schemes for both Homogeneous and Inhomogeneous cases. The numerical results show that these Padé approximation based numerical schemes are quite accurate and easily implemented.

Numerical analysis of three-dimensional turbulent flow in a 90deg bent tube by algebraic Reynolds stress model

International Nuclear Information System (INIS)

Sugiyama, Hitoshi; Akiyama, Mitsunobu; Shinohara, Yasunori; Hitomi, Daisuke

1997-01-01

A numerical analysis has been performed for three dimensional developing turbulent flow in a 90deg bent tube with straight inlet and outlet sections by an algebraic Reynolds stress model. To our knowledge, very little has been reported about detailed comparison between calculated results and experimental data containing Reynolds stresses. In calculation, an algebraic Reynolds stress model together with a boundary-fitted coordinate system is applied to a 90deg bent tube in order to solve anisotropic turbulent flow precisely. The calculated results display comparatively good agreement with the experimental data of time averaged velocity and secondary vectors. In addition, the present method predicts as a characteristic feature that the intensity of secondary flow near the inner wall is increased immediately downstream from the bend outlet by the pressure gradient. With regard to comparison of Reynolds stresses, the present method is able to reproduce well the distributions of streamwise normal stress and shear stress defined streamwise and radial velocity fluctuation except for the shear stress defined streamwise and circumferential velocity fluctuation. The present calculation has been found to simulate many features of the developing flow in bent tube satisfactorily, but it has a tendency to underpredict the Reynolds stresses. (author)

A matrix formalism to solve interface condition equations in a reactor system

Energy Technology Data Exchange (ETDEWEB)

Matausek, M V [Boris Kidric Institute of Nuclear Sciences Vinca, Beograd (Yugoslavia)

1970-05-15

When a nuclear reactor or a reactor lattice cell is treated by an approximate procedure to solve the neutron transport equation, as the last computational step often appears a problem of solving systems of algebraic equations stating the interface and boundary conditions for the neutron flux moments. These systems have usually the coefficient matrices of the block-bi diagonal type, containing thus a large number of zero elements. In the present report it is shown how such a system can be solved efficiently accounting for all the zero elements both in the coefficient matrix and in the free term vector. The procedure is presented here for the case of multigroup P{sub 3} calculation of neutron flux distribution in a cylindrical reactor lattice cell. Compared with the standard gaussian elimination method, this procedure is more advantageous both in respect to the number of operations needed to solve a given problem and in respect to the computer memory storage requirements. A similar formalism can also be applied for other approximate methods, for instance for multigroup diffusion treatment of a multi zone reactor. (author)

Problem Solving and Emotional Distress Among Brain and Breast Cancer Survivors

Science.gov (United States)

2007-03-30

with cancer and their families. Cancer, 74, 2071-2078. Lazarus , R. S., & Folkman , S. (1984). Stress, appraisal, and coping. New York: Springer...being able to access post-treatment rehabilitative care (Eversley et al., 2005). Social Problem Solving Lazarus and Folkman’s stress appraisal...International Neuropsychological Sociology, 9(7), 967-982. Archibald, Y . M., Lunn, D., Ruttan, L. A., MacDonald, D. R., Del Maestro, R. F., Barr, H

Study of effect of a smooth hump on hypersonic boundary layer instability

Science.gov (United States)

Park, Donghun; Park, Seung O.

2016-12-01

Effect of a two-dimensional smooth hump on linear instability of hypersonic boundary layer is studied by using parabolized stability equations. Linear evolution of mode S over a hump is analyzed for Mach 4.5 and 5.92 flat plate and Mach 7.1 sharp cone boundary layers. Mean flow for stability analysis is obtained by solving the parabolized Navier-Stokes equations. Hump with height smaller than local boundary layer thickness is considered. The case of flat plate and sharp cone without the hump are also studied to provide comparable data. For flat plate boundary layers, destabilization and stabilization effect is confirmed for hump located at upstream and downstream of synchronization point, respectively. Results of parametric studies to examine the effect of hump height, location, etc., are also given. For sharp cone boundary layer, stabilization influence of hump is also identified for a specific range of frequency. Stabilization influence of hump on convective instability of mode S is found to be a possible cause of previous experimental observations of delaying transition in hypersonic boundary layers.

Variable and space steps solution of a two phase moving boundary ...

African Journals Online (AJOL)

Equations of a two phase moving boundary problem in cylindrical coordinates are obtained from the formulation of a transient shrinking core model of whole tree combustion in a one dimensional steady state fixed-bed reactor. An hybrid Variable Grid Method is developed to solve the non linear equations and the results are ...

Conference on Boundary and Interior Layers : Computational and Asymptotic Methods

CERN Document Server

2015-01-01

This volume offers contributions reflecting a selection of the lectures presented at the international conference BAIL 2014, which was held from 15th to 19th September 2014 at the Charles University in Prague, Czech Republic. These are devoted to the theoretical and/or numerical analysis of problems involving boundary and interior layers and methods for solving these problems numerically. The authors are both mathematicians (pure and applied) and engineers, and bring together a large number of interesting ideas. The wide variety of topics treated in the contributions provides an excellent overview of current research into the theory and numerical solution of problems involving boundary and interior layers.  .

Fast multipole acceleration of the MEG/EEG boundary element method

International Nuclear Information System (INIS)

Kybic, Jan; Clerc, Maureen; Faugeras, Olivier; Keriven, Renaud; Papadopoulo, Theo

2005-01-01

The accurate solution of the forward electrostatic problem is an essential first step before solving the inverse problem of magneto- and electroencephalography (MEG/EEG). The symmetric Galerkin boundary element method is accurate but cannot be used for very large problems because of its computational complexity and memory requirements. We describe a fast multipole-based acceleration for the symmetric boundary element method (BEM). It creates a hierarchical structure of the elements and approximates far interactions using spherical harmonics expansions. The accelerated method is shown to be as accurate as the direct method, yet for large problems it is both faster and more economical in terms of memory consumption

Unstructured Cartesian refinement with sharp interface immersed boundary method for 3D unsteady incompressible flows

Science.gov (United States)

Angelidis, Dionysios; Chawdhary, Saurabh; Sotiropoulos, Fotis

2016-11-01

A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton-Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates

Solving hyperbolic heat conduction using electrical simulation

International Nuclear Information System (INIS)

Gheitaghy, A. M.; Talaee, M. R.

2013-01-01

In the present study, the electrical network simulation method is proposed to solve the hyperbolic and parabolic heat conduction problem considering Cattaneo-Vernoute (C.V) constitutive relation. Using this new proposed numerical model and the electrical circuit simulation program HSPICE, transient temperature and heat flux profiles at slab can be obtained easily and quickly. To verify the proposed method, the obtained numerical results for cases of one dimensional two-layer slab under periodic boundary temperature with perfect and imperfect thermal contact are compared with the published results. Comparisons show the proposed technique might be considered as a useful tool in the analysis of parabolic and hyperbolic thermal problems.

Transport synthetic acceleration with opposing reflecting boundary conditions

Energy Technology Data Exchange (ETDEWEB)

Zika, M R; Adams, M L

2000-02-01

The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iterating on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented.

Diffusive growth of a single droplet with three different boundary conditions

Science.gov (United States)

Tavassoli, Z.; Rodgers, G. J.

2000-02-01

We study a single, motionless three-dimensional droplet growing by adsorption of diffusing monomers on a 2D substrate. The diffusing monomers are adsorbed at the aggregate perimeter of the droplet with different boundary conditions. Models with both an adsorption boundary condition and a radiation boundary condition, as well as a phenomenological model, are considered and solved in a quasistatic approximation. The latter two models allow particle detachment. In the short time limit, the droplet radius grows as a power of the time with exponents of 1/4, 1/2 and 3/4 for the models with adsorption, radiation and phenomenological boundary conditions, respectively. In the long time limit a universal growth rate as $[t/\\ln(t)]^{1/3}$ is observed for the radius of the droplet for all models independent of the boundary conditions. This asymptotic behaviour was obtained by Krapivsky \\cite{krapquasi} where a similarity variable approach was used to treat the growth of a droplet with an adsorption boundary condition based on a quasistatic approximation. Another boundary condition with a constant flux of monomers at the aggregate perimeter is also examined. The results exhibit a power law growth rate with an exponent of 1/3 for all times.

Finite element time domain modeling of controlled-Source electromagnetic data with a hybrid boundary condition

DEFF Research Database (Denmark)

Cai, Hongzhu; Hu, Xiangyun; Xiong, Bin

2017-01-01

method which is unconditionally stable. We solve the diffusion equation for the electric field with a total field formulation. The finite element system of equation is solved using the direct method. The solutions of electric field, at different time, can be obtained using the effective time stepping...... method with trivial computation cost once the matrix is factorized. We try to keep the same time step size for a fixed number of steps using an adaptive time step doubling (ATSD) method. The finite element modeling domain is also truncated using a semi-adaptive method. We proposed a new boundary...... condition based on approximating the total field on the modeling boundary using the primary field corresponding to a layered background model. We validate our algorithm using several synthetic model studies....

On the wave equation with semilinear porous acoustic boundary conditions

KAUST Repository

Graber, Philip Jameson; Said-Houari, Belkacem

2012-01-01

The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function. © 2012 Elsevier Inc.

On the wave equation with semilinear porous acoustic boundary conditions

KAUST Repository

Graber, Philip Jameson

2012-05-01

The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function. © 2012 Elsevier Inc.

Grain boundary motion and grain rotation in aluminum bicrystals: recent experiments and simulations

International Nuclear Information System (INIS)

Molodov, D A; Barrales-Mora, L A; Brandenburg, J-E

2015-01-01

The results of experimental and computational efforts over recent years to study the motion of geometrically different grain boundaries and grain rotation under various driving forces are briefly reviewed. Novel in-situ measuring techniques based on orientation contrast imaging and applied simulation techniques are described. The experimental results obtained on specially grown aluminum bicrystals are presented and discussed. Particularly, the faceting and migration behavior of low angle grain boundaries under the curvature force is addressed. In contrast to the pure tilt boundaries, which remained flat/faceted and immobile during annealing at elevated temperatures, mixed tilt-twist boundaries readily assumed a curved shape and steadily moved under the capillary force. Computational analysis revealed that this behavior is due to the inclinational anisotropy of grain boundary energy, which in turn depends on boundary geometry. The shape evolution and shrinkage kinetics of cylindrical grains with different tilt and mixed boundaries were studied by molecular dynamics simulations. The mobility of low angle <100> boundaries with misorientation angles higher than 10°, obtained by both the experiments and simulations, was found not to differ from that of the high angle boundaries, but decreases essentially with further decrease of misorientation. The shape evolution of the embedded grains in simulations was found to relate directly to results of the energy computations. Further simulation results revealed that the shrinkage of grains with pure tilt boundaries is accompanied by grain rotation. In contrast, grains with the tilt-twist boundaries composed of dislocations with the mixed edge-screw character do not rotate during their shrinkage. Stress driven boundary migration in aluminium bicrystals was observed to be coupled to a tangential translation of the grains. The activation enthalpy of high angle boundary migration was found to vary non-monotonically with

Analysis of specific factors causing RCS pressure boundary cracking

International Nuclear Information System (INIS)

Song, Taek-Ho; Jeong, Il-Seok

2007-01-01

As nuclear power plants become aged, pressure boundary integrity has become so important issue in domestic and foreign nuclear industry that many related research projects are on-going. KEPRI is going to embark a new research project for managing and preventing these kinds of cracks in nuclear power plants (NPPs). Many nuclear power plants experienced pressure boundary stress corrosion cracking (SCC) and shut downed because of it. In USA, V.C. Summer plant experienced reactor coolant pipe SCC near reactor outlet nozzle and Davis Vesse plant experienced reactor head crack around penetration pipe which is used to control rod drive mechanism. In this paper, RCS pressure boundary cracking cases and corrosion potential have been studied to find out what are the specific factors that have affected crack initiations in the reactor coolant pressure boundaries

Creep of quartz by dislocation and grain boundary processes

Science.gov (United States)

Fukuda, J. I.; Holyoke, C. W., III; Kronenberg, A. K.

2015-12-01

Wet polycrystalline quartz aggregates deformed at temperatures T of 600°-900°C and strain rates of 10-4-10-6 s-1 at a confining pressure Pc of 1.5 GPa exhibit plasticity at low T, governed by dislocation glide and limited recovery, and grain size-sensitive creep at high T, governed by diffusion and sliding at grain boundaries. Quartz aggregates were HIP-synthesized, subjecting natural milky quartz powder to T=900°C and Pc=1.5 GPa, and grain sizes (2 to 25 mm) were varied by annealing at these conditions for up to 10 days. Infrared absorption spectra exhibit a broad OH band at 3400 cm-1 due to molecular water inclusions with a calculated OH content (~4000 ppm, H/106Si) that is unchanged by deformation. Rate-stepping experiments reveal different stress-strain rate functions at different temperatures and grain sizes, which correspond to differing stress-temperature sensitivities. At 600-700°C and grain sizes of 5-10 mm, flow law parameters compare favorably with those for basal plasticity and dislocation creep of wet quartzites (effective stress exponents n of 3 to 6 and activation enthalpy H* ~150 kJ/mol). Deformed samples show undulatory extinction, limited recrystallization, and c-axis maxima parallel to the shortening direction. Similarly fine-grained samples deformed at 800°-900°C exhibit flow parameters n=1.3-2.0 and H*=135-200 kJ/mol corresponding to grain size-sensitive Newtonian creep. Deformed samples show some undulatory extinction and grain sizes change by recrystallization; however, grain boundary deformation processes are indicated by the low value of n. Our experimental results for grain size-sensitive creep can be compared with models of grain boundary diffusion and grain boundary sliding using measured rates of silicon grain boundary diffusion. While many quartz mylonites show microstructural and textural evidence for dislocation creep, results for grain size-sensitive creep may apply to very fine-grained (<10 mm) quartz mylonites.

Online Problem Solving for Adolescent Brain Injury: A Randomized Trial of 2 Approaches.

Science.gov (United States)

Wade, Shari L; Taylor, Hudson Gerry; Yeates, Keith Owen; Kirkwood, Michael; Zang, Huaiyu; McNally, Kelly; Stacin, Terry; Zhang, Nanhua

Adolescent traumatic brain injury (TBI) contributes to deficits in executive functioning and behavior, but few evidence-based treatments exist. We conducted a randomized clinical trial comparing Teen Online Problem Solving with Family (TOPS-Family) with Teen Online Problem Solving with Teen Only (TOPS-TO) or the access to Internet Resources Comparison (IRC) group. Children, aged 11 to 18 years, who sustained a complicated mild-to-severe TBI in the previous 18 months were randomly assigned to the TOPS-Family (49), TOPS-TO (51), or IRC group (52). Parent and self-report measures of externalizing behaviors and executive functioning were completed before treatment and 6 months later. Treatment effects were examined using linear regression models, adjusting for baseline symptom levels. Age, maternal education, and family stresses were examined as moderators. The TOPS-Family group had lower levels of parent-reported executive dysfunction at follow-up than the TOPS-TO group, and differences between the TOPS-Family and IRC groups approached significance. Maternal education moderated improvements in parent-reported externalizing behaviors, with less educated parents in the TOPS-Family group reporting fewer symptoms. On the self-report Behavior Rating Inventory of Executive Functions, treatment efficacy varied with the level of parental stresses. The TOPS-Family group reported greater improvements at low stress levels, whereas the TOPS-TO group reported greater improvement at high-stress levels. The TOPS-TO group did not have significantly lower symptoms than the IRC group on any comparison. Findings support the efficacy of online family problem solving to address executive dysfunction and improve externalizing behaviors among youth with TBI from less advantaged households. Treatment with the teen alone may be indicated in high-stress families.

Coupled diffusion of two species in a slab with an eroding boundary

International Nuclear Information System (INIS)

Leite, S.B.; Ozisik, M.N.; Verghese, K.

1981-01-01

The diffusion of two interchangeable species in a medium with an eroding boundary is analyzed by modeling the problem as the solution of two diffusion equations coupled at the source term for a slab with a moving boundary. Formal solutions are developed for the concentration of the two species as a function of time and position in the slab for arbitrary initial distributions of the diffusing species, arbitrary sources within the medium and boundary conditions of the third kind at the bounding surfaces. It is shown with an illustrative example, that the resulting coupled integral equations for the species can be solved very efficiently by an approach employing both a lower- and upper-bound starting function for the concentrations. (author)

Study on Reflected Shock Wave/Boundary Layer Interaction in a Shock Tube

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