Linear steady heat transfer analysis by boundary element method
The boundary element method for linear steady heat transfer analysis has been developed. Two types of elements, namely, constant elements and linear elements are described. A mention has been made of the analysis of the problems of a square plate subjected to two constant temperature boundaries and other two being insulated, blunt fin with convection boundary condition, and the steady state temperature distribution in circular segment by using this method. (M.G.B.)
Isogeometric analysis based on scaled boundary finite element method
This paper presents a new approach which possesses the semi-analytical feature of scaled boundary finite element method and the exact geometry feature of isogeometric analysis. NURBS basis functions are employed to construct an exact boundary geometry. The domain boundary is discretized by NURBS curves for the 2D case, and NURBS surfaces for the 3D case. Especially the closed-form NURBS curves or surfaces are needed if there are no side-faces. The strategy of using finite elements on domain boundary with NURBS shape functions for approximation of both boundary geometry and displacements arises from the sense of isoparametric concept. With h-,p-,k- refinement strategy implemented, the geometry is refined with maintaining exact geometry at all levels, so the geometry is the same exact represented as the initial geometry imported from CAD system without the necessity of subsequent communication with a CAD system. Additionally, numerical example exhibits that flexible continuity within the NURBS patch rather than traditional shape functions improves continuity and accuracy of derivative stress and strain field across not only boundary elements but also domain elements, as the results of the combination of the intrinsic analytical property along radial direction and the higher continuity property of NURBS basis, i.e. it's more powerful in accuracy of solution and less DOF-consuming than either traditional finite element method or scaled boundary finite element method.
Boundary element analysis of nonlinear transient heat conduction problems
In this paper, the theory of the BEM applied to transient heat-conduction problems is reviewed. New time marching schemes which are based upon full boundary integrals without excessive use of large matrices, are introduced. An algorithm for dealing with the nonlinear boundary condition of radiation is described. An accuracy measure which deals with the singularities in fundamental solution parameters is discussed. A number of case studies with different geometrical shapes and different loading and boundary conditions were analyzed using the developed techniques, and the results were compared with corresponding analytical solutions and/or finite element results. It is clear that the developed boundary element procedure is more accurate and efficient than the finite element method for the analysis of such problems. (author)
Mei, Chuh; Pates, Carl S., III
1994-01-01
A coupled boundary element (BEM)-finite element (FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary element method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary element results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the finite element method models the structure and the boundary element method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels.
Cathodic protection design of seawater pump by boundary element analysis
A three-dimensional boundary element method (3D-BEM) was developed to quantitatively estimate cathodic protection and macro-cell corrosion. To confirm the validity and usefulness of the BEM for analysis of fluid machines handling seawater with complex 3D fields, experiments and analyses were performed. A cast iron vertical pump, with Zn anodes for cathodic protection, was submerged in seawater and operated. Potential distributions inside the pump and anodic currents on the Zn anodes were measured. The polarization curves of the pump material were measured as functions of flow rate, time and temperature, and the polarization characteristics were applied as boundary conditions in performing BEM analysis. Through analyses and experimental work, the following conclusions were obtained. By means of appropriate modelling that takes account of the symmetry of the object being analyzed, it is possible to apply the BEM effectively to corrosion problems of machines with complex 3D fields. Furthermore, extremely high accurate analysis on potential and current density distributions can be performed for fluid machines handling seawater, by precisely ascertaining the dependency of polarization curves on flow rate, time and temperature, and reflecting these dependencies in the boundary conditions. (author)
Analysis of 3-D Frictional Contact Mechanics Problems by a Boundary Element Method
KEUM Bangyong; LIU Yijun
2005-01-01
The development of two boundary element algorithms for solving 3-D, frictional, and linear elastostatic contact problems is reported in this paper. The algorithms employ nonconforming discretizations for solving 3-D boundary element models, which provide much needed flexibility in the boundary element modeling for 3-D contact problems. These algorithms are implemented in a new 3-D boundary element code and verified using several examples. For the numerical examples studied, the results using the new boundary element algorithms match very well with the results using a commercial finite element code, and clearly demonstrate the feasibility of the new boundary element approach for 3-D contact analysis.
Stochastic Boundary Element Analysis of Concrete Gravity Dam
张明; 吴清高
2002-01-01
Stochastic boundary integral equations for analyzing large structures are obtained from the partial derivatives of basic random variables. A stochastic boundary element method based on the equations is developed to solve engineering problems of gravity dams using random factors including material parameters of the dam body and the foundation, the water level in the upper reaches, the anti-slide friction coefficient of the dam base, etc. A numerical example shows that the stochastic boundary element method presented in this paper to calculate the reliability index of large construction projects such as a large concrete gravity dam has the advantages of less input data and more precise computational results.
Analysis of Dynamic Modeling Method Based on Boundary Element
Xu-Sheng Gan
2013-07-01
Full Text Available The aim of this study was to study an improved dynamic modeling method based on a Boundary Element Method (BEM. The dynamic model was composed of the elements such as the beam element, plate element, joint element, lumped mass and spring element by the BEM. An improved dynamic model of a machine structure was established based on plate-beam element system mainly. As a result, the dynamic characteristics of a machine structure were analyzed and the comparison of computational results and experimental’s showed the modeling method was effective. The analyses indicate that the introduced method inaugurates a good way for analyzing dynamic characteristics of a machine structure efficiently.
Probabilistic boundary element method
Cruse, T. A.; Raveendra, S. T.
1989-01-01
The purpose of the Probabilistic Structural Analysis Method (PSAM) project is to develop structural analysis capabilities for the design analysis of advanced space propulsion system hardware. The boundary element method (BEM) is used as the basis of the Probabilistic Advanced Analysis Methods (PADAM) which is discussed. The probabilistic BEM code (PBEM) is used to obtain the structural response and sensitivity results to a set of random variables. As such, PBEM performs analogous to other structural analysis codes such as finite elements in the PSAM system. For linear problems, unlike the finite element method (FEM), the BEM governing equations are written at the boundary of the body only, thus, the method eliminates the need to model the volume of the body. However, for general body force problems, a direct condensation of the governing equations to the boundary of the body is not possible and therefore volume modeling is generally required.
Development of classical boundary element analysis of fracture mechanics in gradient materials
Xiao, HT; Yue, QZQ
2013-01-01
Over the last decade, the authors have extended the classical boundary element methods (BEM) for analysis of the fracture mechanics in functionally gradient materials. This paper introduces the dual boundary element method associated with the generalized Kelvin fundamental solutions of multilayered elastic solids (or Yue’s solution). This dual BEM uses a pair of the displacement and traction boundary integral equations. The former is collocated exclusively on the uncracked boundary, and the l...
An analysis of three-dimensional eddy current distribution by using boundary element method
A boundary element method using vector variables is presented. For the analysis of three-dimensional eddy current distribution, electric field and magnetic flux density are defined as unknown vector variables. In the boundary element method, boundary surfaces are divided into a number of triangular elements on which electric field and magnetic flux density are assumed to be constant. The boundary element method is applied to workshop problem 6; the hollow sphere in uniform magnetic field. The computation results of the hollow sphere model almost agree with analytical solutions. (author)
LIANG Xinhua; ZHU Ping; LIN Zhongqin; ZHANG Yan
2007-01-01
A lightweight automotive prototype using alter- native materials and gauge thickness is studied by a numeri- cal method. The noise, vibration, and harshness (NVH) performance is the main target of this study. In the range of 1-150 Hz, the frequency response function (FRF) of the body structure is calculated by a finite element method (FEM) to get the dynamic behavior of the auto-body structure. The pressure response of the interior acoustic domain is solved by a boundary element method (BEM). To find the most contrib- uting panel to the inner sound pressure, the panel acoustic contribution analysis (PACA) is performed. Finally, the most contributing panel is located and the resulting structural optimization is found to be more efficient.
Comparison of boundary element and finite element methods in two-dimensional inelastic analysis
The finite element method has been commonly used to solve boundary value problems in inelastic deformation of metallic structures. Recently, Mukherjee and his coworkers applied the boundary element method to such problems. Planar time-dependent inelasticity problems were considered and a constitutive model with state variables was used to describe material behavior. The accuracy and computational efficiency of these two methods are compared for certain selected planar problems. In order to make the comparison as meaningful as possible, in house computer codes developed by the same group at Cornell, are used
Seismic analysis of rectangular liquid storage structure is performed by using a coupled boundary element-finite method. The method models the liquid motion as the irrotation motion of ideal fluid by boundary element method. Coupling with finite element method for the containing structure is performed by using compatibility and equilibrium conditions along the interface of the fluid and structure interaction system such as sloshing motion, hydrodynamic pressure, displacement, effect of submerged objects are investigated and compared between two-and three-dimensional analysis results. (author). 6 refs., 12 figs
Ducted propeller performance analysis using a boundary element model
Salvatore, Francesco; Calcagni, Danilo; Greco, Luca
2006-01-01
This report describes the computational analysis of the unviscid flow around a ducted propeller using a BEM model. The activity is performed in the framework of a research program co-funded by the European Union under the "SUPERPROP" Project TST4-CT-2005-516219. The theoretical and computational methodology is described and results of a validation excercise on several test cases is presented and discussed. In particular, the proposed formulation is applied to the analysis of ducted propellers...
Xiushan Sun; Lixin Huang; Yinghua Liu; Zhangzhi Cen; Keren Wang
2005-01-01
Both the orthotropy and the stress concentration are common issues in modern structural engineering. This paper introduces the boundary element method (BEM) into the elastic and elastoplastic analyses for 2D orthotropic media with stress concentration. The discretized boundary element formulations are established, and the stress formulae as well as the fundamental solutions are derived in matrix notations. The numerical procedures are proposed to analyze both elastic and elastoplastic problems of2D orthotropic media with stress concentration. To obtain more precise stress values with fewer elements, the quadratic isoparametric element formulation is adopted in the boundary discretization and numerical procedures. Numerical examples show that there are significant stress concentrations and different elastoplastic behaviors in some orthotropic media, and some of the computational results are compared with other solutions.Good agreements are also observed, which demonstrates the efficiency and reliability of the present BEM in the stress concentration analysis for orthotropic media.
Coupled Finite Element/Boundary Element Analysis of a Vehicle Moving Along a Railway Track
Andersen, Lars; Nielsen, Søren R. K.
Trains running in build-up areas are a source to ground-borne noise. A careful design of the track structure may be one way of minimizing the vibrations in the surroundings. For example, open or in-filled trenches may be constructed along the track, or the soil underneath the track may be improved....... In this work, analyses are carried out with the aim of investigating the influence of the track design and properties on the level of ground vibration due to a vehicle moving with subsonic speed. A coupled finite element and boundary element model of the track and subsoil is employed, adopting a...... or soil stiffening?even at low frequencies. However, for high-speed vehicles rubber chip barriers may be a promising means of vibration screening...
Xiao Tang; Yuzhi Zhanga; Meng Liu; Yan Li
2009-01-01
A numerical analysis of galvanic corrosion of hot-dip galvanized steel immersed in seawater was presented.The analysis was based on the boundary element methods (BEMs) coupled with Newton-Raphson iterative technique to treat the nonlinear boundary conditions, which were determined by the experimental polarization curves. Results showed that galvanic current density concentrates on the boundary of steel substrate and zinc coating, and the sacrificial protection of zinc coating to steel substrate results in overprotection of steel cathode. Not only oxygen reduction but also hydrogen reduction could occur as cathode reactions, which probably led up to the adsorption and absorption of hydrogen atoms. Flat galvanized steel tensile sample shows a brittle behavior similar to hydrogen embrittlement according to the SSRT (show strain rate test) in seawater.
A study of applicability of soil-structure interaction analysis method using boundary element method
Kim, M. K. [KAERI, Taejon (Korea, Republic of); Kim, M. K. [Yonsei University, Seoul (Korea, Republic of)
2003-07-01
In this study, a numerical method for Soil-Structure Interaction (SSI) analysis using FE-BE coupling method is developed. The total system is divided into two parts so called far field and near field. The far field is modeled by boundary element formulation using the multi-layered dynamic fundamental solution and coupled with near field modeled by finite elements. In order to verify the seismic response analysis, the results are compared with those of other commercial code. Finally, several SSI analyses which induced seismic loading are performed to examine the dynamic behavior of the system. As a result, it is shown that the developed method can be an efficient numerical method for solving the SSI analysis.
Yichao Gao
2011-01-01
Full Text Available The dam-reservoir system is divided into the near field modeled by the finite element method, and the far field modeled by the excellent high-order doubly asymptotic open boundary (DAOB. Direct and partitioned coupled methods are developed for the analysis of dam-reservoir system. In the direct coupled method, a symmetric monolithic governing equation is formulated by incorporating the DAOB with the finite element equation and solved using the standard time-integration methods. In contrast, the near-field finite element equation and the far-field DAOB condition are separately solved in the partitioned coupled methodm, and coupling is achieved by applying the interaction force on the truncated boundary. To improve its numerical stability and accuracy, an iteration strategy is employed to obtain the solution of each step. Both coupled methods are implemented on the open-source finite element code OpenSees. Numerical examples are employed to demonstrate the performance of these two proposed methods.
Isogeometric Boundary Element Analysis with elasto-plastic inclusions. Part 1: Plane problems
Beer, Gernot; Zechner, Jürgen; Dünser, Christian; Fries, Thomas-Peter
2015-01-01
In this work a novel approach is presented for the isogeometric Boundary Element analysis of domains that contain inclusions with different elastic properties than the ones used for computing the fundamental solutions. In addition the inclusion may exhibit inelastic material behavior. In this paper only plane stress/strain problems are considered. In our approach the geometry of the inclusion is described using NURBS basis functions. The advantage over currently used methods is that no discretization into cells is required in order to evaluate the arising volume integrals. The other difference to current approaches is that Kernels of lower singularity are used in the domain term. The implementation is verified on simple finite and infinite domain examples with various boundary conditions. Finally a practical application in geomechanics is presented.
Finite element analysis of three dimensional crack growth by the use of a boundary element sub model
Lucht, Tore
2009-01-01
element model containing an approximation of the crack is interpolated to a much smaller boundary element model containing a fine discretization of the real crack. The method is validated through several numerical comparisons and by comparison to crack growth measured in a test specimen for an engineering...... structure....
Scaled Boundary Finite Element Analysis of Wave Passing A Submerged Breakwater
无
2008-01-01
The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique combining the advantage of the finite element method (FEM) and the boundary element method (BEM) with its unique properties. In this paper, the SBFEM is used for computing wave passing submerged breakwaters, and the reflection coefficient and transmission coefficient are given for the case of wave passing by a rectangular submerged breakwater, a rigid submerged barrier breakwater and a trapezium submerged breakwater in a constant water depth. The results are compared with the analytical solution and experimental results. Good agreement is obtained. Through comparison with the results using the dual boundary element method (DBEM), it is found that the SBFEM can obtain higher accuracy with fewer elements. Many submerged breakwaters with different dimensions are computed by the SBFEM, and the changing character of the reflection coefficient and the transmission coefficient are given in the current study.
Schmid, G.; Wang, S.; Chouw, N.
1991-04-01
SSI-FEBEM is a computer program for dynamic soil-structure (or structure-soil-structure) interaction analysis in the frequency domain. The program SAP IV (FEM) and the program SSI 2D/3D (BEM) have been integrated into a new program, which allows a coupling of finite and boundary elements. It is applicable to two- and three-dimensional problems. In this manual, the theoretical concept for both FEM and BEM, as used in the program, are briefly introduced. Details of the coupling of FE and BE, are also discussed. However, emphasis is directed towards the use of the computer program concerning data input and output. Finally, several examples on soil-structure interaction (SSI) and structure-soil-structure interaction (SSSI), together with their data are presented. (orig.). [Deutsch] SSI-FEBEM ist ein Programm zur Berechnung der dynamischen Antwort eines Systems Bauwerk-Boden (oder Bauwerk-Boden-Bauwerk) im Frequenzbereich. Das Programm besteht aus dem Programm SAP IV (FEM) und dem Programm SSI 2D/3D (BEM) und koppelt Finite Elemente und Randelemente. Zwei- und dreidimensionale Probleme koennen damit behandelt werden. In dem vorliegenden Bericht werden die theoretischen Grundlagen der angewendeten Methode der Finiten Elemente und der Randelemente kurz vorgestellt und deren Kopplung beschrieben. Der Bericht ist als Benutzerhandbuch anzusehen. Er beinhaltet auch Beispiele der Wechselwirkung zwischen Bauwerk und Baugrund (SSI) und zwischen Bauwerk-Boden-Bauwerk (SSSI). (orig.).
Seismic site effects in a deep alluvial basin: numerical analysis by the boundary element method
Semblat, Jean-François; Dangla, Patrick; 10.1016/S0266-352X(02)00017-4
2009-01-01
The main purpose of the paper is the numerical analysis of seismic site effects in Caracas (Venezuela). The analysis is performed considering the boundary element method in the frequency domain. A numerical model including a part of the local topography is considered, it involves a deep alluvial deposit on an elastic bedrock. The amplification of seismic motion (SH-waves, weak motion) is analyzed in terms of level, occurring frequency and location. In this specific site of Caracas, the amplification factor is found to reach a maximum value of 25. Site effects occur in the thickest part of the basin for low frequencies (below 1.0 Hz) and in two intermediate thinner areas for frequencies above 1.0 Hz. The influence of both incidence and shear wave velocities is also investigated. A comparison with microtremor recordings is presented afterwards. The results of both numerical and experimental approaches are in good agreement in terms of fundamental frequencies in the deepest part of the basin. The boundary elemen...
BOUNDARY ELEMENT ANALYSIS OF INTERACTION BETWEEN AN ELASTIC RECTANGULAR INCLUSION AND A CRACK
王银邦
2004-01-01
The interaction between an elastic rectangular inclusion and a kinked crack in an infinite elastic body was considered by using boundary element method. The new complex boundary integral equations were derived. By introducing a complex unknown function H(t)related to the interface displacement density and traction and applying integration by parts,the traction continuous condition was satisfied automatically. Only one complex boundary integral equation was obtained on interface and involves only singularity of order l/ r. To verify the validity and effectiveness of the present boundary element method, some typical examples were calculated. The obtained results show that the crack stress intensity factors decrease as the shear modulus of inclusion increases. Thus, the crack propagation is easier near a softer inclusion and the harder inclusion is helpful for crack arrest.
A fast boundary element method for the scattering analysis of high-intensity focused ultrasound.
van 't Wout, Elwin; Gélat, Pierre; Betcke, Timo; Arridge, Simon
2015-11-01
High-intensity focused ultrasound (HIFU) techniques are promising modalities for the non-invasive treatment of cancer. For HIFU therapies of, e.g., liver cancer, one of the main challenges is the accurate focusing of the acoustic field inside a ribcage. Computational methods can play an important role in the patient-specific planning of these transcostal HIFU treatments. This requires the accurate modeling of acoustic scattering at ribcages. The use of a boundary element method (BEM) is an effective approach for this purpose because only the boundaries of the ribs have to be discretized instead of the standard approach to model the entire volume around the ribcage. This paper combines fast algorithms that improve the efficiency of BEM specifically for the high-frequency range necessary for transcostal HIFU applications. That is, a Galerkin discretized Burton-Miller formulation is used in combination with preconditioning and matrix compression techniques. In particular, quick convergence is achieved with the operator preconditioner that has been designed with on-surface radiation conditions for the high-frequency approximation of the Neumann-to-Dirichlet map. Realistic computations of acoustic scattering at 1 MHz on a human ribcage model demonstrate the effectiveness of this dedicated BEM algorithm for HIFU scattering analysis. PMID:26627749
Analysis of the role of diffraction in topographic site effects using boundary element techniques
Gomez, Juan; Restrepo, Doriam; Jaramillo, Juan; Valencia, Camilo
2013-10-01
The role played by the diffraction field on the problem of seismic site effects is studied. For that purpose we solve and analyze simple scattering problems under P and SV in-plane wave assumptions, using two well known direct boundary-element-based numerical methods. After establishing the difference between scattered and diffracted motions, and introducing the concept of artificious and physically based incoming fields, we obtain the amplitude of the Fourier spectra for the diffracted part of the response: this is achieved after establishing the connection between the spatial distribution of the transfer function over the studied simple topographies and the diffracted field. From the numerical simulations it is observed that this diffracted part of the response is responsible for the amplification of the surface ground motions due to the geometric effect. Furthermore, it is also found that the diffraction field sets in a fingerprint of the topographic effect in the total ground motions. These conclusions are further supported by observations in the time-domain in terms of snapshots of the propagation patterns over the complete computational model. In this sense the geometric singularities are clearly identified as sources of diffraction and for the considered range of dimensionless frequencies it is evident that larger amplifications are obtained for the geometries containing a larger number of diffraction sources thus resulting in a stronger topographic effect. The need for closed-form solutions of canonical problems to construct a robust analysis method based on the diffraction field is identified.
Fast multipole boundary element analysis of 2D viscoelastic composites with imperfect interfaces
无
2010-01-01
A fast multipole boundary element method(FMBEM)is developed for the analysis of 2D linear viscoelastic composites with imperfect viscoelastic interfaces.The transformed fast multipole formulations are established using the time domain method. To simulate the viscoelastic behavior of imperfect interfaces that are frequently encountered in practice,the Kelvin type model is introduced.The FMBEM is further improved by incorporating naturally the interaction among inclusions as well as eliminating the phenomenon of material penetration.Since all the integrals are evaluated analytically,high accuracy and fast convergence of the numerical scheme are obtained.Several numerical examples,including planar viscoelastic composites with a single inclusion or randomly distributed multi-inclusions are presented.The numerical results are compared with the developed analytical solutions,which illustrates that the proposed FMBEM is very efficient in determining the macroscopic viscoelastic behavior of the particle-reinforced composites with the presence of imperfect interfaces.The laboratory measurements of the mixture creep compliance of asphalt concrete are also compared with the prediction by the developed model.
ELECTRO-MECHANICAL COUPLING ANALYSIS OF MEMS STRUCTURES BY BOUNDARY ELEMENT METHOD
Zhang Kai; Cui Yunjun; Xiong Chunyang; Wang Congshun; Fang Jing
2004-01-01
In this paper, we present the applications of Boundary Element Method (BEM)to simulate the electro-mechanical coupling responses of Micro-Electro-Mechanical systems (MEMS).The algorithm is programmed in our research group based on BEM modeling for electrostatics and elastostatics. Good agreement is shown while the simulation results of the pull-in voltages are compared with the theoretical/experimental ones for some examples.
Yamazaki, Koetsu; Sakamoto, Jiro; Kitano, Masami
1993-02-01
A design sensitivity calculation technique based on the implicit differentiation method is formulated for isoparametric boundary elements for three-dimensional (3D) shape optimization problems. The practical sensitivity equations for boundary displacements and stresses are derived, and the efficiency and accuracy of the technique are compared with the semi-analytic method by implementing the sensitivity analysis of typical and basic shape design problems numerically. The sensitivity calculation technique is then applied to the minimum weight design problems of 3D bodies under stress constraints, such as the shape optimization of the ellipsoidal cavity in a cube and the connecting rod, where the Taylor series approximation, based on the boundary element sensitivity analysis at current design point, is adopted for the efficient implementation of the optimization.
A study on scattered fields analysis of ultrasonic SH-wave by boundary element method
In this paper, the SH-wave scattering by multi-defects and inclusion using Boundary Element Method is studied. The effects of shape and distance of defects on transmitted and reflected fields are considered. The interaction of multi-defects in SH-wave scattering is also investigated. Numerical calculations by the BEM have been carried out to predict near field solution of scattered fields of ultrasonic SH-wave. The presented results can be used to improve the detection sensitivity and pursue quantitative nondestructive evaluation for inverse problem.
Stability analysis of shallow tunnels subjected to eccentric loads by a boundary element method
Mehdi Panji
2016-08-01
Full Text Available In this paper, stress behavior of shallow tunnels under simultaneous non-uniform surface traction and symmetric gravity loading was studied using a direct boundary element method (BEM. The existing full-plane elastostatic fundamental solutions to displacement and stress fields were used and implemented in a developed algorithm. The cross-section of the tunnel was considered in circular, square, and horseshoe shapes and the lateral coefficient of the domain was assumed as unit quantity. Double-node procedure of the BEM was applied at the corners to improve the model including sudden traction changes. The results showed that the method used was a powerful tool for modeling underground openings under various external as well as internal loads. Eccentric loads significantly influenced the stress pattern of the surrounding tunnel. The achievements can be practically used in completing and modifying regulations for stability investigation of shallow tunnels.
Boundary element analysis of the directional sensitivity of the concentric EMG electrode
Henneberg, Kaj-åge; R., Plonsey
1993-01-01
, where the latter dominates the sensitivity function. The preferential directions of sensitivity are determined by.the amount of geometric offset between the individual sensitivity functions of the core and the cannula. The sensitivity function also reveals a complicated pattern of phase changes in the...... the mutual electrical influence between the electrode surfaces. A three-dimensional sensitivity function is defined from which information about the preferential direction of sensitivity, blind spots, phase changes, rate of attenuation, and range of pick-up radius can be derived. The study focuses on...... waveforms by uniformly averaging the tissue potential at the coordinates of one- or two-dimensional electrode models. By employing the boundary element method, this paper improves earlier models of the concentric EMG electrode by including an accurate geometric representation of the electrode, as well as...
Within a geophysical and paleontological project aimed at a detailed and precise correlation of the Jurassic/Cretaceous (J/K) boundary interval in the Tethyan and Boreal region, detailed magnetostratigraphic and biostratigraphic profiles with a well-defined J/K boundary were selected from several sites for a detailed geochemical characterization. Instrumental neutron activation analysis (INAA) was employed in the characterization of a vertical profile around the assumed J/K boundary in the Boreal Realm situated on the Nordvik peninsula, North of Middle Siberia, Russia, for which a platinum group element (PGE) anomaly has been reported in literature. Multimode INAA included short-time and long-time modes of irradiation either with reactor-pile neutrons or with epithermal/fast neutrons (ENAA) under a Cd shielding. The analyses encompassed about 40 major and trace elements. A radiochemical separation procedure for PGE determination consisting in sample decomposition by alkaline-oxidative fusion, reduction of PGE, and precipitation of their sulfides was tested. Despite difficulties, elevated levels of Pt and Ir were determined in selected samples at ppb and sub-ppb levels, respectively
Dynamic response of liquid storage tanks considering the hydrodynamic interactions due to earthquake ground motion has been extensively studied. Several finite element procedures, such as Balendra et. al. (1982) and Haroun (1983), have been devoted to investigate the dynamic interaction between the deformable wall of the tank and the liquid. Further, if the geometry of the storage tank can not be described by axi-symmetric case, the tank wall and the fluid domain must be discretized by three dimensional finite elements to investigate the fluid-structure-interactions. Thus, the need of large computer memory and expense of vast computer time usually make this analysis impractical. To demonstrate the accuracy and reliability of the solution technique developed herein, the dynamic behavior of ground-supported, deformed, cylindrical tank with incompressible fluid conducted by Haroun (1983) are analyzed. Good correlations of hydrodynamic pressure distribution between the computed results with the referenced solutions are noted. The fluid compressibility significantly affects the hydrodynamic pressures of the liquid-tank-interactions and the work which is done on this discussion is still little attention. Thus, the influences of the compressibility of the liquid on the reponse of the liquid storage due to ground motion are then drawn. By the way, the complex-valued frequency response functions for hydrodynamic forces of Haroun's problem are also displayed. (orig./GL)
Fast Boundary Element Methods in Engineering and Industrial Applications
Schanz, Martin; Steinbach, Olaf; Wendland, Wolfgang
2012-01-01
This volume contains eight state of the art contributions on mathematical aspects and applications of fast boundary element methods in engineering and industry. This covers the analysis and numerics of boundary integral equations by using differential forms, preconditioning of hp boundary element methods, the application of fast boundary element methods for solving challenging problems in magnetostatics, the simulation of micro electro mechanical systems, and for contact problems in solid mechanics. Other contributions are on recent results on boundary element methods for the solution of transient problems. This book is addressed to researchers, graduate students and practitioners working on and using boundary element methods. All contributions also show the great achievements of interdisciplinary research between mathematicians and engineers, with direct applications in engineering and industry.
Shepherd, Micah R; Fahnline, John B; Dare, Tyler P; Hambric, Stephen A; Campbell, Robert L
2015-11-01
Many structural acoustics problems involve a vibrating structure in a heavy fluid. However, obtaining fluid-loaded natural frequencies and damping experimentally can be difficult and expensive. This paper presents a hybrid experimental-numerical approach to determine the heavy-fluid-loaded resonance frequencies and damping of a structure from in-air measurements. The approach combines in-air experimentally obtained mode shapes with simulated in-water acoustic resistance and reactance matrices computed using boundary element (BE) analysis. The procedure relies on accurate estimates of the mass-normalized, in vacuo mode shapes using singular value decomposition and rational fraction polynomial fitting, which are then used as basis modes for the in-water BE analysis. The method is validated on a 4.445 cm (1.75 in.) thick nickel-aluminum-bronze rectangular plate by comparing natural frequencies and damping obtained using the hybrid approach to equivalent data obtained from actual in-water measurements. Good agreement is shown for the fluid-loaded natural frequencies and one-third octave loss factors. Finally, the limitations of the hybrid approach are examined. PMID:26627781
Boundary element method for modelling creep behaviour
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)
Recent advances in boundary element methods
Manolis, GD
2009-01-01
Addresses the needs of the computational mechanics research community in terms of information on boundary integral equation-based methods and techniques applied to a variety of fields. This book collects both original and review articles on contemporary Boundary Element Methods (BEM) as well as on the Mesh Reduction Methods (MRM).
Wan-You Li
2014-01-01
Full Text Available A novel hybrid method, which simultaneously possesses the efficiency of Fourier spectral method (FSM and the applicability of the finite element method (FEM, is presented for the vibration analysis of structures with elastic boundary conditions. The FSM, as one type of analytical approaches with excellent convergence and accuracy, is mainly limited to problems with relatively regular geometry. The purpose of the current study is to extend the FSM to problems with irregular geometry via the FEM and attempt to take full advantage of the FSM and the conventional FEM for structural vibration problems. The computational domain of general shape is divided into several subdomains firstly, some of which are represented by the FSM while the rest by the FEM. Then, fictitious springs are introduced for connecting these subdomains. Sufficient details are given to describe the development of such a hybrid method. Numerical examples of a one-dimensional Euler-Bernoulli beam and a two-dimensional rectangular plate show that the present method has good accuracy and efficiency. Further, one irregular-shaped plate which consists of one rectangular plate and one semi-circular plate also demonstrates the capability of the present method applied to irregular structures.
Using reciprocity in Boundary Element Calculations
Juhl, Peter Møller; Cutanda Henriquez, Vicente
2010-01-01
reciprocal radiation problem. The present paper concerns the situation of having a point source (which is reciprocal to a point receiver) at or near a discretized boundary element surface. The accuracy of the original and the reciprocal problem is compared in a test case for which an analytical solution......The concept of reciprocity is widely used in both theoretical and experimental work. In Boundary Element calculations reciprocity is sometimes employed in the solution of computationally expensive scattering problems, which sometimes can be more efficiently dealt with when formulated as the...
Introducing the Boundary Element Method with MATLAB
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…
An inverse problem by boundary element method
Tran-Cong, T.; Nguyen-Thien, T. [University of Southern Queensland, Toowoomba, QLD (Australia); Graham, A.L. [Los Alamos National Lab., NM (United States)
1996-02-01
Boundary Element Methods (BEM) have been established as useful and powerful tools in a wide range of engineering applications, e.g. Brebbia et al. In this paper, we report a particular three dimensional implementation of a direct boundary integral equation (BIE) formulation and its application to numerical simulations of practical polymer processing operations. In particular, we will focus on the application of the present boundary element technology to simulate an inverse problem in plastics processing.by extrusion. The task is to design profile extrusion dies for plastics. The problem is highly non-linear due to material viscoelastic behaviours as well as unknown free surface conditions. As an example, the technique is shown to be effective in obtaining the die profiles corresponding to a square viscoelastic extrudate under different processing conditions. To further illustrate the capability of the method, examples of other non-trivial extrudate profiles and processing conditions are also given.
Wide-area groundwater flow analysis for the geological disposal of nuclear waste is conducted in areas 10 to 100 km square at a depth of several kilometers. In Japan with complex topography and geological environment, numerical analyses by segmentation based on the region including FE analysis as a typical example involve difficulty in modeling. This study therefore aims at improving simplicity and preciseness of modeling using BEM through segmentation based on the boundary. Test analyses are conducted to organize data on precision and the characteristics of modeling. Then, this paper describes that the proposed method is fully applicable. (author)
Boundary element method for internal axisymmetric flow
Gokhman Alexander
1999-01-01
Full Text Available We present an accurate fast method for the computation of potential internal axisymmetric flow based on the boundary element technique. We prove that the computed velocity field asymptotically satisfies reasonable boundary conditions at infinity for various types of inlet/exit. Computation of internal axisymmetric potential flow is an essential ingredient in the three-dimensional problem of computation of velocity fields in turbomachines. We include the results of a practical application of the method to the computation of flow in turbomachines of Kaplan and Francis types.
9th International Conference on Boundary Elements
Wendland, W; Kuhn, G
1987-01-01
This book contains the edited versions of most of the papers presented at the 9th International Conference on Boundary Elements held at the University of Stuttgart, Germany from August 31st to September 4th, 1987, which was organized in co-operation with the Computational Mechanics Institute and GAMM (Society for Applied Mathematics and Mechanics). This Conference, as the previous ones, aimed to review the latest developments in technique and theory and point out new advanced future trends. The emphasis of the meeting was on the engineering advances versus mathematical formulations, in an effort to consolidate the basis of many new applications. Recently engineers have proposed different techniques to solve non-linear and time dependent problems and many of these formulations needed a better mathematical understanding. Furthermore, new approximate formulations have been proposed for boundary elements which appeared to work in engineering practice, but did not have a proper theoretical background. The Conferen...
The HEFF Code combines a simple boundary-element method of stress analysis with the closed form solutions for constant or exponentially decaying heat sources in an infinite elastic body to obtain an approximate method for analysis of underground excavations in a rock mass with heat generation. This manual describes the theoretical basis for the code, the code structure, model preparation, and step taken to assure that the code correctly performs its intended functions. The material contained within the report addresses the Software Quality Assurance Requirements for the Yucca Mountain Site Characterization Project. 13 refs., 26 figs., 14 tabs
Complex variable boundary elements for fluid flow
The Complex Variable Boundary Element Method is a numerical method for solving two-dimensional problems of Laplace or Poisson type. It is based on the theory of analytic functions. This paper resumes the basic facts about the method. Application of the method to the stationary incompressible irrotational flow is carried out after that. At the end, a sample problem of flow through an abrupt area change channel is shown. (author)
The coupling of boundary elements and finite elements for nondestructive testing applications
Fetzer, J.; Kurz, S.; Lehner, G. [Univ. Stuttgart (Germany). Inst. fuer Theorie der Elektrotechnik
1997-01-01
In this paper, the coupling of finite elements and boundary elements, referred to as BEM-FEM coupling, is used to numerically treat a nondestructive testing (NDT) problem based on eddy currents. BEM-FEM coupling is especially well suited for NDT problems because it greatly reduces the discretization effort. A general formulation for such problems involving FEM and BEM is given. The coupling of both methods is achieved using the boundary conditions on the common boundaries between FEM and BEM domains. Only the conducting parts and the exciting coil are discretized by finite elements. The surrounding air space is taken into account by boundary elements. As an example, problem No. 8 (coil above a crack) of the TEAM workshop (Testing Electromagnetic Analysis Methods) is considered.
The design evaluation of toroidal field coils on the Princeton Large Torus (PLT), the Poloidal Diverter Experiment (PDX) and the Tokamak Fusion Test Reactor (TFTR) has been performed by structural analysis with the finite element method. The technique employed has been simplified with supplementary computer programs that are used to generate the input data for the finite element computer program. Significant automation has been provided by computer codes in three areas of data input. These are the definition of coil geometry by a mesh of node points, the definition of finite elements via the node points and the definition of the node point force/displacement boundary conditions. The computer programs by name that have been used to perform the above functions are PDXNODE, ELEMENT and PDXFORC. The geometric finite element modeling options for toroidal field coils provided by PDXNODE include one-fourth or one-half symmetric sections of circular coils, oval shaped coils or dee-shaped coils with or without a beveled wedging surface. The program ELEMENT which defines the finite elements for input to the finite element computer code can provide considerable time and labor savings when defining the model of coils of non-uniform cross-section or when defining the model of coils whose material properties are different in the R and THETA directions due to the laminations of alternate epoxy and copper windings. The modeling features provided by the program ELEMENT have been used to analyze the PLT and the TFTR toroidal field coils with integral support structures. The computer program named PDXFORC is described. It computes the node point forces in a model of a toroidal field coil from the vector crossproduct of the coil current and the magnetic field. The model can be of one-half or one-fourth symmetry to be consistent with the node model defined by PDXNODE, and the magnetic field is computed from toroidal or poloidal coils
Boundary element methods for electrical engineers
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
Multigroup finite element-boundary element method for neutron diffusion
Full text: The finite element method (FEM) is an efficient method used for the solution of partial differential equations (PDE's) of engineering physics due to its symmetric, sparse and positive-definite coefficient matrix. FEM has been successfully applied for the solution of multigroup neutron transport and diffusion equations since 1970's. The boundary element method (BEM), on the other hand, is a newer method and is unique among the numerical methods used for the solution of PDE's with its property of confining the unknowns only to the boundaries of homogeneous regions, thus, greatly reducing matrix dimensions. The first application of BEM to the neutron diffusion equation (NDE) dates back to 1985 and many researchers are currently working in this area. Although BEM is known to have the desirable property of being an internal-mesh free method, this advantage is lost in some of its application to the NDE due to the existence of fission source volume integrals in fissionable regions unless domain-decomposition methods are used. To exploit the favorable properties of both FEM and BEM, a hybrid FE/BE method has been recently proposed for reflected systems treated by one or two-group diffusion theories in a recent paper co-authored by the first author. In this work, the hybrid FE/BE method for reflected systems is generalized to multigroup diffusion theory. The core is treated by FEM to preserve the high accuracy of FEM in such neutron-producing regions. Using a boundary integral equation formerly proposed by the second author, BEM, is utilized for the discretization of the reflector, thus, eliminating the internal mesh completely for this nonfissionable region. The multigroup FE/BE method has been implemented in our recently developed FORTRAN program. The program is validated by comparison of the calculated effective multiplication factor and the group fluxes with their analytical counterparts for a two-group reflected system. Comparison of these results and
A coupling procedure for modeling acoustic problems using finite elements and boundary elements
Coyette, J.; Vanderborck, G.; Steichen, W.
1994-01-01
Finite element (FEM) and boundary element (BEM) methods have been used for a long time for the numerical simulation of acoustic problems. The development presented in this paper deals with a general procedure for coupling acoustic finite elements with acoustic boundary elements in order to solve efficiently acoustic problems involving non homogeneous fluids. Emphasis is made on problems where finite elements are used for a confined (bounded) fluid while boundary elements are selected for an e...
8th International Conference on Boundary Element Methods
Brebbia, C
1986-01-01
The International Conference on Boundary Element Methods in Engineering was started in 1978 with the following objectives: i) To act as a focus for BE research at a time when the technique wasjust emerging as a powerful tool for engineering analysis. ii) To attract new as weIl as established researchers on Boundary Elements, in order to maintain its vitality and originality. iii) To try to relate the Boundary Element Method to other engineering techniques in an effort to help unify the field of engineering analysis, rather than to contribute to its fragmentation. These objectives were achieved during the last 7 conferences and this meeting - the eighth - has continued to be as innovative and dynamic as any ofthe previous conferences. Another important aim ofthe conference is to encourage the participation of researchers from as many different countries as possible and in this regard it is a policy of the organizers to hold the conference in different locations. It is easy to forget when working on scientific ...
Andersen, Lars; Nielsen, Søren R. K.
2003-01-01
is approximated, but the error which is introduced in this way is insignificant. Numerical examples are given for a moving rectangular load on an elastic half-space. The result from a boundary element code based on the derived Green's function are compared with a semi-analytic solution.......The paper deals with the boundary element method formulation of the steady-state wave propagation through elastic media due to a source moving with constant velocity. The Greens' function for the three-dimensional full-space is formulated in a local frame of reference following the source...
Periodic Boundary Conditions in the ALEGRA Finite Element Code
AIDUN,JOHN B.; ROBINSON,ALLEN C.; WEATHERBY,JOE R.
1999-11-01
This document describes the implementation of periodic boundary conditions in the ALEGRA finite element code. ALEGRA is an arbitrary Lagrangian-Eulerian multi-physics code with both explicit and implicit numerical algorithms. The periodic boundary implementation requires a consistent set of boundary input sets which are used to describe virtual periodic regions. The implementation is noninvasive to the majority of the ALEGRA coding and is based on the distributed memory parallel framework in ALEGRA. The technique involves extending the ghost element concept for interprocessor boundary communications in ALEGRA to additionally support on- and off-processor periodic boundary communications. The user interface, algorithmic details and sample computations are given.
Application of the boundary element method to transient heat conduction
Dargush, G. F.; Banerjee, P. K.
1991-01-01
An advanced boundary element method (BEM) is presented for the transient heat conduction analysis of engineering components. The numerical implementation necessarily includes higher-order conforming elements, self-adaptive integration and a multiregion capability. Planar, three-dimensional and axisymmetric analyses are all addressed with a consistent time-domain convolution approach, which completely eliminates the need for volume discretization for most practical analyses. The resulting general purpose algorithm establishes BEM as an attractive alternative to the more familiar finite difference and finite element methods for this class of problems. Several detailed numerical examples are included to emphasize the accuracy, stability and generality of the present BEM. Furthermore, a new efficient treatment is introduced for bodies with embedded holes. This development provides a powerful analytical tool for transient solutions of components, such as casting moulds and turbine blades, which are cumbersome to model when employing the conventional domain-based methods.
Numerical modelling of solidification process using interval boundary element method
A. Piasecka Belkhayat
2008-01-01
In this paper an application of the interval boundary element method for solving problems with interval thermal parameters and interval source function in a system casting-mould is presented. The task is treated as a boundary-initial problem in which the crystallization model proposed by Mehl-Johnson-Avrami-Kolmogorov has been applied. The numerical solution of the problem discussed has been obtained on the basis of the interval boundary element method (IBEM). The interval Gauss elimination m...
Solution of Exterior Acoustic Problems by the Boundary Element Method.
Kirkup, Stephen Martin
Available from UMI in association with The British Library. The boundary element method is described and investigated, especially in respect of its application to exterior two -dimensional Laplace problems. Both empirical and algebraic analyses (including the effects of approximation of the boundary and boundary functions and the precision of the evaluation of the discrete forms) are developed. Methods for the automatic evaluation of the discrete forms of the Laplace and Helmholtz integral operators are reviewed and extended. Boundary element methods for the solution of exterior Helmholtz problems with general (but most importantly Neumann) boundary conditions are reviewed and some are explicitly stated using a new notation. Boundary element methods based on the boundary integral equations introduced by Brakhage & Werner/ Leis/ Panich/ Kussmaul (indirect) and Burton & Miller (direct) are given prime consideration and implemented for three -dimensional problems. The influence of the choice of weighting parameter on the performance of the methods is explored and further guidance is given. The application of boundary element methods and methods based on the Rayleigh integral to acoustic radiation problems are considered. Methods for speeding up their solution via the boundary element method are developed. Library subroutines for the solution of acoustic radiation problems are described and demonstrated. Computational techniques for the problem of predicting the noise produced by a running engine are reviewed and appraised. The application of the boundary element method to low-noise engine design and in the design of noise shields is considered. The boundary element method is applied to the Ricardo crankcase simulation rig, which is an engine -like structure. A comparison of predicted and measured sound power spectra is given.
Analysis of turbulent boundary layers
Cebeci, Tuncer
2012-01-01
Analysis of Turbulent Boundary Layers focuses on turbulent flows meeting the requirements for the boundary-layer or thin-shear-layer approximations. Its approach is devising relatively fundamental, and often subtle, empirical engineering correlations, which are then introduced into various forms of describing equations for final solution. After introducing the topic on turbulence, the book examines the conservation equations for compressible turbulent flows, boundary-layer equations, and general behavior of turbulent boundary layers. The latter chapters describe the CS method for calculati
Equivariant preconditioners for boundary element methods
Tausch, J. [Colorado State Univ., Fort Collins, CO (United States)
1994-12-31
In this paper the author proposes and discusses two preconditioners for boundary integral equations on domains which are nearly symmetric. The preconditioners under consideration are equivariant, that is, they commute with a group of permutation matrices. Numerical experiments demonstrate their efficiency for the GMRES method.
Development of polygon elements based on the scaled boundary finite element method
We aim to extend the scaled boundary finite element method to construct conforming polygon elements. The development of the polygonal finite element is highly anticipated in computational mechanics as greater flexibility and accuracy can be achieved using these elements. The scaled boundary polygonal finite element will enable new developments in mesh generation, better accuracy from a higher order approximation and better transition elements in finite element meshes. Polygon elements of arbitrary number of edges and order have been developed successfully. The edges of an element are discretised with line elements. The displacement solution of the scaled boundary finite element method is used in the development of shape functions. They are shown to be smooth and continuous within the element, and satisfy compatibility and completeness requirements. Furthermore, eigenvalue decomposition has been used to depict element modes and outcomes indicate the ability of the scaled boundary polygonal element to express rigid body and constant strain modes. Numerical tests are presented; the patch test is passed and constant strain modes verified. Accuracy and convergence of the method are also presented and the performance of the scaled boundary polygonal finite element is verified on Cook's swept panel problem. Results show that the scaled boundary polygonal finite element method outperforms a traditional mesh and accuracy and convergence are achieved from fewer nodes. The proposed method is also shown to be truly flexible, and applies to arbitrary n-gons formed of irregular and non-convex polygons.
Shih, H.R. [Jackson State Univ., MS (United States); Duffield, R.C.; Lin, J. [Univ. of Missouri, Columbia, MO (United States)
1996-10-01
An integral equation formulation and a numerical procedure for a boundary-finite element technique are developed for the static analysis of a stiffened plate with eccentric stiffeners. This formulation employs the fundamental solution associated with unstiffened plate bending and plane stress problems. With this approach, the resulting integral equation not only contained integrals along the perimeter of the stiffened but additional integrals along the stiffeners and the interface between the plate and its stiffeners. Thus the domain of the plate has to be divided into zones between the stiffeners. Each zone is modeled by boundary elements and stiffeners by finite elements. In this paper, the boundary element solution procedures for plate bending and in-plane problems are presented. The zone technique which permits coupling of unstiffened plate boundary element with stiffener finite elements is presented as well. Numerical example is given to demonstrate the effectiveness of this approach.
Boundary element method approach to magnetostatic wave problems
Yashiro, K.; Ohkawa, S.; Miyazaki, M.
1985-03-01
In this paper, the technique for application of the boundary element method (BEM) to analysis of magnetostatic waves (MSWs) is established. To show the availability of the technique, two types of waveguides for the MSW are studied; one is a waveguide constituting a YIG slab shielded with metal plates and the other is a waveguide consisting of an unshielded YIG slab. With the former structure the results obtained by the present technique are compared with the analytical solutions, and with the latter the BEM is compared with Marcatili's approximate method since there is no analytical solution in this case. Those comparisons are performed successfully for both cases. The paper concludes that the BEM is useful and effective for analysis of a wide range of MSW problems.
A Curved, Elastostatic Boundary Element for Plane Anisotropic Structures
Smeltzer, Stanley S.; Klang, Eric C.
2001-01-01
The plane-stress equations of linear elasticity are used in conjunction with those of the boundary element method to develop a novel curved, quadratic boundary element applicable to structures composed of anisotropic materials in a state of plane stress or plane strain. The curved boundary element is developed to solve two-dimensional, elastostatic problems of arbitrary shape, connectivity, and material type. As a result of the anisotropy, complex variables are employed in the fundamental solution derivations for a concentrated unit-magnitude force in an infinite elastic anisotropic medium. Once known, the fundamental solutions are evaluated numerically by using the known displacement and traction boundary values in an integral formulation with Gaussian quadrature. All the integral equations of the boundary element method are evaluated using one of two methods: either regular Gaussian quadrature or a combination of regular and logarithmic Gaussian quadrature. The regular Gaussian quadrature is used to evaluate most of the integrals along the boundary, and the combined scheme is employed for integrals that are singular. Individual element contributions are assembled into the global matrices of the standard boundary element method, manipulated to form a system of linear equations, and the resulting system is solved. The interior displacements and stresses are found through a separate set of auxiliary equations that are derived using an Airy-type stress function in terms of complex variables. The capabilities and accuracy of this method are demonstrated for a laminated-composite plate with a central, elliptical cutout that is subjected to uniform tension along one of the straight edges of the plate. Comparison of the boundary element results for this problem with corresponding results from an analytical model show a difference of less than 1%.
Numerical modelling of solidification process using interval boundary element method
A. Piasecka Belkhayat
2008-12-01
Full Text Available In this paper an application of the interval boundary element method for solving problems with interval thermal parameters and interval source function in a system casting-mould is presented. The task is treated as a boundary-initial problem in which the crystallization model proposed by Mehl-Johnson-Avrami-Kolmogorov has been applied. The numerical solution of the problem discussed has been obtained on the basis of the interval boundary element method (IBEM. The interval Gauss elimination method with the decomposition procedure has been applied to solve the obtained interval system of equations. In the final part of the paper, results of numerical computations are shown.
Use of the iterative solution method for coupled finite element and boundary element modeling
Tunnels buried deep within the earth constitute an important class geomechanics problems. Two numerical techniques used for the analysis of geomechanics problems, the finite element method and the boundary element method, have complementary characteristics for applications to problems of this type. The usefulness of combining these two methods for use as a geomechanics analysis tool has been recognized for some time, and a number of coupling techniques have been proposed. However, not all of them lend themselves to efficient computational implementations for large-scale problems. This report examines a coupling technique that can form the basis for an efficient analysis tool for large scale geomechanics problems through the use of an iterative equation solver
Subregions approach to boundary element neutron diffusion calculations
Full text: The boundary element method (BEM) is a relatively new numerical method for the numerical solution of partial differential equations (PDE). BEM is based on the idea of converting the governing PDE with constant coefficients for a homogeneous region to a boundary integral equation (BIE) which contains unknowns only on the boundary of that region. A boundary element mesh is introduced over the boundary of the homogeneous region and the solution function and its normal derivative is assumed to have a polynomial dependence (constant, linear, quadratic...) over each boundary element. When the BIE is required to be satisfied at each node of the boundary element mesh, a linear system of dimension equal to the number of nodes on the boundary element mesh is obtained; but the number of unknowns is twice the number of equations since the nodal value of both the solution function and its normal derivative appear as unknowns. If the system consists of just one homogeneous region, half of the unknowns are eliminated by boundary conditions and the number of unknowns becomes equal to the number of equations and the linear system can be uniquely solved. When the system consists of more than one homogeneous region, the equations belonging to each region are assembled and the number of unknowns and equations are made equal by application of the continuity of the solution function and its normal derivative. In this work, we investigated a novel approach: a system consisting of one homogeneous region is divided into subregions and each subregion is treated as if it were a separate homogeneous region. This approach naturally increases the dimension of the resulting linear system, but its effect on the accuracy of the solution is a question that requires investigation. We used this subregions approach in the constant BEM solution of the 2-D neutron diffusion equation and investigated its effect on accuracy in terms of the multiplication eigenvalue and flux distribution by
Asymptotic analysis and boundary layers
Cousteix, Jean
2007-01-01
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...
Ginzburg, Irina; Silva, Goncalo; Talon, Laurent
2015-02-01
This work focuses on the numerical solution of the Stokes-Brinkman equation for a voxel-type porous-media grid, resolved by one to eight spacings per permeability contrast of 1 to 10 orders in magnitude. It is first analytically demonstrated that the lattice Boltzmann method (LBM) and the linear-finite-element method (FEM) both suffer from the viscosity correction induced by the linear variation of the resistance with the velocity. This numerical artefact may lead to an apparent negative viscosity in low-permeable blocks, inducing spurious velocity oscillations. The two-relaxation-times (TRT) LBM may control this effect thanks to free-tunable two-rates combination Λ . Moreover, the Brinkman-force-based BF-TRT schemes may maintain the nondimensional Darcy group and produce viscosity-independent permeability provided that the spatial distribution of Λ is fixed independently of the kinematic viscosity. Such a property is lost not only in the BF-BGK scheme but also by "partial bounce-back" TRT gray models, as shown in this work. Further, we propose a consistent and improved IBF-TRT model which vanishes viscosity correction via simple specific adjusting of the viscous-mode relaxation rate to local permeability value. This prevents the model from velocity fluctuations and, in parallel, improves for effective permeability measurements, from porous channel to multidimensions. The framework of our exact analysis employs a symbolic approach developed for both LBM and FEM in single and stratified, unconfined, and bounded channels. It shows that even with similar bulk discretization, BF, IBF, and FEM may manifest quite different velocity profiles on the coarse grids due to their intrinsic contrasts in the setting of interface continuity and no-slip conditions. While FEM enforces them on the grid vertexes, the LBM prescribes them implicitly. We derive effective LBM continuity conditions and show that the heterogeneous viscosity correction impacts them, a property also shared
Parallel computation using boundary elements in solid mechanics
Chien, L. S.; Sun, C. T.
1990-01-01
The inherent parallelism of the boundary element method is shown. The boundary element is formulated by assuming the linear variation of displacements and tractions within a line element. Moreover, MACSYMA symbolic program is employed to obtain the analytical results for influence coefficients. Three computational components are parallelized in this method to show the speedup and efficiency in computation. The global coefficient matrix is first formed concurrently. Then, the parallel Gaussian elimination solution scheme is applied to solve the resulting system of equations. Finally, and more importantly, the domain solutions of a given boundary value problem are calculated simultaneously. The linear speedups and high efficiencies are shown for solving a demonstrated problem on Sequent Symmetry S81 parallel computing system.
Treatment of domain integrals in boundary element methods
Nintcheu Fata, Sylvain [ORNL
2012-01-01
A systematic and rigorous technique to calculate domain integrals without a volume-fitted mesh has been developed and validated in the context of a boundary element approximation. In the proposed approach, a domain integral involving a continuous or weakly-singular integrand is first converted into a surface integral by means of straight-path integrals that intersect the underlying domain. Then, the resulting surface integral is carried out either via analytic integration over boundary elements or by use of standard quadrature rules. This domain-to-boundary integral transformation is derived from an extension of the fundamental theorem of calculus to higher dimension, and the divergence theorem. In establishing the method, it is shown that the higher-dimensional version of the first fundamental theorem of calculus corresponds to the well-known Poincare lemma. The proposed technique can be employed to evaluate integrals defined over simply- or multiply-connected domains with Lipschitz boundaries which are embedded in an Euclidean space of arbitrary but finite dimension. Combined with the singular treatment of surface integrals that is widely available in the literature, this approach can also be utilized to effectively deal with boundary-value problems involving non-homogeneous source terms by way of a collocation or a Galerkin boundary integral equation method using only the prescribed surface discretization. Sample problems associated with the three-dimensional Poisson equation and featuring the Newton potential are successfully solved by a constant element collocation method to validate this study.
Sound source reconstruction using inverse boundary element calculations
Schuhmacher, Andreas; Hald, Jørgen; Rasmussen, Karsten Bo;
2001-01-01
suited for solution by means of an inverse boundary element method. Since the numerical treatment of the inverse source reconstruction results in a discrete ill-posed problem, regularisation is imposed to avoid unstable solutions dominated by errors. In the present work the emphasis is on Tikhonov......Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim of the present work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form...
Sound source reconstruction using inverse boundary element calculations
Schuhmacher, Andreas; Hald, Jørgen; Rasmussen, Karsten Bo;
2003-01-01
for solution by means of an inverse boundary element method. Since the numerical treatment of the inverse source reconstruction results in a discrete ill-posed problem, regularization is imposed to avoid unstable solutions dominated by errors., In the present work the emphasis is on Tikhonov......Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim in this work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form suited...
Anton, I.; Carte, I. N.; Ludescher, H.; Iosif, A.
1990-04-01
The application of the boundary element method to the analysis of axisymmetric motions is examined with particular reference to turbomachines. A procedure for determining the hydrodynamic field in the meridian plane of turbomachine blading using the boundary element method is presented. The method is applied to a Francis turbine impeller with lateral boundaries of the Bovet type. The results obtained are compared with calculations by the finite element method.
Experimental validation of boundary element methods for noise prediction
Seybert, A. F.; Oswald, Fred B.
1992-01-01
Experimental validation of methods to predict radiated noise is presented. A combined finite element and boundary element model was used to predict the vibration and noise of a rectangular box excited by a mechanical shaker. The predicted noise was compared to sound power measured by the acoustic intensity method. Inaccuracies in the finite element model shifted the resonance frequencies by about 5 percent. The predicted and measured sound power levels agree within about 2.5 dB. In a second experiment, measured vibration data was used with a boundary element model to predict noise radiation from the top of an operating gearbox. The predicted and measured sound power for the gearbox agree within about 3 dB.
Effective and neutral stresses in soils using boundary element methods
Alarcón Álvarez, Enrique; García-Suárez, C.; Reverter, A.
1983-01-01
The evaluation of neutral pressures in soil mechanics problems is a fundamental step to evaluate deformations in soils. In this paper, we present some results obtained by using the boundary element method for plane problems, describing the undrained situation as well as the consolidation problem.
A Highly Scalable Parallel Boundary Element Method for Capacitance Extraction
Hsiao, Yu-Chung; Daniel, Luca
2011-01-01
Traditional parallel boundary element methods suffer from low parallel efficiency and poor scalability due to the long system solving time bottleneck. In this paper, we demonstrate how to avoid such a bottleneck by using an instantiable basis function approach. In our demonstrated examples, we achieve 90% parallel efficiency and scalability both in shared memory and distributed memory parallel systems.
2010-01-01
Finite element analysis is an engineering method for the numerical analysis of complex structures. This book provides a bird's eye view on this very broad matter through 27 original and innovative research studies exhibiting various investigation directions. Through its chapters the reader will have access to works related to Biomedical Engineering, Materials Engineering, Process Analysis and Civil Engineering. The text is addressed not only to researchers, but also to professional engineers, engineering lecturers and students seeking to gain a better understanding of where Finite Element Analysis stands today.
A posteriori pointwise error estimates for the boundary element method
Paulino, G.H. [Cornell Univ., Ithaca, NY (United States). School of Civil and Environmental Engineering; Gray, L.J. [Oak Ridge National Lab., TN (United States); Zarikian, V. [Univ. of Central Florida, Orlando, FL (United States). Dept. of Mathematics
1995-01-01
This report presents a new approach for a posteriori pointwise error estimation in the boundary element method. The estimator relies upon the evaluation of hypersingular integral equations, and is therefore intrinsic to the boundary integral equation approach. This property allows some theoretical justification by mathematically correlating the exact and estimated errors. A methodology is developed for approximating the error on the boundary as well as in the interior of the domain. In the interior, error estimates for both the function and its derivatives (e.g. potential and interior gradients for potential problems, displacements and stresses for elasticity problems) are presented. Extensive computational experiments have been performed for the two dimensional Laplace equation on interior domains, employing Dirichlet and mixed boundary conditions. The results indicate that the error estimates successfully track the form of the exact error curve. Moreover, a reasonable estimate of the magnitude of the actual error is also obtained.
St. John, C.M.; Sanjeevan, K. [Agapito (J.F.T.) and Associates, Inc., Grand Junction, CO (United States)
1991-12-01
The HEFF Code combines a simple boundary-element method of stress analysis with the closed form solutions for constant or exponentially decaying heat sources in an infinite elastic body to obtain an approximate method for analysis of underground excavations in a rock mass with heat generation. This manual describes the theoretical basis for the code, the code structure, model preparation, and step taken to assure that the code correctly performs its intended functions. The material contained within the report addresses the Software Quality Assurance Requirements for the Yucca Mountain Site Characterization Project. 13 refs., 26 figs., 14 tabs.
Rahmouni, Lyes; Cools, Kristof; Andriulli, Francesco P
2016-01-01
In this paper we present a new discretization strategy for the boundary element formulation of the Electroencephalography (EEG) forward problem. Boundary integral formulations, classically solved with the Boundary Element Method (BEM), are widely used in high resolution EEG imaging because of their recognized advantages in several real case scenarios. Unfortunately however, it is widely reported that the accuracy of standard BEM schemes is limited, especially when the current source density is dipolar and its location approaches one of the brain boundary surfaces. This is a particularly limiting problem given that during an high-resolution EEG imaging procedure, several EEG forward problem solutions are required for which the source currents are near or on top of a boundary surface. This work will first present an analysis of standardly discretized EEG forward problems, reporting on a theoretical issue of some of the formulations that have been used so far in the community. We report on the fact that several ...
Seybert, A. F.; Wu, T. W.; Wu, X. F.
1994-01-01
This research report is presented in three parts. In the first part, acoustical analyses were performed on modes of vibration of the housing of a transmission of a gear test rig developed by NASA. The modes of vibration of the transmission housing were measured using experimental modal analysis. The boundary element method (BEM) was used to calculate the sound pressure and sound intensity on the surface of the housing and the radiation efficiency of each mode. The radiation efficiency of each of the transmission housing modes was then compared to theoretical results for a finite baffled plate. In the second part, analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise level radiated from the box. The FEM was used to predict the vibration, while the BEM was used to predict the sound intensity and total radiated sound power using surface vibration as the input data. Vibration predicted by the FEM model was validated by experimental modal analysis; noise predicted by the BEM was validated by measurements of sound intensity. Three types of results are presented for the total radiated sound power: sound power predicted by the BEM model using vibration data measured on the surface of the box; sound power predicted by the FEM/BEM model; and sound power measured by an acoustic intensity scan. In the third part, the structure used in part two was modified. A rib was attached to the top plate of the structure. The FEM and BEM were then used to predict structural vibration and radiated noise respectively. The predicted vibration and radiated noise were then validated through experimentation.
THE COUPLING OF NATURAL BOUNDARY ELEMENT AND FINITE ELEMENT METHOD FOR 2D HYPERBOLIC EQUATIONS
De-hao Yu; Qi-kui Du
2003-01-01
In this paper, we investigate the coupling of natural boundary element and finite ele-ment methods of exterior initial boundary value problems for hyperbolic equations. Thegoverning equation is first discretized in time, leading to a time-step scheme, where anexterior elliptic problem has to be solved in each time step. Second, a circular artifi-in an unbounded domain is transformed into the nonlocal boundary value problem in abounded subdomain. And the natural integral equation and the Poisson integral formulaare obtained in the infinite domain Ω2 outside circle of radius R. The coupled variationalformulation is given. Only the function itself, not its normal derivative at artificial bound-and the boundary element stiffness matrix has a few different elements. Such a coupledmethod is superior to the one based on direct boundary element method. This paper dis-cusses finite element discretization for variational problem and its corresponding numericaltechnique, and the convergence for the numerical solutions. Finally, the numerical exampleis presented to illustrate feasibility and efficiency of this method.
GUZELBEY Ibrahim H.; KANBER Bahattin; AKPOLAT Abdullah
2004-01-01
In this study, the stress based finite element method is coupled with the boundary element method in two different ways. In the first one, the ordinary distribution matrix is used for coupling. In the second one, the stress traction equilibrium is used at the interface line of both regions as a new coupling process. This new coupling procedure is presented without a distribution matrix. Several case studies are solved for the validation of the developed coupling procedure. The results of case studies are compared with the distribution matrix coupling, displacement based finite element method, assumed stress finite element method, boundary element method, ANSYS and analytical results whenever possible. It is shown that the coupling of the stress traction equilibrium with assumed stress finite elements gives as accurate results as those by the distribution matrix coupling.
Foundations of the complex variable boundary element method
Hromadka, Theodore
2014-01-01
This book explains and examines the theoretical underpinnings of the Complex Variable Boundary Element Method (CVBEM) as applied to higher dimensions, providing the reader with the tools for extending and using the CVBEM in various applications. Relevant mathematics and principles are assembled and the reader is guided through the key topics necessary for an understanding of the development of the CVBEM in both the usual two- as well as three- or higher dimensions. In addition to this, problems are provided that build upon the material presented. The Complex Variable Boundary Element Method (CVBEM) is an approximation method useful for solving problems involving the Laplace equation in two dimensions. It has been shown to be a useful modelling technique for solving two-dimensional problems involving the Laplace or Poisson equations on arbitrary domains. The CVBEM has recently been extended to 3 or higher spatial dimensions, which enables the precision of the CVBEM in solving the Laplace equation to be now ava...
The prediction of potential flow about zero thickness membranes by the boundary element method constitutes an integral component of the Lagrangian vortex-boundary element simulation of flow about parachutes. To this end, the vortex loop (or the panel) method has been used, for some time now, in the aerospace industry with relative success[1, 2]. Vortex loops (with constant circulation) are equivalent to boundary elements with piecewise constant variation of the potential jump. In this case, extending the analysis in[3], the near field potential velocity evaluations can be shown to be(Omicron)(1). The accurate evaluation of the potential velocity field very near the parachute surface is particularly critical to the overall accuracy and stability of the vortex-boundary element simulations. As we will demonstrate in Section 3, the boundary integral singularities, which arise due to the application of low order boundary elements, may lead to severely spiked potential velocities at vortex element centers that are near the boundary. The spikes in turn cause the erratic motion of the vortex elements, and the eventual loss of smoothness of the vorticity field and possible numerical blow up. In light of the arguments above, the application of boundary elements with (at least) a linear variation of the potential jump--or, equivalently, piecewise constant vortex sheets--would appear to be more appropriate for vortex-boundary element simulations. For this case, two strategies are possible for obtaining the potential flow field. The first option is to solve the integral equations for the (unknown) strengths of the surface vortex sheets. As we will discuss in Section 2.1, the challenge in this case is to devise a consistent system of equations that imposes the solenoidality of the locally 2-D vortex sheets. The second approach is to solve for the unknown potential jump distribution. In this case, for commonly used C(sup o) shape functions, the boundary integral is singular at
Seybert, A. F.; Wu, X. F.; Oswald, Fred B.
1992-01-01
Analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise radiated from the box. The FEM was used to predict the vibration, and the surface vibration was used as input to the BEM to predict the sound intensity and sound power. Vibration predicted by the FEM model was validated by experimental modal analysis. Noise predicted by the BEM was validated by sound intensity measurements. Three types of results are presented for the total radiated sound power: (1) sound power predicted by the BEM modeling using vibration data measured on the surface of the box; (2) sound power predicted by the FEM/BEM model; and (3) sound power measured by a sound intensity scan. The sound power predicted from the BEM model using measured vibration data yields an excellent prediction of radiated noise. The sound power predicted by the combined FEM/BEM model also gives a good prediction of radiated noise except for a shift of the natural frequencies that are due to limitations in the FEM model.
Dina V. Lazareva
2015-06-01
Full Text Available A new mathematical model of asymmetric support structure frame type is built on the basis of numerical-analytical boundary elements method (BEM. To describe the design scheme used is the graph theory. Building the model taken into account is the effect of frame members restrained torsion, which presence is due to the fact that these elements are thin-walled. The built model represents a real object as a two-axle semi-trailer platform. To implement the BEM algorithm obtained are analytical expressions of the fundamental functions and vector load components. The effected calculations are based on the semi-trailer two different models, using finite elements and boundary elements methods. The analysis showed that the error between the results obtained on the basis of two numerical methods and experimental data is about 4%, that indicates the adequacy of the proposed mathematical model.
A boundary element model for structural health monitoring using piezoelectric transducers
In this paper, for the first time, the boundary element method (BEM) is used for modelling smart structures instrumented with piezoelectric actuators and sensors. The host structure and its cracks are formulated with the 3D dual boundary element method (DBEM), and the modelling of the piezoelectric transducers implements a 3D semi-analytical finite element approach. The elastodynamic analysis of the structure is performed in the Laplace domain and the time history is obtained by inverse Laplace transform. The sensor signals obtained from BEM simulations show excellent agreement with those from finite element modelling simulations and experiments. This work provides an alternative methodology for modelling smart structures in structural health monitoring applications. (paper)
Adaptive Boundary Elements and Error Estimation for Elastic Problems
Jingguo Qu
2014-02-01
Full Text Available In traditional thinking, when the elastic problems are solved, we need to repeatedly plot element grids and analyze computing results according to diverse precision requirement. Against the malpractice exists in the above process, a new method of error estimation was suggested on H-R adaptive boundary element method in this paper. Based on the discrete meshes that are generated for the process of H-R adaptive refinement, the solution error was estimated by the interpolation residue. In addition, this method is easy to programming, which is carried out in the program by automatically creating new adaptive data files. Then a great deal of fore-disposal and post-disposal can be saved. Its validity and effectiveness have been confirmed by numerical example
This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available
Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)
1997-12-31
This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)
Walston, W. H., Jr.
1986-01-01
The comparative computational efficiencies of the finite element (FEM), boundary element (BEM), and hybrid boundary element-finite element (HVFEM) analysis techniques are evaluated for representative bounded domain interior and unbounded domain exterior problems in elastostatics. Computational efficiency is carefully defined in this study as the computer time required to attain a specified level of solution accuracy. The study found the FEM superior to the BEM for the interior problem, while the reverse was true for the exterior problem. The hybrid analysis technique was found to be comparable or superior to both the FEM and BEM for both the interior and exterior problems.
Partridge, P; Boundary Elements in Fluid Dynamics
1992-01-01
This book Boundary Elements in Fluid Dynamics is the second volume of the two volume proceedings of the International Conference on Computer Modelling of Seas and Coastal Regions and Boundary Elements and Fluid Dynamics, held in Southampton, U.K., in April 1992. The Boundary Element Method (BEM) is now fully established as an ac curate and successful technique for solving engineering problems in a wide range of fields. The success of the method is due to its advantages in data reduction, as only the boundary of the region is modelled. Thus moving boundaries may be more easily handled, which is not the case if domain methods are used. In addition, the method is easily able to model regions to extending to infinity. Fluid mechanics is traditionally one of the most challenging areas of engi neering, the simulation of fluid motion, particularly in three dimensions, is always a serious test for any numerical method, and is an area in which BEM analysis may be used taking full advantage of its special character...
Electrical machine analysis using finite elements
Bianchi, Nicola
2005-01-01
OUTLINE OF ELECTROMAGNETIC FIELDSVector AnalysisElectromagnetic FieldsFundamental Equations SummaryReferencesBASIC PRINCIPLES OF FINITE ELEMENT METHODSIntroductionField Problems with Boundary ConditionsClassical Method for the Field Problem SolutionThe Classical Residual Method (Galerkin's Method)The Classical Variational Method (Rayleigh-Ritz's Method)The Finite Element MethodReferencesAPPLICATIONS OF THE FINITE ELEMENT METHOD TO TWO-DIMENSIONAL FIELDSIntroductionLinear Interpolation of the Function fApplication of the Variational MethodSimple Descriptions of Electromagnetic FieldsAppendix: I
Submarine Magnetic Field Extrapolation Based on Boundary Element Method
GAO Jun-ji; LIU Da-ming; YAO Qiong-hui; ZHOU Guo-hua; YAN Hui
2007-01-01
In order to master the magnetic field distribution of submarines in the air completely and exactly and study the magnetic stealthy performance of submarine, a mathematic model of submarine magnetic field extrapolation is built based on the boundary element method (BEM). An experiment is designed to measure three components of magnetic field on the envelope surface surrounding a model submarine. The data in differentheights above the model submarine are obtained by use of tri-axial magnetometers. The results show that this extrapolation model has good stabilities and high accuracies compared the measured data with the extrapolated data. Moreover, the model can reflect the submarine magnetic field distribution in the air exactly, and is valuable in practical engineering.
New Petrov-Galerkin formulations on the finite element methods for convection-diffusion problems with boundary layers are presented. Such formulations are based on a consistent new theory on discontinuous finite element methods. Existence and uniqueness of solutions for these problems in the new finite element spaces are demonstrated. Some numerical experiments shows how the new formulation operate and also their efficacy. (author)
A new simple multidomain fast multipole boundary element method
Huang, S.; Liu, Y. J.
2016-09-01
A simple multidomain fast multipole boundary element method (BEM) for solving potential problems is presented in this paper, which can be applied to solve a true multidomain problem or a large-scale single domain problem using the domain decomposition technique. In this multidomain BEM, the coefficient matrix is formed simply by assembling the coefficient matrices of each subdomain and the interface conditions between subdomains without eliminating any unknown variables on the interfaces. Compared with other conventional multidomain BEM approaches, this new approach is more efficient with the fast multipole method, regardless how the subdomains are connected. Instead of solving the linear system of equations directly, the entire coefficient matrix is partitioned and decomposed using Schur complement in this new approach. Numerical results show that the new multidomain fast multipole BEM uses fewer iterations in most cases with the iterative equation solver and less CPU time than the traditional fast multipole BEM in solving large-scale BEM models. A large-scale fuel cell model with more than 6 million elements was solved successfully on a cluster within 3 h using the new multidomain fast multipole BEM.
A new simple multidomain fast multipole boundary element method
Huang, S.; Liu, Y. J.
2016-06-01
A simple multidomain fast multipole boundary element method (BEM) for solving potential problems is presented in this paper, which can be applied to solve a true multidomain problem or a large-scale single domain problem using the domain decomposition technique. In this multidomain BEM, the coefficient matrix is formed simply by assembling the coefficient matrices of each subdomain and the interface conditions between subdomains without eliminating any unknown variables on the interfaces. Compared with other conventional multidomain BEM approaches, this new approach is more efficient with the fast multipole method, regardless how the subdomains are connected. Instead of solving the linear system of equations directly, the entire coefficient matrix is partitioned and decomposed using Schur complement in this new approach. Numerical results show that the new multidomain fast multipole BEM uses fewer iterations in most cases with the iterative equation solver and less CPU time than the traditional fast multipole BEM in solving large-scale BEM models. A large-scale fuel cell model with more than 6 million elements was solved successfully on a cluster within 3 h using the new multidomain fast multipole BEM.
Substantive provisions of Numeral-analytical boundary elements method
V.F. Orobey
2011-06-01
Full Text Available Substantive propositions of the new method of design calculation, that got the name "Numeral-analytical of boundary elements method", offered by authors, are brought. A method consists of development of the fundamental system of decisions (analytically and Green functions (also analytically for every examined task.For the account of certain border terms, or terms of contact between the separate modules (the separate element of the system is so named the small system of linear algebraic equalizations, that must be decided numeral, is made.Discretisation only of border of the area occupied by an object, sharply diminishes the order of the system of resolvent equalizations; there is possibility of decline of regularity of the decided task. A method is strictly reasonable mathematically, as uses the fundamental decisions of differential equalizations, and, means, within the framework of the accepted hypotheses allows to get the exact meaning of parameters of task (efforts, moving, tensions, currents, frequencies of eigentones, critical forces of loss of stability et cetera into an area.Simplicity of logic of algorithm, good convergence of decision, high stability and small accumulation of errors at numeral operations, are marked also.
Portable element analysis unit
A field portable X-ray fluorescent spectrometer is described, including a multichannel analyzer and a plurality of interchangeable sensor heads. Each sensor head includes a shutter which, when open, permits one of several radiation sources to irradiate the material to be analyzed. The returned radiation is detected by a corresponding detector which provides corresponding data in response. When the shutter is open, the multichannel analyzer utilizes the detector data to accumulate an energy spectrum of the material being analyzed, and displays the spectrum on a display screen. A cursor control allows the operator to move a cursor along the displayed spectrum. The symbol of the element having its major spectral peak at the position identified by the cursor, is automatically displayed on another display screen. Memory is provided for storing a number of reference spectra which may be displayed on the first screen along with the acquired spectrum for comparison purposes. The memory also stores previously acquired spectra for later analyses. To permit quantitative chemical analysis of materials in the field, the analyzer also includes other operational features such as normalization, window control and ratio and concentration determination
Boundary Element Method Solution in the Time Domain For a Moving Time-Dependent Force
Nielsen, Søren R.K.; Kirkegaard, Poul Henning; Rasmussen, K. M.
2001-01-01
The problem of a moving time dependent concentrated force on the surface of an elastic halfspace is of interest in the analysis of traffic generated noise. The Boundary element method (BEM) is superior to the finite element method (FEM) in solving such problems due to its inherent ability so...... satisfy the radiation conditions exactly. In this paper a model based on the BEM is formulated for the solution of the mentioned problem. A numerical solution is obtained for the 2D plane strain case, and comparison is made with the results obtained from a corresponding FEM solution with an impedance...
Itagaki, M. (Japan Atomic Energy Research Inst., Dept. of Nuclear Ship Engineering, Aza-Kitasekine, Oaza-Sekine, Mutsu, Aomori 035 (JP)); Brebbia, C.A. (Computational Mechanics Inst., Ashurst Lodge, Ashurst, Southampton SO4 2AA (GB))
1991-03-01
This paper reports on the boundary element method used to generate energy-dependent matrix-type boundary conditions along core/reflector interfaces and along baffle-plate surfaces of pressurized water reactors. This method enables one to deal with all types of boundary geometries including convex and concave corners. The method is applicable to neutron diffusion problems with more than two energy groups and also can be used to model a reflector with or without a baffle plate. Excellent eigenvalue and flux shape results can be obtained when the boundary conditions generated by this technique are coupled with core-only finite difference calculations.
Seismic response of three-dimensional rockfill dams using the Indirect Boundary Element Method
The Indirect Boundary Element Method (IBEM) is used to compute the seismic response of a three-dimensional rockfill dam model. The IBEM is based on a single layer integral representation of elastic fields in terms of the full-space Green function, or fundamental solution of the equations of dynamic elasticity, and the associated force densities along the boundaries. The method has been applied to simulate the ground motion in several configurations of surface geology. Moreover, the IBEM has been used as benchmark to test other procedures. We compute the seismic response of a three-dimensional rockfill dam model placed within a canyon that constitutes an irregularity on the surface of an elastic half-space. The rockfill is also assumed elastic with hysteretic damping to account for energy dissipation. Various types of incident waves are considered to analyze the physical characteristics of the response: symmetries, amplifications, impulse response and the like. Computations are performed in the frequency domain and lead to time response using Fourier analysis. In the present implementation a symmetrical model is used to test symmetries. The boundaries of each region are discretized into boundary elements whose size depends on the shortest wavelength, typically, six boundary segments per wavelength. Usually, the seismic response of rockfill dams is simulated using either finite elements (FEM) or finite differences (FDM). In most applications, commercial tools that combine features of these methods are used to assess the seismic response of the system for a given motion at the base of model. However, in order to consider realistic excitation of seismic waves with different incidence angles and azimuth we explore the IBEM.
Driessen, B.J.; Dohner, J.L.
1998-08-01
In this paper a hybrid, finite element--boundary element method which can be used to solve for particle advection-diffusion in infinite domains with variable advective fields is presented. In previous work either boundary element, finite element, or difference methods have been used to solve for particle motion in advective-diffusive domains. These methods have a number of limitations. Due to the complexity of computing spatially dependent Green`s functions, the boundary element method is limited to domains containing only constant advective fields, and due to their inherent formulation, finite element and finite difference methods are limited to only domains of finite spatial extent. Thus, finite element and finite difference methods are limited to finite space problems for which the boundary element method is not, and the boundary element method is limited to constant advection field problems for which finite element and finite difference methods are not. In this paper it is proposed to split a domain into two sub-domains, and for each of these sub domains, apply the appropriate solution method; thereby, producing a method for the total infinite space, variable advective field domain.
Sangita A Chakraborty
Full Text Available Chromatin boundary elements serve as cis-acting regulatory DNA signals required to protect genes from the effects of the neighboring heterochromatin. In the yeast genome, boundary elements act by establishing barriers for heterochromatin spreading and are sufficient to protect a reporter gene from transcriptional silencing when inserted between the silencer and the reporter gene. Here we dissected functional topography of silencers and boundary elements within circular minichromosomes in Saccharomyces cerevisiae. We found that both HML-E and HML-I silencers can efficiently repress the URA3 reporter on a multi-copy yeast minichromosome and we further showed that two distinct heterochromatin boundary elements STAR and TEF2-UASrpg are able to limit the heterochromatin spreading in circular minichromosomes. In surprising contrast to what had been observed in the yeast genome, we found that in minichromosomes the heterochromatin boundary elements inhibit silencing of the reporter gene even when just one boundary element is positioned at the distal end of the URA3 reporter or upstream of the silencer elements. Thus the STAR and TEF2-UASrpg boundary elements inhibit chromatin silencing through an antisilencing activity independently of their position or orientation in S. cerevisiae minichromosomes rather than by creating a position-specific barrier as seen in the genome. We propose that the circular DNA topology facilitates interactions between the boundary and silencing elements in the minichromosomes.
The representation of boundary currents in a finite element shallow water model
Düben, Peter D
2015-01-01
We evaluate the influence of local resolution, eddy viscosity, coastline structure, and boundary conditions on the numerical representation of boundary currents in a finite element shallow-water model. The use of finite element discretization methods offers a higher flexibility compared to finite difference and finite volume methods, that are mainly used in previous publications. This is true for the geometry of the coast lines and for the realization of boundary conditions. For our investigations we simulate steady separation of western boundary currents from idealized and realistic coast lines. The use of grid refinement allows a detailed investigation of boundary separation at reasonable numerical cost.
Temperature and stress distribution in pressure vessel by the boundary element method
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)
A practical guide to boundary element methods with the software library BEMLIB
Pozrikidis, C
2002-01-01
LAPLACE'S EQUATION IN ONE DIMENSIONGreen's First and Second Identities and the Reciprocal Relation Green's FunctionsBoundary-Value Representation Boundary-Value EquationLAPLACE'S EQUATION IN TWO DIMENSIONS Green's First and Second Identities and the Reciprocal RelationGreen's Functions Integral Representation Integral Equations Hypersingular Integrals Irrotational FlowGeneralized Single- and Double-Layer Representations BOUNDARY-ELEMENT METHODS FOR LAPLACE'S EQUATION IN TWO DIMENSIONSBoundary Element Discretization .Discretization of
Wet Friction-Elements Boundary Friction Mechanism and Friction Coefficient Prediction
Wang, Yanzhong; Wu, Xiangyu; Wei, Bin
2012-01-01
The friction mechanism for the boundary friction course of friction elements engagement was explicitly expressed. The boundary friction model was built up by the surface topography. The model contained the effect of boundary film, adhesion, plough and lubrication. Based on the model, a coefficient for weakening plough for the lubrication was proposed. The modified model could fit for the working condition of wet friction elements. The friction coefficient as a function curve of rotating speed...
Fourier analysis and boundary value problems
Gonzalez-Velasco, Enrique A
1996-01-01
Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...
Boundary element method for natural convection in non-Newtonian fluid saturated square porous cavity
Jecl, Renata; Škerget, Leopold
2012-01-01
The main purpose of this work is to present the use of the Boundary Element Method (BEM) in the analysis of the natural convection in the square porous cavity saturated by the non-Newtonian fluid. The results of hydrodynamic and heat transfer evaluations are reported for the configuration in which the enclosure is heated from a side wall while the horizontal walls are insulated.The flow in the porous medium is modelled using the modified Brinkman extended Darcy model taking into account the n...
Hybrid finite-element/boundary-element method to calculate Oersted fields
The article presents a general-purpose hybrid finite-element/boundary-element method (FEM/BEM) to calculate magnetostatic fields generated by stationary electric currents. The efficiency of this code lies in its ability to simulate Oersted fields in complex geometries with non-uniform current density distributions. As a precursor to the calculation of the Oersted field, an FEM algorithm is employed to calculate the electric current density distribution. The accuracy of the code is confirmed by comparison with analytic results. Two examples show how this method provides important numerical data that can be directly plugged into micromagnetic simulations: The current density distribution in a thin magnetic strip with a notch, and the Oersted field in a three-dimensional contact geometry; similar to the type commonly used in spin-torque driven nano-oscillators. It is argued that a precise calculation of both, the Oersted field and the current density distribution, is essential for a reliable simulation of current-driven micromagnetic processes. - Highlights: • We present a numerical method to calculate Oersted fields for arbitrary geometries. • Description of a FEM algorithm to calculate current density distributions. • It is argued that these methods are valuable for micromagnetic STT-simulations. • Several examples are shown, highlighting the methods’ importance and accuracy
Analysis of Laminar Boundary Layer Equations
R. Yesman
2012-01-01
Full Text Available The paper proposes methodology for analysis and calculation of laminar fluid flow processes in a boundary layer.The presented dependences can be used for practical calculations while power carriers of various application are moving in the channels of heat and power devices.
韩玉超; 卢晓平; 王中
2015-01-01
The Boundary Element Method(BEM),as a key numerical method,has been widely applied in many fields. However,the research on the Direct Boundary Element Method(DBEM)for ship hydrody⁃namic numerical calculation problems is still insufficient,especially when it comes to the ship hydrody⁃namic potential flow theory. The general method-‘panel method’- is based on Hess-Smith method, which is an Indirect Boundary Element Method(IBEM)whose major flaws exist in both theory and numeri⁃cal calculation. This paper,based on the ship hydrodynamic potential flow theory,adopts DBEM to calcu⁃late the example of two-dimensional unbounded potential flow around a cylinder,and analyzes the influ⁃ence of the boundary element discrete forms and the numerical integral methods on the calculation accura⁃cy. The results carried out by Matlab clearly indicate that using the constant element and Romberg algo⁃rithm method could yield high calculation speed and accuracy.%边界元法作为一种重要的数值方法已在许多领域得到广泛应用，但在船舶水动力势流理论数值计算方面，有关直接边界元法的研究并不充分，尤其是在船舶兴波阻力势流理论求解方面，以往的“面元法”通常是基于Hess-Smith法的间接法，这类方法在理论和数值计算上都存在着缺陷。针对船舶水动力势流理论计算，采用直接边界元法，对二维势流无界绕流算例进行系统的数值计算，并根据二维势流问题的计算结果详细探讨边界单元离散形式和单元上的数值积分方法对计算精度的影响，各项数值计算均以Matlab软件编程实现。结果表明，采用常数单元和龙贝格积分法能够得到较准确的结果，且计算速度较快。
Two simple finite element methods for Reissner--Mindlin plates with clamped boundary condition
Bishnu P. Lamichhane
2013-01-01
We present two simple finite element methods for the discretization of Reissner--Mindlin plate equations with {\\em clamped} boundary condition. These finite element methods are based on discrete Lagrange multiplier spaces from mortar finite element techniques. We prove optimal a priori error estimates for both methods.
Global stability analysis of axisymmetric boundary layers
Vinod, N
2016-01-01
This paper presents the linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inlet. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier-Stokes(LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi's iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes are nega...
Argeso, Hakan; Mengi, Yalcin
2014-02-01
A unified formulation is presented, based on the boundary element method, to perform the interaction analysis for the problems involving poroviscoelastic media. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices at a single step in terms of system matrices of boundary element method without solving any special problem, such as, unit displacement or load problem, as required by conventional methods. It further eliminates the complicated procedure and the need for using scattering analysis in the evaluation of input motion functions. The formulation is explained by considering a simple interaction problem involving an inclusion embedded in an infinite poroviscoelastic medium, which is under the influence of a dynamic excitation induced by seismic waves. In the formulation, an impedance relation is established for this interaction problem, suitable for performing the interaction analysis by substructure method, which permits carrying out the analysis for inclusion and its surrounding medium separately. The inclusion is first treated as poroviscoelastic, then viscoelastic and finally rigid, where the formulation in each of these cases is obtained consecutively as a special case of the previous one. It is remarkable to note that, a cavity problem where there is a hole in place of inclusion can be also considered within the framework of the present formulation. The formulation is assessed by applying it to some sample problems. The extension of the formulation to other types of interaction problems, such as, multi-inclusion problems, the analyses of foundations supported by a poroviscoelastic medium, etc., will be the subject of a separate study.
A Boundary Element Method for Steady Infiltration from Periodic Channels.
Azis, Moh. Ivan; Clements, D. L.; Lobo, M
2003-01-01
The matric flux potential and horizontal and vertical flux distributions are obtained for periodic irrigation channels by using boundary integral equation techniques. Numerical results are given for the special cases of semicircular and rectangular channels and the results compared with those of Batu [Soil Science Society of America Journal, 42:545??? 549, 1978] and Warrick and Lomen [Soil Science Society of America Journal, 40:639???643, 1976] for a flat strip. The re...
The interaction between membrane structure and wind based on the discontinuous boundary element
无
2010-01-01
Small disturbance potential theory is widely used in solving aerodynamic problems with low Mach numbers, and it plays an important role in engineering design. Concerning structure wind engineering, the body of the structure is in a low velocity wind field, with a low viscosity of air and thin boundary layer, therefore, the tiny shear stress caused by the boundary layer can be ignored, only wind pressure being considered. In this paper, based on small disturbance potential theory, the fluid-structure interaction between the wind and membrane structure is analyzed by joint utilization of the boundary element method (BEM) and finite element method (FEM) through a loose-coupling procedure. However, the boundary of flow field to be calculated is not fully smooth, corners and edges still exist, so the discontinuous boundary element is introduced. Furthermore, because a large scale boundary element equation set with a nonsymmetrical coefficient matrix must be solved, this paper imports a preconditioning GMRES (the generalized minimum residual) iterative algorithm, which takes full advantage of the boundary element method. Several calculation examples have verified the correctness and soundness of the treatments mentioned above.
Murat Ünal
2002-01-01
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 com...
Three-dimensional shape optimization using the boundary element method
Yamazaki, Koetsu; Sakamoto, Jiro; Kitano, Masami
1994-06-01
A practical design sensitivity calculation technique of displacements and stresses for three-dimensional bodies based on the direct differentiation method of discrete boundary integral equations is formulated in detail. Then the sensitivity calculation technique is applied to determine optimum shapes of minimum weight subjected to stress constraints, where an approximated subproblem is constructed repeatedly and solved sequentially by the mathematical programming method. The shape optimization technique suggested here is applied to determine optimum shapes of a cavity in a cube and a connecting rod.
Three-dimensional shape optimization using boundary element method
Yamazaki, Koetsu; Sakamoto, Jiro; Kitano, Masami
1993-04-01
A practical design sensitivity calculation technique of displacements and stresses for three-dimensional bodies based on the direct differentiation method of discrete boundary integral equations is formulated in detail. Then, the sensitivity calculation technique is applied to determine optimum shapes of minimum weight subjected to stress constraints, where an approximated subproblem is constructed repeatedly and solved sequentially by the mathematical programming method. The shape optimization technique suggested here is applied to determine optimum shapes of a cavity shape in a cube and a connecting rod.
无
2011-01-01
The scaled boundary finite element method(SBFEM) is a semi-analytical numerical method,which models an analysis domain by a small number of large-sized subdomains and discretises subdomain boundaries only.In a subdomain,all fields of state variables including displacement,stress,velocity and acceleration are semi-analytical,and the kinetic energy,strain energy and energy error are all integrated semi-analytically.These advantages are taken in this study to develop a posteriori h-hierarchical adaptive SBFEM for transient elastodynamic problems using a mesh refinement procedure which subdivides subdomains.Because only a small number of subdomains are subdivided,mesh refinement is very simple and efficient,and mesh mapping to transfer state variables from an old mesh to a new one is also very simple but accurate.Two 2D examples with stress wave propagation were modelled.The results show that the developed method is capable of capturing propagation of steep stress regions and calculating accurate dynamic responses,using only a fraction of degrees of freedom required by adaptive finite element method.
Yoon, Gil Ho; Park, Y.K.; Kim, Y.Y.
2007-01-01
element models or topology optimization reformulation may be necessary. The key idea of the proposed method is to stack multiple elements on the same discretization pixel and select a single or no element. In this method, stacked elements on the same pixel have the same coordinates but may have......A new topology optimization scheme, called the element stacking method, is developed to better handle design optimization involving material-dependent boundary conditions and selection of elements of different types. If these problems are solved by existing standard approaches, complicated finite...
Practical application of inverse boundary element method to sound field studies of tyres
Schuhmacher, Andreas
1999-01-01
An approach based on boundary element modelling of sound sources and regularisation techniques was compared with Near-field Acoustical Holography in a study of vibration patterns on a rolling tyre [1]. In the present paper, a further investigation of this Inverse Boundary Element Method (IBEM) is...... reconstruction process is to feed our model of the problem with as much a priori knowledge as possible, e.g. in the sense of known velocity data on some surfaces. In the modelling of the tyre this can be done by imposing a boundary condition to the nodes belonging to the rim structure, where the normal surface...
Boundary Element Method with Non—overlapping Domain Decomposition for Diffusion Equation
ZHUJialin; ZHANGTaiping
2002-01-01
A boundary element method based on non-overlapping domain decomposition method to solve the time-dependent diffusion equations is presented.The time-dependent fundamental solution is used in the formulation of boundary integrals and the time integratioin process always restarts from the initial time condition.The process of replacing the interface values,which needs a summation of boundary integrals related to the boundary values at previous time steps can be treated in parallel parallel iterative procedure,Numerical experiments demonstrate that the implementation of the present alogrithm is efficient.
BOOK REVIEW: Finite Element and Boundary Element Applications in Quantum Mechanics
Ueta, Tsuyoshi
2003-08-01
L Ramdas Ram-Mohan Oxford: Oxford University Press (2002) £26.50 (paperback), ISBN 0-19-852522-2 Although this book is one of the Oxford Texts in Applied and Engineering Mathematics, we may think of it as a physics book. It explains how to solve the problem of quantum mechanics using the finite element method (FEM) and the boundary element method (BEM). Many examples analysing actual problems are also shown. As for the ratio of the number of pages of FEM and BEM, the former occupies about 80%. This is, however, reasonable reflecting the flexibility of FEM. Although many explanations of FEM and BEM exist, most are written using special mathematical expressions and numerical computation fields. However, this book is written in the `language of physicists' throughout. I think that it is very readable and easy to understand for physicists. In the derivation of FEM and the argument on calculation accuracy, the action integral and a variation principle are used consistently. In the numerical computation of matrices, such as simultaneous equations and eigen value problems, a description of important points is also fully given. Moreover, the practical problems which become important in the electron device design field and the condensed matter physics field are dealt with as example computations, so that this book is very practical and applicable. It is characteristic and interesting that FEM is applied to solve the Schrödinger and Poisson equations consistently, and to the solution of the Ginzburg--Landau equation in superconductivity. BEM is applied to treat electric field enhancements due to surface plasmon excitations at metallic surfaces. A number of references are cited at the end of all the chapters, and this is very helpful. The description of quantum mechanics is also made appropriately and the actual application of quantum mechanics in condensed matter physics can also be surveyed. In the appendices, the mathematical foundation, such as numerical quadrature
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2013-01-01
The formulation presented in this paper is based on the Boundary Element Method (BEM) and implements Kirchhoff’s decomposition into viscous, thermal and acoustic components, which can be treated independently everywhere in the domain except on the boundaries. The acoustic variables with losses...... 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...... as is the case with the existing Finite Element Method (FEM) implementations with losses. The suitability of this approach is demonstrated using an axisymmetrical BEM and two test cases where the numerical results are compared with analytical solutions....
An interpolating boundary element-free method (IBEFM) for elasticity problems
无
2010-01-01
The paper begins by discussing the interpolating moving least-squares (IMLS) method. Then the formulae of the IMLS method obtained by Lancaster are revised. On the basis of the boundary element-free method (BEFM), combining the boundary integral equation method with the IMLS method improved in this paper, the interpolating boundary element-free method (IBEFM) for two-dimensional elasticity problems is presented, and the corresponding formulae of the IBEFM for two-dimensional elasticity problems are obtained. In the IMLS method in this paper, the shape function satisfies the property of Kronecker δ function, and then in the IBEFM the boundary conditions can be applied directly and easily. The IBEFM is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution to the nodal variables. Thus it gives a greater computational precision. Numerical examples are presented to demonstrate the method.
Margolis, S. V.; Doehne, E. F.
1988-01-01
Trace element and stable isotope analyses were performed on a series of sediment samples crossing the Cretaceous-Tertiary (K-T) boundary from critical sections at Aumaya and Sopelano, Spain. The aim is to possibly distinguish extraterrestrial vs. volcanic or authigenic concentration of platinum group and other elements in K-T boundary transitional sediments. These sediments also have been shown to contain evidence for step-wise extinction of several groups of marine invertebrates, associated with negative oxygen and carbon isotope excursions occurring during the last million years of the Cretaceous. These isotope excursions have been interpreted to indicate major changes in ocean thermal regime, circulation, and ecosystems that may be related to multiple events during latest Cretaceous time. Results to date on the petrographic and geochemical analyses of the Late Cretaceous and Early Paleocene sediments indicate that diagenesis has obviously affected the trace element geochemistry and stable isotope compositions at Zumaya. Mineralogical and geochemical analysis of K-T boundary sediments at Zumaya suggest that a substantial fraction of anomalous trace elements in the boundary marl are present in specific mineral phases. Platinum and nickel grains perhaps represent the first direct evidence of siderophile-rich minerals at the boundary. The presence of spinels and Ni-rich particles as inclusions in aluminosilicate spherules from Zumaya suggests an original, non-diagenetic origin for the spherules. Similar spherules from southern Spain (Caravaca), show a strong marine authigenic overprint. This research represents a new approach in trying to directly identify the sedimentary mineral components that are responsible for the trace element concentrations associated with the K-T boundary.
Plasma boundary identification in HL-2A by means of the finite current element method
You Tian-Xue; Yuan Bao-Shan; Liu Li; Li Fang-Zhu
2005-01-01
In this paper, the finite current element(FCE)method used in HL-2A is described. The calculation and test results show that the error of the reconsturcted boundary given by the FCE method(<3mm)is smaller than that obtained by the current filament medthod used before(<6mm).Even if some current elements are Iocated out of the plasma boundary,the FCE method can also identify the plasma boundary successfully.If the location of the finite current elements is changed is a certain area, the error of the reconstructed boundary is always very small. By employing a conventional PC(Pentium 4 2.4 GHz),the calculation time of one set of plasma discharge parameters does nto exceed 1ms. Thus, the FCM method can identify the diverted plamma configuration quickly and accurately.This is essential and important for real-time shape control in IIL-2A.
A coupled boundary element-finite difference solution of the elliptic modified mild slope equation
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 with...
Automatic Recognition of Element Classes and Boundaries in the Birdsong with Variable Sequences.
Koumura, Takuya; Okanoya, Kazuo
2016-01-01
Researches on sequential vocalization often require analysis of vocalizations in long continuous sounds. In such studies as developmental ones or studies across generations in which days or months of vocalizations must be analyzed, methods for automatic recognition would be strongly desired. Although methods for automatic speech recognition for application purposes have been intensively studied, blindly applying them for biological purposes may not be an optimal solution. This is because, unlike human speech recognition, analysis of sequential vocalizations often requires accurate extraction of timing information. In the present study we propose automated systems suitable for recognizing birdsong, one of the most intensively investigated sequential vocalizations, focusing on the three properties of the birdsong. First, a song is a sequence of vocal elements, called notes, which can be grouped into categories. Second, temporal structure of birdsong is precisely controlled, meaning that temporal information is important in song analysis. Finally, notes are produced according to certain probabilistic rules, which may facilitate the accurate song recognition. We divided the procedure of song recognition into three sub-steps: local classification, boundary detection, and global sequencing, each of which corresponds to each of the three properties of birdsong. We compared the performances of several different ways to arrange these three steps. As results, we demonstrated a hybrid model of a deep convolutional neural network and a hidden Markov model was effective. We propose suitable arrangements of methods according to whether accurate boundary detection is needed. Also we designed the new measure to jointly evaluate the accuracy of note classification and boundary detection. Our methods should be applicable, with small modification and tuning, to the songs in other species that hold the three properties of the sequential vocalization. PMID:27442240
Fast multipole acceleration of the MEG/EEG boundary element method
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
An introductory study of the convergence of the direct boundary element method
Juhl, Peter Møller
Although boundary element methods have been used for three decades for the numerical solution of acoustic problems, the issue of convergence is not well known among acoustic engineers. In this paper the concept of convergence is introduced in an intuitive and empirical style. The convergence of an...... axisymmetric boundary element formulation is studied using linear, quadratic or superparametric elements. It is demonstrated that the rate of convergence of these formulations is reduced for calculations involving bodies with edges (geometric singularities). Two methods for improving the rate of convergence...
Galerkin Boundary Integral Analysis for the 3D Helmholtz Equation
Swager, Melissa [Emporia State University; Gray, Leonard J [ORNL; Nintcheu Fata, Sylvain [ORNL
2010-01-01
A linear element Galerkin boundary integral analysis for the three-dimensional Helmholtz equation is presented. The emphasis is on solving acoustic scattering by an open (crack) surface, and to this end both a dual equation formulation and a symmetric hypersingular formulation have been developed. All singular integrals are defined and evaluated via a boundary limit process, facilitating the evaluation of the (finite) hypersingular Galerkin integral. This limit process is also the basis for the algorithm for post-processing of the surface gradient. The analytic integrations required by the limit process are carried out by employing a Taylor series expansion for the exponential factor in the Helmholtz fundamental solutions. For the open surface, the implementations are validated by comparing the numerical results obtained by using the two different methods.
Elements of abstract harmonic analysis
Bachman, George
2013-01-01
Elements of Abstract Harmonic Analysis provides an introduction to the fundamental concepts and basic theorems of abstract harmonic analysis. In order to give a reasonably complete and self-contained introduction to the subject, most of the proofs have been presented in great detail thereby making the development understandable to a very wide audience. Exercises have been supplied at the end of each chapter. Some of these are meant to extend the theory slightly while others should serve to test the reader's understanding of the material presented. The first chapter and part of the second give
Strong, Stuart L.; Meade, Andrew J., Jr.
1992-01-01
Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.
Li, FengLian; Wang, YueSheng; Zhang, ChuanZeng
2016-06-01
A boundary element method (BEM) is presented to compute the transmission spectra of two-dimensional (2-D) phononic crystals of a square lattice which are finite along the x-direction and infinite along the y-direction. The cross sections of the scatterers may be circular or square. For a periodic cell, the boundary integral equations of the matrix and the scatterers are formulated. Substituting the periodic boundary conditions and the interface continuity conditions, a linear equation set is formed, from which the elastic wave transmission can be obtained. From the transmission spectra, the band gaps can be identified, which are compared with the band structures of the corresponding infinite systems. It is shown that generally the transmission spectra completely correspond to the band structures. In addition, the accuracy and the efficiency of the boundary element method are analyzed and discussed.
The basic principles of the boundary element method numerical treatment of the radial flow heat diffusion equation are presented. The algorithm copes the time dependent Dirichlet and Neumann boundary conditions, temperature dependent material properties and regions from different materials in thermal contact. It is verified on the several analytically obtained test cases. The developed method is used for the modelling of unsteady radial heat flow in pressurized water reactor fuel rod. (author)
A finite element kinematic analysis of planar granular solids flow
Watson, G.R.; Rotter, J.M. [University of Edinburgh, Edinburgh (United Kingdom). Dept. of Civil Engineering and Building Science
1996-08-01
A finite element analysis is presented to calculate the steady-state velocity fields in a cohesionless granular solid discharging from a planar flat-bottomed silo. The work treats a wide range of geometries, material properties and boundary conditions. The approach is kinematic and gravity-based, solving for the velocity field and assuming complete stress independence. 36 refs., 22 figs.
A coupled finite-element, boundary-integral method for simulating ultrasonic flowmeters.
Bezdĕk, Michal; Landes, Hermann; Rieder, Alfred; Lerch, Reinhard
2007-03-01
Today's most popular technology of ultrasonic flow measurement is based on the transit-time principle. In this paper, a numerical simulation technique applicable to the analysis of transit-time flowmeters is presented. A flowmeter represents a large simulation problem that also requires computation of acoustic fields in moving media. For this purpose, a novel boundary integral method, the Helmholtz integral-ray tracing method (HIRM), is derived and validated. HIRM is applicable to acoustic radiation problems in arbitrary mean flows at low Mach numbers and significantly reduces the memory demands in comparison with the finite-element method (FEM). It relies on an approximate free-space Green's function which makes use of the ray tracing technique. For simulation of practical acoustic devices, a hybrid simulation scheme consisting of FEM and HIRM is proposed. The coupling of FEM and HIRM is facilitated by means of absorbing boundaries in combination with a new, reflection-free, acoustic-source formulation. Using the coupled FEM-HIRM scheme, a full three-dimensional (3-D) simulation of a complete transit-time flowmeter is performed for the first time. The obtained simulation results are in good agreement with measurements both at zero flow and under flow conditions. PMID:17375833
E-coil: an inverse boundary element method for a quasi-static problem
Sanchez, Clemente Cobos; Garcia, Salvador Gonzalez [Depto. Electromagnetismo y F. de la Materia Facultad de Ciencias University of Granada Avda. Fuentenueva E-18071 (Spain); Power, Henry, E-mail: ccobos@ugr.e [School of Mechanical, Materials and Manufacturing Engineering, The University of Nottingham, Nottingham Park, Nottingham NG7 2RD (United Kingdom)
2010-06-07
Boundary element methods represent a valuable approach for designing gradient coils; these methods are based on meshing the current carrying surface into an array of boundary elements. The temporally varying magnetic fields produced by gradient coils induce electric currents in conducting tissues and so the exposure of human subjects to these magnetic fields has become a safety concern, especially with the increase in the strength of the field gradients used in magnetic resonance imaging. Here we present a boundary element method for the design of coils that minimize the electric field induced in prescribed conducting systems. This work also details some numerical examples of the application of this coil design method. The reduction of the electric field induced in a prescribed region inside the coils is also evaluated.
BOUNDARY ELEMENT METHOD FOR MOVING AND ROLLING CONTACT OF 2D ELASTIC BODIES WITH DEFECTS
姚振汉; 蒲军平; 金哲植
2001-01-01
A scheme of boundary element method for moving contact of two dimensional elastic bodies using conforming discretization is presented. Both the displacement and the traction boundary conditions are satisfied on the contacting region in the sense of discretization. An algorithm to deal with the moving of the contact boundary on a larger possible contact region is presented. The algorithm is generalized to rolling contact problem as well. Some numerical examples of moving and rolling contact of 2D elastic bodies with or without friction, including the bodies with a hole-type defect, are given to show the effectiveness and the accuracy of the presented schemes.
Dynamic Stationary Response of Reinforced Plates by the Boundary Element Method
Luiz Carlos Facundo Sanches
2007-01-01
Full Text Available A direct version of the boundary element method (BEM is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs. Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state (membrane and for the out-of-plane state (bending. These uncoupled systems are joined to form a macro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs. A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM.
Sheng Zhang; Dehao Yu
2007-01-01
In this paper, some V-cycle multigrid algorithms are presented for the coupling system arising from the discretization of the Dirichlet exterior problem by coupling the natural boundary element method and finite element method. The convergence of these multigrid algorithms is obtained even with only one smoothing on all levels. The rate of convergence is found uniformly bounded independent of the number of levels and the mesh sizes of all levels, which indicates that these multigrid algorithms are optimal. Some numerical results are also reported.
A cell boundary element method applied to laminar vortex shedding from circular cylinders
Farrant, T; Tan, M; Price, W.G.
2001-01-01
The two-dimensional unsteady incompressible Navier–Stokes equations are solved for flows around arrangements of circular cylinders at Reynolds number 100 and 200. A hybrid boundary element/finite element method is used to discretise the spatial domain together with a second order implicit finite difference approximation in time. The numerical scheme of study is validated for a uniform stream past an isolated circular cylinder by comparing findings with experimental and numerical studies. Both...
CALCULATION OF MILL RIGIDITY BY THREE DIMENSION CONTACT BOUNDARY ELEMENT METHOD
无
2001-01-01
Vertical rigidity of the space self-adaptive 530 high rigidity mill is calculated by applying the boundary element method (BEM) of three-dimension elastic contact problem,which can update the existed deforming separation calculating theory and corresponding methods of material mechanics,elastic mechanics and finite element method.The method has less hypotheses and stronger synthesis in contact-type calculating model.The advantages of the method are high calculating rate,high calculating accuracy,etc..
Downhole Elemental Analysis with LIBS
Moreschini, Paolo; Zacny, Kris; Rickman, Doug
2011-01-01
In this paper we discuss a novel instrument, currently under development at Honeybee Robotics with SBIR funding from NASA. The device is designed to characterize elemental composition as a function of depth in non-terrestrial geological formations. The instrument consists of a miniaturized laser-induced breakdown spectrometer (LIBS) analyzer integrated in a 2" diameter drill string. While the drill provides subsurface access, the LIBS analyzer provides information on the elemental composition of the borehole wall. This instrument has a variety of space applications ranging from exploration of the Moon for which it was originally designed, to Mars, as well as a variety of terrestrial applications. Subsurface analysis is usually performed by sample acquisition through a drill or excavator, followed by sample preparation and subsequent sample presentation to an instrument or suite of instruments. An alternative approach consisting in bringing a miniaturized version of the instrument to the sample has many advantages over the traditional methodology, as it allows faster response, reduced probability of cross-contamination and a simplification in the sampling mechanisms. LIBS functions by focusing a high energy laser on a material inducing a plasma consisting of a small fraction of the material under analysis. Optical emission from the plasma, analyzed by a spectrometer, can be used to determine elemental composition. A triangulation sensor located in the sensor head determines the distance of the sensor from the borehole wall. An actuator modifies the position of the sensor accordingly, in order to compensate for changes due to the profile of the borehole walls. This is necessary because LIBS measurements are negatively affected by changes in the relative position of the focus of the laser with respect to the position of the sample (commonly referred to as the "lens to sample distance"). Profiling the borehole is done by adjusting the position of the sensor with a
Downhole elemental analysis with LIBS
Moreschini, P.; Zacny, K.; Rickman, D.
2011-12-01
In this paper we discuss a novel instrument, currently under development at Honeybee Robotics with SBIR funding from NASA. The device is designed to characterize elemental composition as a function of depth in non-terrestrial geological formations. The instrument consists of a miniaturized LIBS analyzer integrated in a 2" diameter drill string. While the drill provides subsurface access, the LIBS analyzer provides information on the elemental composition of the borehole wall. This instrument has a variety of space applications ranging from exploration of the Moon for which it was originally designed, to Mars, as well as a variety of terrestrial applications. Subsurface analysis is usually performed by sample acquisition through a drill or excavator, followed by sample preparation and subsequent sample presentation to an instrument or suite of instruments. An alternative approach consisting in bringing a miniaturized version of the instrument to the sample has many advantages over the traditional methodology, as it allows faster response, reduced probability of cross-contamination and a simplification in the sampling mechanisms. LIBS functions by focusing a high energy laser on a material inducing a plasma consisting of a small fraction of the material under analysis. Optical emission from the plasma, analyzed by a spectrometer, can be used to determine elemental composition. A triangulation sensor located in the sensor head determines the distance of the sensor from the borehole wall. An actuator modifies the position of the sensor accordingly, in order to compensate for changes due to the profile of the borehole walls. This is necessary because LIBS measurements are negatively affected by changes in the relative position of the focus of the laser with respect to the position of the sample (commonly referred to as the "lens to sample distance"). Profiling the borehole is done by adjusting the position of the sensor with a vertical stage; a second actuator at the
Trace Element Analysis of Selenium
The present thesis divided into four chapters as follows:Chapter (1):This chapter contains an introduction on different oxidation states of organic and inorganic species for selenium in environmental and biological samples, the process for separation of selenium from these samples and the importance of selenium as a component for these samples. Also gives notes about the techniques which are used in the elemental analysis for selenium species and the detection limits for selenium in these techniques, selenium species in human body and the importance of these species in protecting the body from the different types of cancer and the sources of selenium in environmental samples (soil and water) and distribution levels of selenium in these samples.Chapter (2):This chapter is divided into two parts :The first part deals with the sample collection process for environmental samples (underground water, soil) and the wet digestion ( microwave digestion ) process of soil samples. It also contains the theory of work of the closed microwave digestion system.The second part contains detailed information concerning the theoretical considerations of the used analytical techniques. These techniques include Hydride generation - Atomic Absorption Spectrometer (HG-AAS), Inductively Coupled Plasma Mass Spectrometer (ICP-MS) and Neutron Activation Analysis (NAA).Chapter (3): This chapter includes the methods of sampling, sample preparation, and sample digesition. The measures of quality assurance are disscused in this chapter. It describes in details the closed microwave digestion technique and the analytical methods used in this study which are present in Central Laboratory for Elemental and Isotopic Analysis (CLEIA) and the Egypt Second Research Reactor (ETRR-2). The described techniques are Atomic Absorption Spectrometer (AAS 6 vario, Analytical Jena GmbH, Germany), JMS-PLASMAX2 Mass Spectrometer (ICP-MS) and the Egypt Second Research Reactor (NAA).
A comparison of inverse boundary element method and near-field acoustical holography
Schuhmacher, Andreas; Hald, Jørgen; Saemann, E.-U.
1999-01-01
An inverse boundary element method (IBEM) is used to estimate the surface velocity of a rolling tyre from measurements of the near-field pressure. Subsequently, the sound pressure is calculated over a finite plane surface next to the tyre from the reconstructed velocity field on the tyre surface...
A MATLAB Code for Three Dimensional Linear Elastostatics using Constant Boundary Elements
P, Kirana Kumara
2013-01-01
Present work presents a code written in the very simple programming language MATLAB, for three dimensional linear elastostatics, using constant boundary elements. The code, in full or in part, is not a translation or a copy of any of the existing codes. Present paper explains how the code is written, and lists all the formulae used. Code is verified by using the code to solve a simple problem which has the well known approximate analytical solution. Of course, present work does not make any contribution to research on boundary elements, in terms of theory. But the work is justified by the fact that, to the best of author's knowledge, as of now, one cannot find an open access MATLAB code for three dimensional linear elastostatics using constant boundary elements. Author hopes this paper to be of help to beginners who wish to understand how a simple but complete boundary element code works, so that they can build upon and modify the present open access code to solve complex engineering problems quickly and easi...
Duggen, Lars; Lopes, Natasha; Willatzen, Morten; Rubahn, Horst-Günter
2011-01-01
The finite-element method (FEM) is used to simulate the photoacoustic signal in a cylindrical resonant photoacoustic cell. Simulations include loss effects near the cell walls that appear in the boundary conditions for the inhomogeneous Helmholtz equation governing the acoustic pressure. Reasonably...
Stress Wave Propagation in Soils Modelled by the Boundary Element Method
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...
Finite Element Convergence for the Joule Heating Problem with Mixed Boundary Conditions
Jensen, Max; Målqvist, Axel
2012-01-01
We prove strong convergence of conforming finite element approximations to the stationary Joule heating problem with mixed boundary conditions on Lipschitz domains in three spatial dimensions. We show optimal global regularity estimates on creased domains and prove a priori and a posteriori bounds for shape regular meshes.
A boundary element regularised Stokeslet method applied to cilia and flagella-driven flow
Smith, David J
2010-01-01
A boundary element implementation of the regularised Stokeslet method of Cortez is applied to cilia and flagella-driven flows in biology. Previously-published approaches implicitly combine the force discretisation and the numerical quadrature used to evaluate boundary integrals. By contrast, a boundary element method can be implemented by discretising the force using basis functions, and calculating integrals using accurate numerical or analytic integration. This substantially weakens the coupling of the mesh size for the force and the regularisation parameter, and greatly reduces the number of degrees of freedom required. When modelling a cilium or flagellum as a one-dimensional filament, the regularisation parameter can be considered a proxy for the body radius, as opposed to being a parameter used to minimise numerical errors. Modelling a patch of cilia, it is found that: (1) For a fixed number of cilia, reducing cilia spacing reduces transport. (2) For fixed patch dimension, increasing cilia number increa...
Wet Friction-Elements Boundary Friction Mechanism and Friction Coefficient Prediction
WANG Yanzhong
2012-12-01
Full Text Available The friction mechanism for the boundary friction course of friction elements engagement was explicitly expressed. The boundary friction model was built up by the surface topography. The model contained the effect of boundary film, adhesion, plough and lubrication. Based on the model, a coefficient for weakening plough for the lubrication was proposed. The modified model could fit for the working condition of wet friction elements. The friction coefficient as a function curve of rotating speed could be finally obtained by the data k and s/sm. The method provides a well interpretation of friction condition and friction coefficient prediction and the agreement between theoretical and experimental friction coefficients is reasonably good.
P-Finite-Element Program For Analysis Of Plates
Smith, James P.
1995-01-01
BUCKY is p-finite-element computer program for highly accurate analysis of structures. Used to analyze buckling, bending, and in-plane stress-and-strain behaviors of plates. Provides elastic-plastic solutions for isotropic plates in states of plane stress, and axisymmetric solution sequence used to treat three-dimensional problems. Computes response of plate to variety of loading and boundary conditions by use of higher-order displacement function in p-finite-element method. Enables user to obtain results more accurate than obtained by use of traditional h-finite elements. Written in FORTRAN 77.
Anisotropic Superconvergence Analysis for the Wilson Nonconforming Element
Shaochun Chen; Huixia Sun; Shipeng Mao
2006-01-01
The regular condition (there exists a constant c independent of the element K and the mesh such that hK/ρK ≤ c, where hK and ρK are diameters of K and the biggest ball contained in K, respectively) or the quasi-uniform condition is a basic assumption in the analysis of classical finite elements. In this paper, the supercloseness for consistency error and the superconvergence estimate at the central point of the element for the Wilson nonconforming element in solving second-order elliptic boundary value problem are given without the above assumption on the meshes. Furthermore the global superconvergence for the Wilson nonconforming element is obtained under the anisotropic meshes. Lastly, a numerical test is carried out which confirms our theoretical analysis.
Finite element analysis of multilayer coextrusion.
Hopkins, Matthew Morgan; Schunk, Peter Randall; Baer, Thomas A. (Proctor & Gamble Company, West Chester, OH); Mrozek, Randy A. (Army Research Laboratory, Adelphi, MD); Lenhart, Joseph Ludlow (Army Research Laboratory, Adelphi, MD); Rao, Rekha Ranjana; Collins, Robert (Oak Ridge National Laboratory); Mondy, Lisa Ann
2011-09-01
Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.
A mixed-grid finite element method with PML absorbing boundary conditions for seismic wave modelling
We have developed a mixed-grid finite element method (MGFEM) to simulate seismic wave propagation in 2D structurally complex media. This method divides the physical domain into two subdomains. One subdomain covering the major part of the physical domain is divided by regular quadrilateral elements, while the other subdomain uses triangular elements to correctly fit a rugged free surface topography. The local stiffness matrix of any quadrilateral element is identical and matrix-vector production is calculated using an element-by-element technique, which avoids assembling a huge global stiffness matrix. As only a few triangular elements exist in the subdomain containing the rugged free surface topography, the memory requirements for storing the assembled subdomain global stiffness matrix are significantly reduced. To eliminate artificial boundary reflections, the MGFEM is also implemented to solve the system equations of PML absorbing boundary conditions (PML ABC). The accuracy and efficiency of the MGFEM is tested in numerical experiments by comparing it with conventional methods, and numerical comparisons also indicate its tremendous ability to describe rugged surfaces. (paper)
Li, Jianbo; Liu, Jun; Lin, Gao
2013-12-01
Consideration of structure-foundation-soil dynamic interaction is a basic requirement in the evaluation of the seismic safety of nuclear power facilities. An efficient and accurate dynamic interaction numerical model in the time domain has become an important topic of current research. In this study, the scaled boundary finite element method (SBFEM) is improved for use as an effective numerical approach with good application prospects. This method has several advantages, including dimensionality reduction, accuracy of the radial analytical solution, and unlike other boundary element methods, it does not require a fundamental solution. This study focuses on establishing a high performance scaled boundary finite element interaction analysis model in the time domain based on the acceleration unit-impulse response matrix, in which several new solution techniques, such as a dimensionless method to solve the interaction force, are applied to improve the numerical stability of the actual soil parameters and reduce the amount of calculation. Finally, the feasibility of the time domain methods are illustrated by the response of the nuclear power structure and the accuracy of the algorithms are dynamically verified by comparison with the refinement of a large-scale viscoelastic soil model.
Second-order wave diffraction by a circular cylinder using scaled boundary finite element method
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.
Finite element analysis of photonic crystal fibers
Uranus, H.P.; Hoekstra, H.J.W.M.; Groesen, van E.
2005-01-01
A finite-element-based vectorial optical mode solver, furnished with Bayliss-Gunzburger-Turkel-like transparent boundary conditions, is used to rigorously analyze photonic crystal fibers (PCFs). Both the real and imaginary part of the modal indices can be computed in a relatively small computational
Boundary element simulation of surface waves on a deformed half-space
Litvinchuk, S. Yu.; Belov, A. A.; Markov, I. P.; Ipatov, A. A.; Petrov, A. N.
2015-11-01
Homogeneous and two-layer half-spaces consisting of an anisotropic elastic, isotropic viscoelastic, or poroelastic material are considered. The Kelvin-Voigt model and the model with the Abel kernel are used as models of the viscoelastic material; the poroelastic material is studied within the framework of the model of the compressible Biot material. The case where the half-space contains a cavity is also considered. Propagation of surface waves is studied by the boundary element method. The numerical solution involves the method of collocations for a regularized boundary integral equation.
Habib Ammari; Gang Bao
2008-01-01
Consider a time-harmonic electromagnetic plane wave incident on a biperiodic structure in R3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and nonhomogeneous. In this paper, variational formulations coupling finite element methods in the chiral medium with a method of integral equations on the periodic interfaces are studied. The well-posedness of the continuous and discretized problems is established. Uniform convergence for the coupling variational approximations of the model problem is obtained.
Two-dimensional finite-element temperature variance analysis
Heuser, J. S.
1972-01-01
The finite element method is extended to thermal analysis by forming a variance analysis of temperature results so that the sensitivity of predicted temperatures to uncertainties in input variables is determined. The temperature fields within a finite number of elements are described in terms of the temperatures of vertices and the variational principle is used to minimize the integral equation describing thermal potential energy. A computer calculation yields the desired solution matrix of predicted temperatures and provides information about initial thermal parameters and their associated errors. Sample calculations show that all predicted temperatures are most effected by temperature values along fixed boundaries; more accurate specifications of these temperatures reduce errors in thermal calculations.
Contreras Zazueta, M. A.; Perton, M.; Sanchez-Sesma, F. J.; Sánchez-Alvaro, E.
2013-12-01
The seismic hazard assessment of extended developments, such as a dam, a bridge or a pipeline, needs the strong ground motion simulation taking into account the effects of surface geology. In many cases the incoming wave field can be obtained from attenuation relations or simulations for layered media using Discrete Wave Number (DWN). Sometimes there is a need to include in simulations the seismic source as well. A number of methods to solve these problems have been developed. Among them the Finite Element and Finite Difference Methods (FEM and FDM) are generally preferred because of the facility of use. Nevertheless, the analysis of realistic dynamic loading induced by earthquakes requires a thinner mesh of the entire domain to consider high frequencies. Consequently this may imply a high computational cost. The Indirect Boundary Element Method (IBEM) can also be employed. Here it is used to study the response of a site to historical seismic activity. This method is particularly suited to model wave propagation through wide areas as it requires only the meshing of boundaries. Moreover, it is well suited to represent finely the diffraction that can occur on a fault. However, the IBEM has been applied mainly to simple geometrical configurations. In this communication significant refinements of the formulation are presented. Using IBEM we can simulate wave propagation in complex geometrical configurations such as a stratified medium crossed by thin faults or having a complex topography. Two main developments are here described; one integrates the DWN method inside the IBEM in order to represent the Green's functions of stratified media with relatively low computational cost but assuming unbounded parallel flat layers, and the other is the extension of IBEM to deal with multi-regions in contact which allows more versatility with a higher computational cost compared to the first one but still minor to an equivalent FEM formulation. The two approaches are fully
So Gu Kim
2013-01-01
On March 26, 2010 an underwater explosion (UWE) led to the sinking of the ROKS Cheonan. The official Multinational Civilian-Military Joint Investigation Group (MCMJIG) report concluded that the cause of the underwater explosion was a 250 kg net explosive weight (NEW) detonation at a depth of 6−9 m from a DPRK “CHT-02D” torpedo. Kim and Gitterman (2012a) determined the NEW and seismic magnitude as 136 kg at a depth of approximately 8m and 2.04, respectively using basic hydrodynamics based on theoretical and experimental methods as well as spectral analysis and seismic methods. The purpose of this study was to clarify the cause of the UWE via more detailed methods using bubble dynamics and simulation of propellers as well as forensic seismology. Regarding the observed bubble pulse period of 0.990 s, 0.976 s and 1.030 s were found in case of a 136 NEW at a detonation depth of 8 m using the boundary element method (BEM) and 3D bubble shape simulations derived for a 136 kg NEW detonation at a depth of 8 m approximately 5 m portside from the hull centerline. Here we show through analytical equations, models and 3D bubble shape simulations that the most probable cause of this underwater explosion was a 136 kg NEW detonation at a depth of 8m attributable to a ROK littoral “land control” mine (LCM).
Electrostatic force microscopy (EFM) is a special design of non-contact atomic force microscopy used for detecting electrostatic interactions between the probe tip and the sample. Its resolution is limited by the finite probe size and the long-range characteristics of electrostatic forces. Therefore, quantitative analysis is crucial to understanding the relationship between the actual local surface potential distribution and the quantities obtained from EFM measurements. To study EFM measurements on bimetallic samples with surface potential inhomogeneities as a special case, we have simulated such measurements using the boundary element method and calculated the force component and force gradient component that would be measured by amplitude modulation (AM) EFM and frequency modulation (FM) EFM, respectively. Such analyses have been performed for inhomogeneities of various shapes and sizes, for different tip-sample separations and tip geometries, for different applied voltages, and for different media (e.g., vacuum or water) in which the experiment is performed. For a sample with a surface potential discontinuity, the FM-EFM resolution expression agrees with the literature; however, the simulation for AM-EFM suggests the existence of an optimal tip radius of curvature in terms of resolution. On the other hand, for samples with strip- and disk-shaped surface potential inhomogeneities, we have obtained quantitative expressions for the detectability size requirements as a function of experimental conditions for both AM- and FM-EFMs, which suggest that a larger tip radius of curvature is moderately favored for detecting the presence of such inhomogeneities
Cutanda Henríquez, Vicente; Juhl, Peter Møller
2008-01-01
) when field points are calculated very close to the boundary. The difficulty is due to the near-singularity of the integrand, which causes failure of the numerical integration over the element. There are a number of techniques to overcome this problem, in many cases involving a reformulation of the...... interest. The subdivision is adapted to the strength of the near-singularity and is only performed when needed, not adding excessive calculation time and storage. The implementation is examined and verified with test cases....
Quantum corrected model for plasmonic nanoparticles: A boundary element method implementation
Hohenester, Ulrich
2015-05-01
We present a variant of the recently developed quantum corrected model (QCM) for plasmonic nanoparticles [Nat. Commun. 3, 825 (2012), 10.1038/ncomms1806] using nonlocal boundary conditions. The QCM accounts for electron tunneling in narrow gap regions of coupled metallic nanoparticles, leading to the appearance of new charge-transfer plasmons. Our approach has the advantages that it emphasizes the nonlocal nature of tunneling and introduces only contact resistance, but not ohmic losses through tunneling. Additionally, it can be implemented much more easily in boundary element method (BEM) approaches. We develop the methodology for the QCM using nonlocal boundary conditions and present simulation results of our BEM implementation, which are in good agreement with those of the original QCM.
无
2009-01-01
According to the electric potential of oblique multi-needle electrodes (OMNE) in biological tissue, the discrete equations based on the indetermination linear current density were established by the boundary element integral equations (BEIE). The non-uniform distribution of the current flowing from multi-needle electrodes to conductive biological tissues was imaged by solving a set of linear equa- tions. Then, the electric field and potential generated by OMNE in biological tissues at any point may be determined through the boundary element method (BEM). The time of program running and stability of computing method are examined by an example. It demonstrates that the algorithm possesses a quick speed and the steady computed results. It means that this method has an important referenced sig- nificance for computing the field and the potential generated by OMNE in bio-tissue, which is a fast, effective and accurate computing method.
Pan Xiaomin; Sheng Xinqing
2008-01-01
A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finite-element-boundary-integral-multi-level fast multipole algorithm (FE-BI-MLFMA). Among many algorithms of FE-BI-MLFMA, the decomposition algorithm (DA) is chosen as a basis for the parallelization of FE-BI-MLFMA because of its distinct numerical characteristics suitable for parallelization. On the basis of the DA, the parallelization of FE-BI-MLFMA is carried out by employing the parallelized multi-frontal method for the matrix from the finite-element method and the parallelized MLFMA for the matrix from the boundary integral method respectively. The programming and numerical experiments of the proposed parallel approach are carried out in the high perfor-mance computing platform CEMS-Liuhui. Numerical experiments demonstrate that FE-BI-MLFMA is efficiently parallelized and its computational capacity is greatly improved without losing accuracy, efficiency, and generality.
Wu, Shih-Jeh; Kuo, Ihyuan; Shung, K Kirk
2005-01-01
High frequency ultrasonic imaging (e.g. >30 MHz) from blood is difficult due to its tenuous backscattered pressure and the interference from adjacent tissues as well. To increase the sensitivity focused transducer has to be used, thus raising the complexity of interpreting the received signals. A numerical simulation of the ultrasonic scattering property from erythrocyte and rouleaux based on boundary element method was performed with experimental results based on a modified substitution method. The results (proportional relationship between backscattered pressure and frequency and the frequency limit for Rayleigh scattering) closely coincide with experimental data for erythrocyte. Rouleaux model results also show the dependence of degree of red cell aggregation on backscattering properties. The boundary element method serves as a good means to calculate the acoustic scattering from blood cells under arbitrary incident waves. PMID:15556649
Chang-Jun Zheng; Hai-Bo Chen; Lei-Lei Chen
2013-01-01
This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.
Boundary element method for the solution of the diffusion equation in cylindrical symmetry
Equations for the solution of the diffusion equation in plane Cartesian geometry with the Boundary Element method was derived. The equation for the axi-symmetric case were set and included in the computer program. The results were compared to those obtained by the Finite Difference method. Comparing the results some advantages of the proposed method can be observed, with implications on the multidimensional problems. (author)
Pai, Ravindra
1991-01-01
A numerical method has been developed for computing the steady state flow about arbitrary shaped three dimensional bodies on or below the free surface using a Boundary Integral Element Method ( Panel Method). The method uses a singularity distribution over the body surface and the free surface. The method can solve for the potential distribution as well as the source density distribution. In this study a constant source distribution is assumed on each panel. The free surface bo...
FLUID BOUNDARY ELEMENT METHOD AND ORTHOGONAL TRANSFORM OF DOUBLE COMPLEX VARIABLES
罗义银
2003-01-01
A concept of orthogonal double function and its complex variables space was putforward. Its corresponding operation rules, the concept of analytic function and conformaltransform are established. And using this concept discussed its foreground for application offluid boundary element method. In results, this concept and special marks may be toenlarge the plane complex into three-dimensional space, and then extensive application maybe obtained in physics and mathematics.
Implementation aspects of the Boundary Element Method including viscous and thermal losses
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2014-01-01
The implementation of viscous and thermal losses using the Boundary Element Method (BEM) is based on the Kirchhoff’s dispersion relation and has been tested in previous work using analytical test cases and comparison with measurements. Numerical methods that can simulate sound fields in fluids...... with mesh definition, geometrical singularities and treatment of closed cavities. These issues are specific of the BEM with losses. Using examples, some strategies are presented that can alleviate shortcomings and improve performance....
Noise source localization on tyres using an inverse boundary element method
Schuhmacher, Andreas; Saemann, E-U; Hald, J
1998-01-01
A dominating part of tyre noise is radiated from a region close to the tyre/road contact patch, where it is very difficult to measure both the tyre vibration and the acoustic near field. The approach taken in the present paper is to model the tyre and road surfaces with a Boundary Element Model...... from tyre noise measurements will be presented at the conference....
Inexact Krylov iterations and relaxation strategies with fast-multipole boundary element method
Layton, Simon K.; Barba, Lorena A.
2015-01-01
Boundary element methods produce dense linear systems that can be accelerated via multipole expansions. Solved with Krylov methods, this implies computing the matrix-vector products within each iteration with some error, at an accuracy controlled by the order of the expansion, $p$. We take advantage of a unique property of Krylov iterations that allow lower accuracy of the matrix-vector products as convergence proceeds, and propose a relaxation strategy based on progressively decreasing $p$. ...
Modeling the 3D Terrain Effect on MT by the Boundary Element Method
Ruan Baiyao; Xu Shizhe; Xu Zhifeng
2006-01-01
A numerical method is put forward in this paper, using the boundary element method(BEM) to model 3D terrain effects on magnetotelluric (MT) surveys. Using vector integral theory and electromagnetic field boundary conditions, the boundary problem of two electromagnetic fields in the upper half space (air) and lower half space (earth medium) was transformed into two vector integral equations just related to the topography: one magnetic equation for computing the magnetic field and the other electrical equation for computing the electrical field. The topography integral is decomposed into a series of integrals in a triangle element. For the integral in a triangle element, we suppose that the electromagnetic field in it is the stack of the electromagnetic field in the homogeneous earth and the topography response which is a constant; so the computation becomes simple, convenient and highly accurate. By decomposition and computation, each vector integral equation can be calculated by solving three linear equations that are related to the three Cartesian directions. The matrix of these linear equations is diagonally dominant and can be solved using the Symmetric Successive Over-Relaxation (SSOR) method. The apparent resistivity curve of MT on two 3D terrains calculated by BEM is shown in this paper.
Perton, Mathieu; Contreras-Zazueta, Marcial A.; Sánchez-Sesma, Francisco J.
2016-06-01
A new implementation of indirect boundary element method allows simulating the elastic wave propagation in complex configurations made of embedded regions that are homogeneous with irregular boundaries or flat layers. In an older implementation, each layer of a flat layered region would have been treated as a separated homogeneous region without taking into account the flat boundary information. For both types of regions, the scattered field results from fictitious sources positioned along their boundaries. For the homogeneous regions, the fictitious sources emit as in a full-space and the wave field is given by analytical Green's functions. For flat layered regions, fictitious sources emit as in an unbounded flat layered region and the wave field is given by Green's functions obtained from the discrete wavenumber (DWN) method. The new implementation allows then reducing the length of the discretized boundaries but DWN Green's functions require much more computation time than the full-space Green's functions. Several optimization steps are then implemented and commented. Validations are presented for 2-D and 3-D problems. Higher efficiency is achieved in 3-D.
A virtual-reality real-time simulation of surgical operations that incorporates the inclusion of a hard tumour is presented. The software is based on Boundary Element (BE) technique. A review of the BE formulation for real-time analysis of two-domain deformable objects, using the pre-solution technique, is presented. The two-domain BE software is incorporated into a surgical simulation system called VIRS to simulate the initiation of a cut on the surface of the soft tissue and extending the cut deeper until the tumour is reached.
Bhattacharyya, S. K.; Premkumar, R.
2003-12-01
In a domain method of solution of exterior scalar wave equation, the radiation condition needs to be imposed on a truncation boundary of the modeling domain. The Bayliss, Gunzberger, and Turkel (BGT) boundary dampers, which require a circular cylindrical and spherical truncation boundaries in two-(2D) and three-(3D)-dimensional problems, respectively, have been particularly successful in the analysis of scattering and radiation problems. However, for an elongated body, elliptical (2D) or spheroidal (3D) truncation boundaries have potential to reduce the size of modeling domain and hence computational effort. For harmonic problems, such extensions of the first- and second-order BGT dampers are available in the literature. In this paper, BGT dampers in both elliptical and spheroidal coordinate systems have been developed for transient problems involving acoustic radiation as well as fluid-structure interaction and implemented in the context of finite-element method based upon unsymmetric pressure-displacement formulation. Applications to elongated radiators and shells are reported using several numerical examples with excellent comparisons. It is demonstrated that significant computational economy can be achieved for elongated bodies with the use of these dampers.
Application of scaled boundary finite element method in static and dynamic fracture problems
Zhenjun Yang
2006-01-01
The scaled boundary finite element method (SBFEM) is a recently developed numerical method combining advantages of both finite element methods (FEM)and boundary element methods (BEM) and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors (SIFs) directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion.F0r dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.
Trace element analysis in flour
Trace elements in five kinds of flour which were made in Japan, America and Canada, have been measured by means of in-air PIXE. Twelve kinds of trace elements were detected, such as Cl, K, Ca, Sc, Cr, Mn, Fe, Co, Ni, Cu, Zn and Br. The concentration of these elements varied depending on the place where they were made. In order to check the target preparation procedure, two types of sample preparation have been used, such as wet ashing by nitric acid in a microwave oven and making a paste by an internal standard solution. Comparisons of the results of both samples ensures that bromine was not lost during micro-wave oven heating. Analytic fitting of PIXE spectra by a personal computer and a commercial application software was successfully used. (author)
Ren, Zhengyong; Kalscheuer, Thomas; Greenhalgh, Stewart; Maurer, Hansruedi
2014-02-01
A novel hybrid boundary element-finite element scheme which is accelerated by an adaptive multi-level fast multipole algorithm is presented to simulate 3D plane wave electromagnetic induction responses in the Earth. The remarkable advantages of this novel scheme are the complete removal of the volume discretization of the air space and the capability of simulating large-scale complicated geo-electromagnetic induction problems. To achieve this goal, first the Galerkin edge-based finite-element method (FEM) using unstructured meshes is adopted to solve the electric field differential equation in the heterogeneous Earth, where arbitrary distributions of conductivity, magnetic permeability and dielectric permittivity are allowed for. Second, the point collocation boundary-element method (BEM) is used to solve a surface integral formula in terms of the reduced electrical vector potential on the arbitrarily shaped air-Earth interface. Third, to avoid explicit storage of the system matrix arising from large-scale problems and to reduce the horrendous time complexity of the product of the system matrix with an initial vector of unknowns, the adaptive multilevel fast multipole method is applied. This leads to a matrix-free form suitable for the application of iterative solvers. Furthermore, a highly sparse problem-dependent preconditioner is developed to significantly reduce the number of iterations used by the iterative solvers. The efficacy of the presented hybrid scheme is verified on two synthetic examples against different numerical techniques such as goal-oriented adaptive finite-element methods. Numerical experiments show that at low frequencies, where the quasi-static approximation is applicable, standard FEM methods prove to be superior to our hybrid BEM-FEM solutions in terms of computational time, because the FEM method requires only a coarse discretization of the air domain and offers an advantageous sparsity of the system matrix. At radio
Gumerov, Nail A; Duraiswami, Ramani
2009-01-01
The development of a fast multipole method (FMM) accelerated iterative solution of the boundary element method (BEM) for the Helmholtz equations in three dimensions is described. The FMM for the Helmholtz equation is significantly different for problems with low and high kD (where k is the wavenumber and D the domain size), and for large problems the method must be switched between levels of the hierarchy. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements), and these errors must be balanced against approximations introduced by the FMM and the convergence criterion for iterative solution. These different errors must all be chosen in a way that, on the one hand, excess work is not done and, on the other, that the error achieved by the overall computation is acceptable. Details of translation operators for low and high kD, choice of representations, and BEM quadrature schemes, all consistent with these approximations, are described. A novel preconditioner using a low accuracy FMM accelerated solver as a right preconditioner is also described. Results of the developed solvers for large boundary value problems with 0.0001 less, similarkD less, similar500 are presented and shown to perform close to theoretical expectations. PMID:19173406
Dynamical analysis of separated boundary layer flow
Uruba, Václav
Berlin : Technische Universität Berlin, 2009. s. 1-2 ISBN N. [Nonlinear Normal Modes, Dimension Reduction and Localization in Vibrating Systems. 27.09.2009-02.10.2009, Frascati (Rome)] R&D Projects: GA ČR GA101/08/1112 Institutional research plan: CEZ:AV0Z20760514 Keywords : boundary layer * separation * dynamics Subject RIV: BK - Fluid Dynamics
Authors have been working in particle accelerator wake field analysis by using the Time Domain Boundary Element Method (TDBEM). A stable TDBEM scheme was presented and good agreements with conventional wake field analysis of the FDTD method were obtained. On the other hand, the TDBEM scheme still contains difficulty of initial value setting on interior region problems for infinitely long accelerator beam pipe. To avoid this initial value setting, we adopted a numerical model of beam pipes with finite length and wall thickness on open scattering problems. But the use of such finite beam pipe models causes another problem of unwanted scattering fields at the beam pipe edge, and leads to the involvement of interior resonant solutions. This paper presents a modified TDBEM scheme, Scattered-field Time Domain Boundary Element Method (S-T-TDBEM) to treat the infinitely) to treat the infinitely long beam pipe on interior region problems. It is shown that the S-TDBEM is able to avoid the excitation of the edge scattering fields and the involvement of numerical instabilities caused by interior resonance, which occur in the conventional TDBEM. (author)
2-D Numerical Wave Tank by Boundary Element Method Using Different Numerical Techniques
Farid Habashi Aliabadi
2013-03-01
Full Text Available In this article, numerical modeling of a 2-D wave tank has been investigated by applying completely nonlinear condition for water surface elevation. This has been accomplished based on potential theory, the combined Eulerian-Lagrangian scheme for time marching and using boundary element method. Other physical and numerical attributes of the current work are: physical modeling in time domain, time integration by 4th order Runge-Kutta method, implementation of appropriate condition at the entrance boundary for wave generation, application of artificial dampers at the exit part of the wave tank, and ultimately numerical smoothing of the resulting free surface by using interpolation through spline functions. At the end, effective parameters on the generated wave have been analyzed and the generated wave has also been validated against the result of the linear wave theory.
A simple finite element method for boundary value problems with a Riemann–Liouville derivative
Jin, Bangti
2016-02-01
© 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-^{1} in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and ^{L2}(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.
Elements of stock market analysis
Suciu, T.
2013-12-01
Full Text Available The paper represents a starting point in the presentation of the two types of stock/market analysis: the fundamental analysis and the technical analysis. The fundamental analysis consist in the assessment of the financial and economic status of the company together with the context and macroeconomic environment where it activates. The technical analysis deals with the demand and supply of securities and the evolution of their trend on the market, using a range of graphics and charts to illustrate the market tendencies for the quick identification of the best moments to buy or sell.
Haas, M.
2004-07-01
The three-dimensional Symmetrical Galerkin Boundary Element Method is presented. The necessary coupling equations for FEM/BEM coupling are established in consideration of the dimensional jump at the coupling surface. The author shows how a commercial FE program system (ABAQUS) can be coupled with the boundary element method in industrial practice. (orig.) [German] Im Leichtbau spielt die beansprechungsgerechte Auslegung von Bauteilen eine immer groessere Rolle. Meist handelt es sich um flaechige Strukturen, fuer deren Simulation sich finite Schalenelemente als effizient erwiesen haben. In Iokalen Bereichen dieser flaechigen Bauteile liegt jedoch oft ein dreidimensionaler Spannungszustand vor. Bei linear-elastischem Materialverhalten stellt fuer solche Bereiche die Randelementmethode eine Alternative zur volumenorientieren Finite-Elemente-Methode dar. In der Arbeit wird die dreidimensionale Symmetrische Galerkin-Randelementmethode vorgestellt. Es werden die notwendigen Kopplungsbeziehungen fuer die FEM/BEM-Kopplung aufgestellt, wobei der an der Kopplungsflaeche auftretende Dimensionssprung Beruecksichtigung findet. In der Arbeit wird ein Weg gezeigt, wie in der industriellen Praxis ein kommerzielles FE-Programmsystem (ABAQUS) mit der Randelementmethode gekoppelt werden kann. (orig.)
Ma, Zhibo; Li, Mo; Roy, Sharmila; Liu, Kevin J; Romine, Matthew L; Lane, Derrick C; Patel, Sapna K; Cai, Haini N
2016-08-26
The three-dimensional (3D) organization of the eukaryotic genome is critical for its proper function. Evidence suggests that extensive chromatin loops form the building blocks of the genomic architecture, separating genes and gene clusters into distinct functional domains. These loops are anchored in part by a special type of DNA elements called chromatin boundary elements (CBEs). CBEs were originally found to insulate neighboring genes by blocking influences of transcriptional enhancers or the spread of silent chromatin. However, recent results show that chromatin loops can also play a positive role in gene regulation by looping out intervening DNA and "delivering" remote enhancers to gene promoters. In addition, studies from human and model organisms indicate that the configuration of chromatin loops, many of which are tethered by CBEs, is dynamically regulated during cell differentiation. In particular, a recent work by Li et al has shown that the SF1 boundary, located in the Drosophila Hox cluster, regulates local genes by tethering different subsets of chromatin loops: One subset enclose a neighboring gene ftz, limiting its access by the surrounding Scr enhancers and restrict the spread of repressive histones during early embryogenesis; and the other loops subdivide the Scr regulatory region into independent domains of enhancer accessibility. The enhancer-blocking activity of these CBE elements varies greatly in strength and tissue distribution. Further, tandem pairing of SF1 and SF2 facilitate the bypass of distal enhancers in transgenic flies, providing a mechanism for endogenous enhancers to circumvent genomic interruptions resulting from chromosomal rearrangement. This study demonstrates how a network of chromatin boundaries, centrally organized by SF1, can remodel the 3D genome to facilitate gene regulation during development. PMID:27621770
Ma, Zhibo; Li, Mo; Roy, Sharmila; Liu, Kevin J; Romine, Matthew L; Lane, Derrick C; Patel, Sapna K; Cai, Haini N
2016-01-01
The three-dimensional (3D) organization of the eukaryotic genome is critical for its proper function. Evidence suggests that extensive chromatin loops form the building blocks of the genomic architecture, separating genes and gene clusters into distinct functional domains. These loops are anchored in part by a special type of DNA elements called chromatin boundary elements (CBEs). CBEs were originally found to insulate neighboring genes by blocking influences of transcriptional enhancers or the spread of silent chromatin. However, recent results show that chromatin loops can also play a positive role in gene regulation by looping out intervening DNA and “delivering” remote enhancers to gene promoters. In addition, studies from human and model organisms indicate that the configuration of chromatin loops, many of which are tethered by CBEs, is dynamically regulated during cell differentiation. In particular, a recent work by Li et al has shown that the SF1 boundary, located in the Drosophila Hox cluster, regulates local genes by tethering different subsets of chromatin loops: One subset enclose a neighboring gene ftz, limiting its access by the surrounding Scr enhancers and restrict the spread of repressive histones during early embryogenesis; and the other loops subdivide the Scr regulatory region into independent domains of enhancer accessibility. The enhancer-blocking activity of these CBE elements varies greatly in strength and tissue distribution. Further, tandem pairing of SF1 and SF2 facilitate the bypass of distal enhancers in transgenic flies, providing a mechanism for endogenous enhancers to circumvent genomic interruptions resulting from chromosomal rearrangement. This study demonstrates how a network of chromatin boundaries, centrally organized by SF1, can remodel the 3D genome to facilitate gene regulation during development.
Boundary element modeling of earthquake site effects including the complete incident wavefield
Kim, Kyoung-Tae
Numerical modeling of earthquake site effects in realistic, three-dimensional structures, including high frequencies, low surface velocities and surface topography, has not been possible simply because the amount of computer memory constrains the number of grid points available. In principle, this problem is reduced in the Boundary Element Method (BEM) since only the surface of the velocity discontinuity is discretized; wave propagation both inside and outside this boundary is computed analytically. Equivalent body forces are determined on the boundary by solving a matrix equation containing frequency-domain displacement and stress Green's functions from every point on the boundary to every other point. This matrix problem has imposed a practical limit on the size or maximum frequency of previous BEM models. Although the matrix can be quite large, it also seems to be fairly sparse. We have used iterative matrix algorithms of the PETSc package and direct solution algorithms of the ScaLAPACK on the massively parallel supercomputers at Cornell, San Diego and Michigan. Preconditioning has been applied using blockwise ILU decomposition for the iterative approach or LU decomposition for the direct approach. The matrix equation is solved using the GMRES method for the iterative approach and a tri-diagonal solver for the direct approach. Previous BEM applications typically have assumed a single, incident plane wave. However, it is clear that for more realistic ground motion simulations, we need to consider the complete incident wavefield. If we assume that the basin or three-dimensional structure of interest is embedded in a surrounding plane-layered medium, we may use the propagator matrix method to solve for the displacements and stresses at depth on the boundary. This is done in the frequency domain with integration over wavenumber so that all P, S, mode conversions, reverberations and surface waves are included. The Boundary Element Method succeeds in modeling
OpenBEM - An open source Boundary Element Method software in Acoustics
Cutanda Henriquez, Vicente; Juhl, Peter Møller
-symmetric and half-space problems. It also contains a number of improvements such a dealing with thin objects and close surfaces, meshing for 2D and axisymmetrical problems, analytical solutions for verification, and a number of additional functions. This paper gives an overview of the capabilities of the......OpenBEM is a collection of open source programs for solving the Helmholtz Equation using the Boundary Element Method. The collection is written in Matlab by the authors and contains codes for dealing with exterior and interior problems in two or three dimensions as well as implementation of axi...
The residual stress due to butt-welds may affect the reliability of a welded structure because brittle fracture, buckling fracture, and fatigue life may be affected. The measurement of welding residual stress is conducted by destructive or nondestructive methods, but these methods require much time and labor. A simplified identification method based on the boundary element method is proposed to estimate the residual stress distribution due to butt-welding of thin plates. The validity of the proposed method was confirmed by numerical experiments when random measurement errors are included in the measured value. (author)
A fast multipole boundary element method for three dimensional potential flow problems
TENG Bin; NING Dezhi; GOU Ying
2004-01-01
A fast multipole methodology (FMM) is developed as a numerical approach to reduce the computational cost and memory requirements in solving large-scale problems. It is applied to the boundary element method (BEM) for threedimensional potential flow problems. The algorithm based on mixed multipole expansion and numerical integration is implemented in combination with an iterative solver. Numerical examinations, on Dirichlet and Neumann problems,are carried out to demonstrate the capability and accuracy of the present method. It has been shown that the method has evident advantages in saving memory and computing time when used to solve huge-scale problems which may be prohibitive for the traditional BEM implementation.
Dancette, S.; Browet, A.; Martin, G.; Willemet, M.; Delannay, L.
2016-06-01
A new procedure for microstructure-based finite element modeling of polycrystalline aggregates is presented. The proposed method relies (i) on an efficient graph-based community detection algorithm for crystallographic data segmentation and feature contour extraction and (ii) on the generation of selectively refined meshes conforming to grain boundaries. It constitutes a versatile and close to automatic environment for meshing complex microstructures. The procedure is illustrated with polycrystal microstructures characterized by orientation imaging microscopy. Hot deformation of a Duplex stainless steel is investigated based on ex-situ EBSD measurements performed on the same region of interest before and after deformation. A finite element mesh representing the initial microstructure is generated and then used in a crystal plasticity simulation of the plane strain compression. Simulation results and experiments are in relatively good agreement, confirming a large potential for such directly coupled experimental and modeling analyses, which is facilitated by the present image-based meshing procedure.
Computational Acoustics of Noise Propagation in Fluids - Finite and Boundary Element Methods
Marburg, Steffen
2008-01-01
Among numerical methods applied in acoustics, the Finite Element Method (FEM) is normally favored for interior problems whereas the Boundary Element Method (BEM) is quite popular for exterior ones. That is why this valuable reference provides a complete survey of methods for computational acoustics, namely FEM and BEM. It demonstrates that both methods can be effectively used in the complementary cases. The chapters by well-known authors are evenly balanced: 10 chapters on FEM and 10 on BEM. An initial conceptual chapter describes the derivation of the wave equation and supplies a unified approach to FEM and BEM for the harmonic case. A categorization of the remaining chapters and a personal outlook complete this introduction. In what follows, both FEM and BEM are discussed in the context of very different problems. Firstly, this comprises numerical issues, e.g. convergence, multi-frequency solutions and highly efficient methods; and secondly, solutions techniques for the particular difficulties that arise wi...
Finite-Element Composite-Analysis Program
Bowles, David E.
1990-01-01
Finite Element Composite Analysis Program, FECAP, special-purpose finite-element program for analyzing behavior of composite material with microcomputer. Procedure leads to set of linear simultaneous equations relating unknown nodal displacement to applied loads. Written in HP BASIC 3.0.
Finite Element Analysis of 2-D Elastic Contacts Involving FGMs
Abhilash, M. N.; Murthy, H.
2014-05-01
The response of elastic indenters in contact with Functionally Graded Material (FGM) coated homogeneous elastic half space has been presented in the current paper. Finite element analysis has been used due to its ability to handle complex geometry, material, and boundary conditions. Indenters of different typical surface profiles have been considered and the problem has been idealized as a two-dimensional (2D) plane strain problem considering only normal loads. Initially, indenters were considered to be rigid and the results were validated with the solutions presented in the literature. The analysis has then been extended to the case of elastic indenters on FGM-coated half spaces and the results are discussed.
A time-domain finite element boundary integration method for ultrasonic nondestructive evaluation.
Shi, Fan; Choi, Wonjae; Skelton, Elizabeth A; Lowe, Michael J S; Craster, Richard V
2014-12-01
A 2-D and 3-D numerical modeling approach for calculating the elastic wave scattering signals from complex stress-free defects is evaluated. In this method, efficient boundary integration across the complex boundary of the defect is coupled with a time-domain finite element (FE) solver. The model is designed to simulate time-domain ultrasonic nondestructive evaluation in bulk media. This approach makes use of the hybrid concept of linking a local numerical model to compute the near-field scattering behavior and theoretical mathematical formulas for postprocessing to calculate the received signals. It minimizes the number of monitoring signals from the FE calculation so that the computation effort in postprocessing decreases significantly. In addition, by neglecting the conventional regular monitoring box, the region for FE calculation can be made smaller. In this paper, the boundary integral method is implemented in a commercial FE code, and it is validated by comparing the scattering signals with results from corresponding full FE models. The coupled method is then implemented in real inspection scenarios in both 2-D and 3-D, and the accuracy and the efficiency are demonstrated. The limitations of the proposed model and future works are also discussed. PMID:25474780
A boundary element approach to estimate the free surface in stratified two-phase flow
Two-phase flows widely exist in many industries. Measuring the phase distribution in two-phase flow is important for the optimization and control of some industrial processes. Electrical resistance tomography (ERT) is a promising non-intrusive visualization technique for monitoring the two-phase flow. However, due to its nonlinear and ill-posed character, high-quality image reconstruction is difficult and some iterative approach is time consuming. In this paper, a boundary element approach is presented for directly estimating the free-surface in two-phase flow using ERT. The unknown free surface is parameterized by a Bézier curve. Coefficients of its control points are estimated by minimizing a residual function using the iterative Levenberg–Marquardt method. To speed up the estimation process, the physical model of ERT is formulated using a boundary element method. Based on this formulation, the forward problem is fast solved through a small size system matrix and the Jacobian matrix is efficiently calculated using an analytic method. After several numerical experiments, this approach is proved fast and precise and several factors influencing the estimation quality are analyzed based on these simulations. (paper)
Inexact Krylov iterations and relaxation strategies with fast-multipole boundary element method
Layton, Simon K
2015-01-01
Boundary element methods produce dense linear systems that can be accelerated via multipole expansions. Solved with Krylov methods, this implies computing the matrix-vector products within each iteration with some error, at an accuracy controlled by the order of the expansion, $p$. We take advantage of a unique property of Krylov iterations that allow lower accuracy of the matrix-vector products as convergence proceeds, and propose a relaxation strategy based on progressively decreasing $p$. Via extensive numerical tests, we show that the relaxed Krylov iterations converge with speed-ups of between 2x and 4x for Laplace problems and between 3.5x and 4.5x for Stokes problems. We include an application to Stokes flow around red blood cells, computing with up to 64 cells and problem size up to 131k boundary elements and nearly 400k unknowns. The study was done with an in-house multi-threaded C++ code, on a quad-core CPU.
Boundary elements method for microfluidic two-phase flows in shallow channels
Nagel, Mathias
2014-01-01
In the following work we apply the boundary element method to two-phase flows in shallow microchannels, where one phase is dispersed and does not wet the channel walls. These kinds of flows are often encountered in microfluidic Lab-on-a-Chip devices and characterized by low Reynolds and low capillary numbers. Assuming that these channels are homogeneous in height and have a large aspect ratio, we use depth-averaged equations to describe these two-phase flows using the Brinkman equation, which constitutes a refinement of Darcy's law. These partial differential equations are discretized and solved numerically using the boundary element method, where a stabilization scheme is applied to the surface tension terms, allowing for a less restrictive time step at low capillary numbers. The convergence of the numerical algorithm is checked against a static analytical solution and on a dynamic test case. Finally the algorithm is applied to the non-linear development of the Saffman-Taylor instability and compared to expe...
Efficiency analysis of betavoltaic elements
Sachenko, A. V.; Shkrebtii, A. I.; Korkishko, R. M.; Kostylyov, V. P.; Kulish, M. R.; Sokolovskyi, I. O.
2015-09-01
The conversion of energy of electrons produced by a radioactive β-source into electricity in a Si and SiC p-n junctions is modeled. The features of the generation function that describes the electron-hole pair production by an electron flux and the emergence of a "dead layer" are discussed. The collection efficiency Q that describes the rate of electron-hole pair production by incident beta particles, is calculated taking into account the presence of the dead layer. It is shown that in the case of high-grade Si p-n junctions, the collection efficiency of electron-hole pairs created by a high-energy electrons flux (such as, e.g., Pm-147 beta flux) is close or equal to unity in a wide range of electron energies. For SiC p-n junctions, Q is near unity only for electrons with relatively low energies of about 5 keV (produced, e.g., by a tritium source) and decreases rapidly with further increase of electron energy. The conditions, under which the influence of the dead layer on the collection efficiency is negligible, are determined. The open-circuit voltage is calculated for realistic values of the minority carriers' diffusion coefficients and lifetimes in Si and SiC p-n junctions, irradiated by a high-energy electrons flux. Our calculations allow to estimate the attainable efficiency of betavoltaic elements.
Finite element analysis of piezoelectric materials
This guide is intended to help people wanting to do finite element analysis of piezoelectric materials by answering some of the questions that are peculiar to piezoelectric materials. The document is not intended as a complete beginners guide for finite element analysis in general as this is better dealt with by the individual software producers. The guide is based around the commercial package ANSYS as this is a popular package amongst piezoelectric material users, however much of the information will still be useful to users of other finite element codes. (author)
Igumnov, Leonid; Ipatov, Aleksandr; Belov, Aleksandr; Petrov, Andrey
2015-09-01
The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach boundary integral equations of 3-D isotropic linear theories of elasticity and poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four and five base functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods. The boundary-element method is used in combination with the collocation method, local element-by-element approximation based on the matched interpolation model. The results of analyzing wave problems of the effect of a non-stationary force on elastic and poroelastic finite bodies, a poroelastic half-space (also with a fictitious boundary) and a layered half-space weakened by a cavity, and a half-space with a trench are presented. Excitation of a slow wave in a poroelastic medium is studied, using the stepped BEM-scheme on the nodes of Runge-Kutta methods.
Igumnov Leonid
2015-01-01
Full Text Available The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach boundary integral equations of 3-D isotropic linear theories of elasticity and poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four and five base functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods. The boundary-element method is used in combination with the collocation method, local element-by-element approximation based on the matched interpolation model. The results of analyzing wave problems of the effect of a non-stationary force on elastic and poroelastic finite bodies, a poroelastic half-space (also with a fictitious boundary and a layered half-space weakened by a cavity, and a half-space with a trench are presented. Excitation of a slow wave in a poroelastic medium is studied, using the stepped BEM-scheme on the nodes of Runge-Kutta methods.
Finite element analysis of tibial fractures
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner; Darvann, Tron; Gebuhr, Peter Henrik
2010-01-01
INTRODUCTION: Fractures of the tibial shaft are relatively common injuries. There are indications that tibial shaft fractures share characteristics in terms of site, type and local fracture mechanisms. In this study, we aimed to set up a mathematical, computer-based model using finite element...... bony healing. The biomechanical results are the basis for fracture healing, biomechanical fall analysis and stability analysis of osteosynthesis. MATERIAL AND METHODS: A finite element model of the bony part of the lower leg was generated on the basis of computed tomography data from the Visible Human...... Project. The data consisted of 21,219 3D elements with a cortical shell and a trabecular core. Three types of load of torsion, a direct lateral load and axial compression were applied. RESULTS: The finite element linear static analysis resulted in relevant fracture localizations and indicated relevant...
FECAP - FINITE ELEMENT COMPOSITE ANALYSIS PROGRAM FOR A MICROCOMPUTER
Bowles, D. E.
1994-01-01
Advanced composite materials have gained use in the aerospace industry over the last 20 years because of their high specific strength and stiffness, and low coefficient of thermal expansion. Design of composite structures requires the analysis of composite material behavior. The Finite Element Composite Analysis Program, FECAP, is a special purpose finite element analysis program for analyzing composite material behavior with a microcomputer. Composite materials, in regard to this program, are defined as the combination of at least two distinct materials to form one nonhomogeneous anisotropic material. FECAP assumes a state of generalized plane strain exists in a material consisting of two or more orthotropic phases, subjected to mechanical and/or thermal loading. The finite element formulation used in FECAP is displacement based and requires the minimization of the total potential energy for each element with respect to the unknown variables. This procedure leads to a set of linear simultaneous equations relating the unknown nodal displacements to the applied loads. The equations for each element are assembled into a global system, the boundary conditions are applied, and the system is solved for the nodal displacements. The analysis may be performed using either 4-mode linear or 8-mode quadratic isoparametric elements. Output includes the nodal displacements, and the element stresses and strains. FECAP was written for a Hewlett Packard HP9000 Series 200 Microcomputer with the HP Basic operating system. It was written in HP BASIC 3.0 and requires approximately 0.5 Mbytes of RAM in addition to what is required for the operating system. A math coprocessor card is highly recommended. FECAP was developed in 1988.
Boundary element method applied to a gas-fired pin-fin-enhanced heat pipe
Andraka, C.E.; Knorovsky, G.A.; Drewien, C.A.
1998-02-01
The thermal conduction of a portion of an enhanced surface heat exchanger for a gas fired heat pipe solar receiver was modeled using the boundary element and finite element methods (BEM and FEM) to determine the effect of weld fillet size on performance of a stud welded pin fin. A process that could be utilized by others for designing the surface mesh on an object of interest, performing a conversion from the mesh into the input format utilized by the BEM code, obtaining output on the surface of the object, and displaying visual results was developed. It was determined that the weld fillet on the pin fin significantly enhanced the heat performance, improving the operating margin of the heat exchanger. The performance of the BEM program on the pin fin was measured (as computational time) and used as a performance comparison with the FEM model. Given similar surface element densities, the BEM method took longer to get a solution than the FEM method. The FEM method creates a sparse matrix that scales in storage and computation as the number of nodes (N), whereas the BEM method scales as N{sup 2} in storage and N{sup 3} in computation.
Finite elements for analysis and design
Akin, J E; Davenport, J H
1994-01-01
The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material.Key Features* Akin clearly explains the FEM, a numerical analysis tool for problem-solving throughout applied mathematics, engineering and scientific computing* Basic theory has bee
Open Rotor Computational Aeroacoustic Analysis with an Immersed Boundary Method
Brehm, Christoph; Barad, Michael F.; Kiris, Cetin C.
2016-01-01
Reliable noise prediction capabilities are essential to enable novel fuel efficient open rotor designs that can meet the community and cabin noise standards. Toward this end, immersed boundary methods have reached a level of maturity where more and more complex flow problems can be tackled with this approach. This paper demonstrates that our higher-order immersed boundary method provides the ability for aeroacoustic analysis of wake-dominated flow fields generated by a contra-rotating open rotor. This is the first of a kind aeroacoustic simulation of an open rotor propulsion system employing an immersed boundary method. In addition to discussing the methodologies of how to apply the immersed boundary method to this moving boundary problem, we will provide a detailed validation of the aeroacoustic analysis approach employing the Launch Ascent and Vehicle Aerodynamics (LAVA) solver. Two free-stream Mach numbers with M=0.2 and M=0.78 are considered in this analysis that are based on the nominally take-off and cruise flow conditions. The simulation data is compared to available experimental data and other computational results employing more conventional CFD methods. Spectral analysis is used to determine the dominant wave propagation pattern in the acoustic near-field.
Tet-to-Hex Conversion for Finite Element Analysis
McDill, J. M. J.; Carmona Garcia, A.
2004-06-01
It is well known that hexahedra; i.e., brick elements, provide superior performance to tetrahedra in certain types of finite element analysis, notably dynamic cases and in processes such as welding in which elasto-plastic boundaries and phase changes are present. The development of robust and complete free meshing schemes for hexahedra has been problematic. Typically, the user employs time consuming mapped meshing to create the necessary hexahedral meshes. On the other hand, complex geometries can be quickly free meshed, or populated, with tetrahedra, a main stay of commercial CAD/CAM packages. This does not require the time consuming operations of mapped meshing with hexahedra. Clearly, there is a need for a simple tetrahedra-to-hexahedra (TTH) conversion algorithm, which exploits the advantages of tetrahedral meshing. The development and testing of a TTH algorithm is presented. It uses a simple splitting method in which each hexahedron is divided into four hexahedra. A number of mesh optimization routines are implemented to improve the overall quality of the resulting finite element mesh. It is shown that the TTH algorithm is capable of handling a variety of geometries incorporating features typical in finite element analysis. While poorly formed elements cannot be entirely eliminated, the resulting meshes are useful. A number of initiatives in the continued development of the TTH are also presented.
Finite Element Analysis of Deep Excavations
Bentler, David J.
1998-01-01
This dissertation describes enhancements made to the finite element program, SAGE, and research on the performance of deep excavations This dissertation describes enhancements made to the finite element program, SAGE, and research on the performance of deep excavations. SAGE was developed at Virginia Tech for analysis of soil-structure interaction problems (Morrison, 1995). The purpose of the work described in this text with SAGE was to increase the capabilities o...
Formulation of natural convection around repository for dual reciprocity boundary element solution
The disposal of high-level radioactive wastes in deep geological formations is of pronounced technological importance for nuclear safety. The understanding of related fluid flow, heat and mass transport in geological systems is of great interest. This article prepares necessary physical, mathematical and numerical fundamentals for computational modeling of related phenomena. The porous media is described by the simple Darcy law and momentum-energy coupling is due to Boussinesq approximation. The Dual Reciprocity of Boundary Element Method (DRBEM) is used for solving coupled mass, momentum and energy equations in two-dimensions for the steady buoyancy induced convection problem in an semi-infinite porous media. It is structured by weighting with the fundamental solution of the Laplace equation. The inverse multi quadrics are used in the DRBEM transformation. The solution is obtained in an iterative way.(author)
Research on the cyclostationary nearfield acoustic holography based on boundary element method
ZHANG Haibin; WAN Quan; JIANG Weikang
2009-01-01
Cyclostationary sound field is a special kind of nonstationary sound field, in which the pressure signal is modulated seriously and sidebands exist in its spectrum. The reconstructed sound field can't figure the cyclostationary features in conventional Nearfield Acoustic Holography (NAH) procedure. On the basis of planar cyclostationary NAH, the cyclostationary NAH based on boundary element method is proposed which can be utilized to analyze radiators with complicated surface. Replacing the Fourier's transform with the second-order cyclic statistics, the Cyclic Spectral Density (CSD) functions is used as the reconstructed physical quantity in the proposed NAH technique, instead of the spectrum or power spectral density of pressure signal. By virtue of the demodulation ability of CSD function, the reconstructed CSD can effectively express the information of modulating and carrier wave respectively. The simulation and experiment illustrate that the validity and accuracy of this cyclostationary NAH technique satisfy the request of engineering.
Noise simulation of aircraft engine fans by the boundary element method
Pyatunin, K. R.; Arkharova, N. V.; Remizov, A. E.
2016-07-01
Numerical simulation results of the civil aircraft engine fan stage noise in the far field are presented. Non-steady-state rotor-stator interaction is calculated the commercial software that solves the Navier-Stokes equations using differentturbulence models. Noise propagation to the far acoustic field is calculated by the boundary element method using acoustic Lighthill analogies without taking into account the mean current in the air inlet duct. The calculated sound pressure levels at points 50 m from the engine are presented, and the directional patterns of the acoustic radiation are shown. The use of the eddy resolving turbulence model to calculate rotor-stator interaction increases the accuracy in predicting fan stage noise.
A simulation method of combinding boundary element method with generalized Langevin dynamics
无
2000-01-01
A new simulation approach to incorporate hydration force into generalized Langevin dynamics (GLD) is developed in this note. The hydration force determined by the boundary element method (BEM) is taken into account as the mean force terms of solvent including Coulombic interactions with the induced surface charge and the surface pressure of solvent. The exponential model is taken for the friction kernel. A simulation study has been performed on the cyclic undecapeptide cyclosporin A (CPA). The results obtained from the new method (GLDBEM) have been analyzed and compared with that obtained from the molecular dynamics (MD) simulation and the conventional stochastic dynamics (SD) simulation. We have found that the results obtained from GLDBEM show the obvious improvement over the SD simulation technique in the study of molecular structure and dynamic properties.
Mitharwal, Rajendra
2015-01-01
This work presents a Boundary Element Method (BEM) formulation for contactless electromagnetic field assessments. The new scheme is based on a regularized BEM approach that requires the use of electric measurements only. The regularization is obtained by leveraging on an extension of Calderon techniques to rectangular systems leading to well-conditioned problems independent of the discretization density. This enables the use of highly discretized Huygens surfaces that can be consequently placed very near to the radiating source. In addition, the new regularized scheme is hybridized with both surfacic homogeneous and volumetric inhomogeneous forward BEM solvers accelerated with fast matrix-vector multiplication schemes. This allows for rapid and effective dosimetric assessments and permits the use of inhomogeneous and realistic head phantoms. Numerical results corroborate the theory and confirms the practical effectiveness of all newly proposed formulations.
Boundary element simulation of size effect in quasi-brittle aggregate materials
无
2000-01-01
A nonlinear multi-zone boundary element method is applied to simulate the size effect of a series of geome trically similar three-point-bend specimens. The material in which particles are randomly dispersed in a relatively hard matrix can bo applicable to various aggregate materials as well as unidirectionally reinforced fiber composites in the transverse plane. A single edge macrocrack and interfacial microcracks randomly distributed between particles and ma trix are prescribed as initial defects. The shape, size and location of the fracture process zone (FPZ) are realistically simulated and described. The nominal strength of the material is in agreement with the Bazant size effect law. In addi tion, the results show that microcracking is one of the most important micromechanisms for the size effect in aggregate materials.
Cutanda Henriquez, Vicente; Barrera Figueroa, Salvador; Juhl, Peter Møller
2008-01-01
The project Euromet-792 aims to investigate and improve methods for secondary free-field calibration of microphones. In this framework, the comparison method is being studied at DFM in relation to the more usual substitution method of microphone calibration. The design of the sound source is of...... particular importance to achieve a sound field that reaches both microphones with the same level and that is sufficiently uniform at the microphone positions, in order to reduce the effect of misalignment. An existing sound source has been modeled using the Boundary Element Method, and the simulations have...... been used to modify the source and make it suitable for this kind of calibration. It has been found that a central plug, already present in the device, can be re-shaped in such a way that makes the sound field on the microphone positions more uniform, even at rather high frequencies. Measurements have...
Kryuchkov, S.; Sanger, S.; Barden, R. [Vertex Petroleum Systems, Englewood, CO (United States)
2001-06-01
The mathematical basis of a newly developed reservoir modeling software based on the Boundary Element Method (BEM) was presented. The software includes a fully graphical interface which provides accurate and fast solutions for most engineering problems. The model capabilities include modeling of arbitrary shaped heterogenous oil and gas reservoirs with fractured, radial and horizontal wells. In addition, the software can be used to model water injection and edge water drive. The model is suitable for managing small and midsize oil and gas fields, and is particularly useful for performing case studies at each field in real time. A comparison was also conducted between the BEM model and other well known analytical solutions such as steady state and transient solutions for standard reservoirs. Results showed good agreement between the two modeling methods. for vertical, fractured and horizontal wells. 24 refs., 8 figs.
A boundary element model for lined circular ducts with uniform flow
Juhl, Peter Møller
1996-01-01
application the prediction of attenuation at very high frequencies (up to ka=30) is important. However, it was found that the computational costs of a three-dimensional model would by far exceed the performance of a normal workstation. Therefore, an axisymmetric model with significantly reduced calculation...... time and storage requirements has been developed, and the model has been extended with a new formulation to allow for non-axisymmetric excitation. These co-called spinning modes are very important for the application to aeroacoustics. Another innovation of this work is the development of an iterative......A boundary element method has been developed for predicting the acoustics in a circular duct in which a uniform flow propagates. Such a model may be used to predict the performance of different liner designs for inlets of turbo fan engines, which is important for the aeronautics industry. For this...
张超; 许希武; 严雪
2013-01-01
针对纺织复合材料细观有限元分析中单胞网格的快速生成与顺利施加周期性边界条件之间的矛盾,提出了非周期性网格划分条件下,一般性周期性边界条件的数学表达形式.基于ABAQUS有限元软件平台,通过在单胞模型的相对面、相对边及相对角点施加多点约束(MPC)方程,实现了一般性周期性边界条件的施加.结合三维四向编织复合材料单胞模型,对比分析了周期性网格划分和非周期性网格划分情况下,单胞模型受载下的变形状态、应力分布及弹性性能的预测结果,验证了一般性周期性边界条件的正确性和有效性.研究表明:一般性周期性边界条件可以实现复杂细观结构单胞模型的自由网格划分,降低网格划分的难度,提高网格生成的质量.%In order to resolve the conflict between the quick mesh generation of a unit-cell and the successful application of the periodic boundary conditions,a more general method is developed in the micromechanical finite element analysis of textile composites with an aperiodic mesh.The application of the general periodic boundary conditions is realized by enforcing multi-point constraints (MPC) on the corresponding nodes on paired faces,edges and corners of the unit-cell on the platform of ABAQUS software.The deformation,stress distribution and the predicted mechanical properties of 3D four-directional braided composites are compared between the unit-cell models with periodic and aperiodic mesh,thus verifying the validity and applicability of the proposed boundary conditions.The results show that the general periodic boundary conditions can achieve the free meshing of unit-cells with complicated microstructures,reduce the difficulty of meshing and improve the quality of mesh generation.
A boundary element model for diffraction of water waves on varying water depth
Poulin, Sanne
1997-12-31
In this thesis a boundary element model for calculating diffraction of water waves on varying water depth is presented. The varying water depth is approximated with a perturbed constant depth in the mild-slope wave equation. By doing this, the domain integral which is a result of the varying depth is no longer a function of the unknown wave potential but only a function of position and the constant depth wave potential. The number of unknowns is the resulting system of equations is thus reduced significantly. The integration procedures in the model are tested very thoroughly and it is found that a combination of analytical integration in the singular region and standard numerical integration outside works very well. The gradient of the wave potential is evaluated successfully using a hypersingular integral equation. Deviations from the analytical solution are only found on the boundary or very close to, but these deviations have no significant influence on the accuracy of the solution. The domain integral is evaluated using the dual reciprocity method. The results are compared with a direct integration of the integral, and the accuracy is quite satisfactory. The problem with irregular frequencies is taken care of by the CBIEM (or CHIEF-method) together with a singular value decomposition technique. This method is simple to implement and works very well. The model is verified using Homma`s island as a test case. The test cases are limited to shallow water since the analytical solution is only valid in this region. Several depth ratios are examined, and it is found that the accuracy of the model increases with increasing wave period and decreasing depth ratio. Short waves, e.g. wind generated waves, can allow depth variations up to approximately 2 before the error exceeds 10%, while long waves can allow larger depth ratios. It is concluded that the perturbation idea is highly usable. A study of (partially) absorbing boundary conditions is also conducted. (EG)
Yokoi, T. [Building Research Institute, Tokyo (Japan); Sanchez-Sesma, F. [Universidad National Autonoma de Mexico, (Mexico). Institute de Ingenieria
1997-05-27
Formulation is introduced for discretizing a boundary integral equation into an indirect boundary element method for the solution of 3-dimensional topographic problems. Yokoi and Takenaka propose an analytical solution-capable reference solution (solution for the half space elastic body with flat free surface) to problems of topographic response to seismic motion in a 2-dimensional in-plane field. That is to say, they propose a boundary integral equation capable of effectively suppressing the non-physical waves that emerge in the result of computation in the wake of the truncation of the discretized ground surface making use of the wave field in a semi-infinite elastic body with flat free surface. They apply the proposed boundary integral equation discretized into the indirect boundary element method to solve some examples, and succeed in proving its validity. In this report, the equation is expanded to deal with 3-dimensional topographic problems. A problem of a P-wave vertically landing on a flat and free surface is solved by the conventional boundary integral equation and the proposed boundary integral equation, and the solutions are compared with each other. It is found that the new method, different from the conventional one, can delete non-physical waves from the analytical result. 4 figs.
Grosveld, Ferdinand W.; Schiller, Noah H.; Cabell, Randolph H.
2011-01-01
Comet Enflow is a commercially available, high frequency vibroacoustic analysis software founded on Energy Finite Element Analysis (EFEA) and Energy Boundary Element Analysis (EBEA). Energy Finite Element Analysis (EFEA) was validated on a floor-equipped composite cylinder by comparing EFEA vibroacoustic response predictions with Statistical Energy Analysis (SEA) and experimental results. Statistical Energy Analysis (SEA) predictions were made using the commercial software program VA One 2009 from ESI Group. The frequency region of interest for this study covers the one-third octave bands with center frequencies from 100 Hz to 4000 Hz.
A simple boundary element formulation for shape optimization of 2D continuous structures
For the design of nuclear equipment like pressure vessels, steam generators, and pipelines, among others, it is very important to optimize the shape of the structural systems to withstand prescribed loads such as internal pressures and prescribed or limiting referential values such as stress or strain. In the literature, shape optimization of frame structural systems is commonly found but the same is not true for continuous structural systems. In this work, the Boundary Element Method (BEM) is applied to simple problems of shape optimization of 2D continuous structural systems. The proposed formulation is based on the BEM and on deterministic optimization methods of zero and first order such as Powell's, Conjugate Gradient, and BFGS methods. Optimal characterization for the geometric configuration of 2D structure is obtained with the minimization of an objective function. Such function is written in terms of referential values (such as loads, stresses, strains or deformations) prescribed at few points inside or at the boundary of the structure. The use of the BEM for shape optimization of continuous structures is attractive compared to other methods that discretized the whole continuous. Several numerical examples of the application of the proposed formulation to simple engineering problems are presented. (authors)
The boundary element method for the solution of the multidimensional inverse heat conduction problem
This work focuses on the solution of the inverse heat conduction problem (IHCP), which consists in the determination of boundary conditions from a given set of internal temperature measurements. This problem is difficult to solve due to its ill-posedness and high sensitivity to measurement error. As a consequence, numerical regularization procedures are required to solve this problem. However, most of these methods depend on the dimension and the nature, stationary or transient, of the problem. Furthermore, these methods introduce parameters, called hyper-parameters, which have to be chosen optimally, but can not be determined a priori. So, a new general method is proposed for solving the IHCP. This method is based on a Boundary Element Method formulation, and the use of the Singular Values Decomposition as a regularization procedure. Thanks to this method, it's possible to identify and eliminate the directions of the solution where the measurement error plays the major role. This algorithm is first validated on two-dimensional stationary and one-dimensional transient problems. Some criteria are presented in order to choose the hyper-parameters. Then, the methodology is applied to two-dimensional and three-dimensional, theoretical or experimental, problems. The results are compared with those obtained by a standard method and show the accuracy of the method, its generality, and the validity of the proposed criteria. (author)
A Boundary Element Investigation of Liquid Sloshing in Coupled Horizontal and Vertical Excitation
De-Zhi Ning
2012-01-01
Full Text Available Sloshing flows in a two-dimensional rigid rectangular tank under specified excitations in the coupled horizontal and vertical modes are simulated by using a higher-order boundary element method (BEM. The liquid sloshing is formulated as an initial-boundary-value problem based on the fully nonlinear potential flow theory. And a semi-mixed Eulerian-Lagrangian technique combined with the 4th-order Runge-Kutta scheme is employed to advance the solutions in the time marching process. A smoothing technique is applied to the free surface at every several time steps to avoid the possible numerical instabilities. Numerical results obtained are compared with the available solutions to validate the developed model. The parametric studies are carried out to show the liquid sloshing effects in terms of the slosh frequencies and excitation amplitudes in horizontal and vertical modes, the second-order resonance frequency, a bottom-mounted vertical rigid baffle, free surface displacement, and hydrodynamic forces acting on the tank.
A finite element model updating technique for adjustment of parameters near boundaries
Gwinn, Allen Fort, Jr.
Even though there have been many advances in research related to methods of updating finite element models based on measured normal mode vibration characteristics, there is yet to be a widely accepted method that works reliably with a wide range of problems. This dissertation focuses on the specific class of problems having to do with changes in stiffness near the clamped boundary of plate structures. This class of problems is especially important as it relates to the performance of turbine engine blades, where a change in stiffness at the base of the blade can be indicative of structural damage. The method that is presented herein is a new technique for resolving the differences between the physical structure and the finite element model. It is a semi-iterative technique that incorporates a "physical expansion" of the measured eigenvectors along with appropriate scaling of these expanded eigenvectors into an iterative loop that uses the Engel's model modification method to then calculate adjusted stiffness parameters for the finite element model. Three example problems are presented that use eigenvalues and mass normalized eigenvectors that have been calculated from experimentally obtained accelerometer readings. The test articles that were used were all thin plates with one edge fully clamped. They each had a cantilevered length of 8.5 inches and a width of 4 inches. The three plates differed from one another in thickness from 0.100 inches to 0.188 inches. These dimensions were selected in order to approximate a gas turbine engine blade. The semi-iterative modification technique is shown to do an excellent job of calculating the necessary adjustments to the finite element model so that the analytically determined eigenvalues and eigenvectors for the adjusted model match the corresponding values from the experimental data with good agreement. Furthermore, the semi-iterative method is quite robust. For the examples presented here, the method consistently converged
The boundary element method for light scattering by ice crystals and its implementation in BEM++
Groth, S. P.; Baran, A. J.; Betcke, T.; Havemann, S.; Śmigaj, W.
2015-12-01
A number of methods exist for solving the problem of electromagnetic scattering by atmospheric ice crystals. Amongst these methods, only a few are used to generate "benchmark" results in the atmospheric science community. Most notably, the T-matrix method, Discrete Dipole Approximation, and the Finite-Difference Time-Domain method. The Boundary Element Method (BEM), however, has received considerably less attention in this community despite its extensive use and development in other areas of applied mathematics and engineering. Recently the group of Betcke et al. (2015 [1]) at University College London has released a high performance open source boundary element library called BEM++. In this paper, we employ BEM++ to calculate the scattering properties of hexagonal ice columns of fixed orientation, as well as more complicated particles such as hollow columns and bullet-rosettes. The results for hexagonal columns are compared to those obtained using a highly accurate and well-established T-matrix method (Baran et al., 2001 [2]) for a range of different wavelengths and size parameters. It is shown that the results are in excellent agreement and that BEM++ is a fast alternative to the T-matrix method and others for generating benchmark results. However, the large memory requirements of BEM++ cause it to be limited to size parameters ~15 on a standard desktop PC if an accuracy of roughly 1% is required. The main advantages of BEM++ over many other methods are its flexibility to be applied to homogeneous dielectric particles of arbitrarily complex shape, and its open availability. This flexibility is illustrated by the application of BEM++ to scattering by hollow columns with different cavity types, as well as bullet-rosettes with 2-6 branches.
The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region
Meshfree analysis with the aid of NURBS boundary
Chi, Sheng-Wei; Lin, Shih-Po
2016-05-01
We present a meshfree analysis framework to integrate the geometric exactness of non-uniform rational B-splines (NURBS)-based isogeometric analysis (IGA) (Hughes et al., Comput Methods Appl Mech Eng 194:4135-4195, 2005) with the flexibility of meshfree approximations. In the framework, only the NURBS boundary surface immediately available from CAD tools is used to describe the exact problem domain, and meshfree particles are inserted inside the boundary surface, in a flexible manner, for construction of the approximation for analysis. Nitche's method is employed for imposing essential boundary conditions and the domain integration in the Galerkin formulation is performed based on variationally consistent integration (VCI) to recover integration exactness. The NURBS boundary surface from CAD serves as an aid in selecting particle distributions and as the integration net for the boundary integration required both for the Nitche's method and the VCI. As shown in numerical studies, the VCI is essential for the solution accuracy of the method. Several benchmarks are tested to examine the effectiveness of the proposed framework and numerical results are compared with those obtained by the IGA.
This paper presents an efficient boundary element alternating method for analyzing the interactions among multiple elliptical holes in a two dimensional infinite domain under remote uniform stresses. Instead of the analytical solution used in the conventional alternating method, the stress distribution in an infinite domain with a single elliptical hole subjected to the arbitrary tractions across the boundary is solved by the boundary element method. Then this solution correlates with a successive iterative superposition process capable of satisfying the prescribed boundary for each elliptical holes of the problem. Both the effects of various sizes of holes and ligaments among ellipses on the stress concentration are studied in detail. In addition, the computed results and the available referenced solutions closely corresponds to each other indicate the method's accuracy and efficiency. (orig.)
Roncal, Julissa; Guyot, Romain; Hamon, Perla; Crouzillat, Dominique; Rigoreau, Michel; Konan, Olivier N'Guessan; Rakotomalala, Jean-Jacques; Nowak, Michael D; Davis, Aaron P; de Kochko, Alexandre
2016-02-01
The completion of the genome assembly for the economically important coffee plant Coffea canephora (Rubiaceae) has allowed the use of bioinformatic tools to identify and characterize a diverse array of transposable elements (TEs), which can be used in evolutionary studies of the genus. An overview of the copy number and location within the C. canephora genome of four TEs is presented. These are tested for their use as molecular markers to unravel the evolutionary history of the Millotii Complex, a group of six wild coffee (Coffea) species native to Madagascar. Two TEs from the Gypsy superfamily successfully recovered some species boundaries and geographic structure among samples, whereas a TE from the Copia superfamily did not. Notably, species occurring in evergreen moist forests of eastern and southeastern Madagascar were divergent with respect to species in other habitats and regions. Our results suggest that the peak of transpositional activity of the Gypsy and Copia TEs occurred, respectively, before and after the speciation events of the tested Madagascan species. We conclude that the utilization of active TEs has considerable potential to unravel the evolutionary history and delimitation of closely related Coffea species. However, the selection of TE needs to be experimentally tested, since each element has its own evolutionary history. Different TEs with similar copy number in a given species can render different dendrograms; thus copy number is not a good selection criterion to attain phylogenetic resolution. PMID:26231981
De Corato, M.; Slot, J. J. M.; Hütter, M.; D'Avino, G.; Maffettone, P. L.; Hulsen, M. A.
2016-07-01
In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation-dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered within the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.
Igumnov Leonid; Ipatov Aleksandr; Belov Aleksandr; Petrov Andrey
2015-01-01
The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach bound...
A FINITE ELEMENT MODEL OF IN VIVO MOUSE TIBIAL COMPRESSION LOADING: INFLUENCE OF BOUNDARY CONDITIONS
Hajar Razi
2014-12-01
Full Text Available Though bone is known to adapt to its mechanical challenges, the relationship between the local mechanical stimuli and the adaptive tissue response seems so far unclear. A major challenge appears to be a proper characterization of the local mechanical stimuli of the bones (e.g. strains. The finite element modeling is a powerful tool to characterize these mechanical stimuli not only on the bone surface but across the tissue. However, generating a predictive finite element model of biological tissue strains (e.g., physiological-like loading encounters aspects that are inevitably unclear or vague and thus might significantly influence the predicted findings. We aimed at investigating the influence of variations in bone alignment, joint contact surfaces and displacement constraints on the predicted strains in an in vivo mouse tibial compression experiment. We found that the general strain state within the mouse tibia under compressive loading was not affected by these uncertain factors. However, strain magnitudes at various tibial regions were highly influenced by specific modeling assumptions. The displacement constraints to control the joint contact sites appeared to be the most influential factor on the predicted strains in the mouse tibia. Strains could vary up to 150% by modifying the displacement constraints. To a lesser degree, bone misalignment (from 0 to 20° also resulted in a change of strain (+300 µε = 40%. The definition of joint contact surfaces could lead to up to 6% variation. Our findings demonstrate the relevance of the specific boundary conditions in the in vivo mouse tibia loading experiment for the prediction of local mechanical strain values using finite element modeling.