Boundary Element Method

The main objective of this paper is to propose a new efficient time domain boundary element technique for design sensitivity analysis and topology optimization of anisotropic thermo-poroelastic structures. The spatial regularization scheme based on integration by parts is performed in Laplace domain in conjunction with time-domain convolution variational boundary element method (CVBEM). The generating optimization problem is solved using the Moving Asymptotes Method (MAM) with the adjoint variable method to obtain optimal material distribution, influence of anisotropy on the thermo-poroelastic stresses sensitivities. The results from the numerical model demonstrate the validity, efficiency and accuracy of the proposed technique.

The weighted-residual technique, the indirect boundary element method, the truncated indirect boundary element method and the direct boundary element method can be used to analyse nonlinear soil-structure interaction in the time domain. They are illustrated and compared by using the one-dimensional dynamic problem of the spherical cavity in an infinite space. For realistic time steps, all formulations lead to accurate results, but the weighted-residual technique and the truncated indirect boundary element method are much more efficient than the direct boundary element method in the time domain. Hysteretic damping leads to noncausal behaviour, which can, however, be neglected from a practical point of view.

The extended Kalman filtering (EKF) method is used as an automatic calibration procedure for the estimation of hydrogeological parameters based on groundwater head observation. The numerical tool employed is the dual reciprocity boundary element method (DRBEM). Numerical results for steady and unsteady flow in heterogeneous aquifers have demonstrated the potential of this combined procedure for groundwater applications.

The displacement and stress models of the hybrid-Trefftz finite element formulation are pplied to the elastostatic and elastodynamic analysis of two-dimensional saturated and unsaturated porous media problems. The formulation develops from the classical separation of variables in time and space, but it leads to two time integration strategies. The first is applied to periodic problems, which are discretized in time using Fourier analysis. A mixed finite element approach is used in the second strategy for discretization in time of non-periodic/transient problems. These strategies lead to a series of uncoupled problems in the space dimension, which is subsequently discretized using either the displacement or the stress model of the hybrid-Trefftz finite element formulation. The main distinction between the two models is in the way that the interelement continuity is enforced. The displacement model enforces the interelement compatibility, while the stress model enforces the intereleme...

Tese submetida ao corpo docent pós-graduação em engenharia civil da Universidade Federal de Pernambuco como parte integrante dos requisitos necessários à obtenção do título de doutor em Engenharia Civil. Agradeço a toda minha família pelo apoio e compreensão ao longo desses anos e em especial a minha mãe, que me incentivou a continuar na jornada acadêmica após o fim do meu mestrado. Agradeço a todos que contribuíram de alguma forma com o desenvolvimento desta tese, em especial aos meus orientadores Leonardo Guimarães e Osvaldo Manzoli pelos ensinamentos e atenção ao longo desses últimos anos. Agradeço também a todos os amigos que estiveram comigo nesses anos de doutorado ou em parte deles: Débora, Julliana, Rafael, Inaldo, Nayra, Manuel, Leonardo Cabral, Rose e, em especial, Leila, que dividiu comigo a casa e seus conhecimentos sobre o programa CODE_BRIGHT, e Jonathan, que me ajudou muito compartilhando comigo seus conhecimentos de programação.

We have developed a modeling method suitable to analyze single-and multiple-electron resonances detected by electric-field-sensitive scanning probe techniques. The method is based on basic electrostatics and a numerical boundary-element approach. The results compare well to approximate analytical expressions and experimental data.

Localization phenomena, as e.g. shear bands, is a narrow zone of local concentrations of plastic strains. Classical continuum theory does not include material length scale parameters and is inadequate when localization phenomena occur. Therefore, numerical results based on classical continuum theory strongly depend on the mesh size of the finite element discretization. The present study explored the application of an extended finite element model in the nonlocal continuum mechanics of fluid-saturated material for numerical simulation of shear band localization. In the present paper, a new relation was proposed to calculate the stress rate based on the integral-type nonlocal model. It was shown that the inclusion of fluid viscosity and nonlocal plasticity for saturated cases leads to a regularization of the shear band problem. The goal of the present paper was to propose a new numerical method for reduction of computational effort and mesh dependency. For nonlocal plasticity, element...

Recently the Method of Difference Potentials has been extended to Linear Elastic Fracture Mechanics. The solution was calculated on a grid boundary belonging to the domain of an auxiliary problem, which must be solved multiple times. Singular enrichment functions, such as those used within the Extended Finite Element Method, were introduced in order to improve the approximation near the crack tip leading to near-optimal convergence rates. Now the method is further developed by significantly reducing the computation time. This is achieved via the implementation of a system of basis functions introduced along the physical boundary of the problem. The basis functions form an approximation of the trace of the solution at the physical boundary. This method has proven efficient for the solution of problems on regular (Lipschitz) domains. By introducing the singularity into the finite element space, the approximation of the crack can be realised by regular functions. Near optimal convergence rates are then achieved for the enriched formulation. A solution algorithm using the Fast Fourier Transform is provided with the aim of further increasing the efficiency of the method.

The Difference Potential Method (DPM) proved to be a very efficient tool for solving boundary value problems (BVPs) in the case of complex geometries. It allows BVPs to be reduced to a boundary equation without the knowledge of Green's functions. The method has been successfully used for solving very different problems related to the solution of partial differential equations. However, it has mostly been considered in regular (Lipschitz) domains. In the current paper, for the first time, the method has been applied to a problem of linear elastic fracture mechanics. This problem requires solving BVPs in domains containing cracks. For the first time, DPM technology has been combined with the finite element method. Singular enrichment functions, such as those used within the extended finite element formulations, are introduced into the system in order to improve the approximation of the crack tip singularity. Near-optimal convergence rates are achieved with the application of these enrichment functions. For the DPM, the reduction of the BVP to a boundary equation is based on generalised surface projections. The projection is fully determined by the clear trace. In the current paper, for the first time, the minimal clear trace for such problems has been numerically realised for a domain with a cut.

SummaryRecently, the method of difference potentials has been extended to linear elastic fracture mechanics. The solution was calculated on a grid boundary belonging to the domain of an auxiliary problem, which must be solved multiple times. Singular enrichment functions, such as those used within the extended finite element method, were introduced to improve the approximation near the crack tip leading to near‐optimal convergence rates. Now, the method is further developed by significantly reducing the computation time. This is achieved via the implementation of a system of basis functions introduced along the physical boundary of the problem. The basis functions form an approximation of the trace of the solution at the physical boundary. This method has been proven efficient for the solution of problems on regular (Lipschitz) domains. By introducing the singularity into the finite element space, the approximation of the crack can be realised by regular functions. Near‐optimal conv...

Processes of liquid sloshing in rigid shells of revolution filled with an ideal incompressible liquid are studied. The shells are subjected to longitudinal excitations. The liquid motion in these containers is supposed to be irrotational. The problems of liquid sloshing are considered in weakly nonlinear formulations when the free surface elevation is small compared with the shell radius. The spectral boundary problem on natural sloshing modes and frequencies is solved using the in-house computational tool based on boundary element methods. The linear and constant interpolations of unknown functions inside boundary elements are involved. The modes obtained are considered as basic functions for analysis of forced liquid vibrations. The numerical procedure based on boundary element method and the multimodal approach is developed for numerical analysis of nonlinear sloshing effects in rigid shells of revolution under longitudinal excitations. The free-surface elevation and velocity potential are expanded into infinite series with obtained basic functions and unknown time-dependent coefficients. The problems of liquid vibrations are reduced to solving nonlinear systems of second order ordinary differential equations about these coefficients that in linear formulation turns to the system of uncoupled Mathieu equations. The parametric oscillations are considered both in linear and nonlinear statements.

In recent years, Trefftz methods have received increasing attention, as being alternatives of the already well-established element-based simulation methods (e.g., finite element and boundary element methods). The wave-based technique is based on the indirect Trefftz approach for the solution of steady-state, time-harmonic acoustic problems. The dynamic field variables are expanded in terms of wave functions, which satisfy the governing partial differential equation, but do not necessarily satisfy the imposed boundary conditions. Therefore, the approximation error of the method is exclusively caused by the error on the boundary, since there is no additional error present in the domain. The authors investigate the potentials of a novel boundary error indicator-controlled adaptive local refinement strategy. Practical, industrial-oriented application of the method is presented on the 3D free-field sound radiation model of a simplified combustion engine. Results and efficiency of the app...

The 1994 workshop Green's Functions and Boundary Element Analysis for Modeling of Mechanical Behavior of Advanced Materials was organized by Dr. Vinod Tewary and Prof. John Berger to demonstrate the potential of Green's functions and boundary element methods in solving a broad range of practical materials science problems. The workshop assembled an outstanding and diverse group of researchers from the National Institute of Standards and Technology and other government laboratories, universities, and industry to assess the current state of the art and to identify research opportunities. The technical presentations by the researchers were an excellent review of recent progress in the field. The contributions of the participants from industry helped all of the workshop participants to understand the technical areas in which GF/BEM research can contribute significantly to improved materials and materials processing methods for commercial use. They also defined specific problems, which will be the basis for follow-on research projects. From the beginning, Dr. Tewary and Prof. Berger designed the workshop to nucleate these ongoing research projects involving teams of workshop participants and their colleagues. Several focused research projects, most of them built around a specific industrial technology need, were started shortly after the workshop. The Green's Functions/Boundary Element Methods Consortium that encompasses these projects recently created its own web site. For further information on the projects and the members of the research teams, see their web site at -jberger/greens/. The research projects continue under the Center for Theoretical and Computational Materials Science (CTCMS), which was established in 1994 to develop and apply state-of-the-art theoretical and computational materials science techniques and to help industry integrate them into technology development. The center's technical projects emphasize the solution of problems in materials design, processing, and application and the transfer of the results to industry through research collaborations. Each of the center's active research projects typically involves a team of re- searchers from several institutions focused on an industrially important technical problem defined by the industrial participants. Projects may also be affiliated with established research groups. The CTCMS has an active web site that is used for col- laboration among center researchers and to provide general and scientific information to the technical community. For more information on the CTCMS, see the web site at . ctcms . nist . gov The project on Green's functions and boundary element analysis began, as most projects begin, with a workshop to define a focused research area in which the center can make a meaningful contribution. Collaboration continues, with project team members working at their own institutions; in future workshops and meetings, the research team members will review progress on achieving the goals of this workshop.

A biomimetic semi-activated oscillating-foil device with multiple foils in a parallel configuration is studied for the extraction of marine renewable energy. For the present investigation, an unsteady boundary element method (BEM) is used for the simulation of 3D lifting flows. For this work, the device is assumed to be submerged far from the free surface and the sea bottom. However, the geometry of the body and the initial shape of the wake are general. For the numerical simulations, a high performance in-house GPU-accelerated code (GPU-BEM) is developed. For the calculation of singular integrals, an adaptive algorithm based on the Gauss-Lobatto quadrature is used. Concerning the numerical scheme of GPU-BEM, the convergence of the method was tested, the numerical characteristics were determined and the method was validated. A parametric study of a single-foil device is presented to determine the performance characteristics of such devices. Next, twin-foil devices are investigated in parallel and staggered configurations with a phase difference between the two foils. Finally, the multiple-foil parallel configuration is compared against turbines. After enhancement and further verification, the present method is proposed for the design and control of such biomimetic devices for the extraction of energy from waves and tidal currents nearshore.

A biomimetic semi-activated oscillating-foil device with multiple foils in a parallel configuration is studied for the extraction of marine renewable energy. For the present investigation, an unsteady boundary element method (BEM) is used for the simulation of 3D lifting flows. For this work, the device is assumed to be submerged far from the free surface and the sea bottom. However, the geometry of the body and the initial shape of the wake are general. For the numerical simulations, a high performance in-house GPU-accelerated code (GPU-BEM) is developed. For the calculation of singular integrals, an adaptive algorithm based on the Gauss–Lobatto quadrature is used. Concerning the numerical scheme of GPU-BEM, the convergence of the method was tested, the numerical characteristics were determined and the method was validated. A parametric study of a single-foil device is presented to determine the performance characteristics of such devices. Next, twin-foil devices are investigated i...

This paper presents an extension over a novel, three dimensional high frequency method for the calculation of the scattered electromagnetic (EM) field from a Perfect Electric Conductor (PEC) plate, which is based on the Physical Optics (PO) approximation and the Stationary Phase Method (SPM). This extension defines a new analytical method which is proved to be very efficient in computer execution time and enhances the accuracy of its predecessor around the area of the main scattering lobe. This new analytical method accomplishes high accuracy through the use of higher order approximation terms, which imply the use of Fresnel functions (SPM-F method). By using higher order Fresnel approximation terms, no impact on the time efficiency of the SPM method appears to

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This work presents a time-truncation scheme, based on the Lagrange interpolation polynomial, for the solution of the two-dimensional scalar wave problem by the time-domain boundary element method. The aim is to reduce the number of stored matrices, due to the convolution integral performed from the initial time to the current time, and to keep a compromise between computational economy and efficiency and the numerical accuracy. In order to verify the accuracy of the proposed formulation, three examples are presented and discussed at the end of the article.

An iterative coupling of finite element and boundary element methods for the investigation of coupled fluid-solid systems is presented. While finite elements are used to model the solid, the adjacent fluid is represented by boundary elements. In order to perform the coupling of the two numerical methods, a successive renewal of the variables on the interface between the two subdomains is performed through an iterative procedure until the final convergence is achieved.

Boundary element formulations for the static analysis of Euler-Bernoulli and Timoshenko beams are presented in this work. As the problems are stated in one dimension, the boundary is constituted only by the extreme nodes of the beam. The four usual types of beams, i.e. pinned-pinned, fixed-fixed, fixed-pinned and fixed-free are solved for a loading uniformly distributed along the length of the beam. The potentialities of the proposed formulations are assessed by comparing the numerical results with the analytical ones.

This work presents a Boundary Element Method formulation for the analysis of scalar wave propagation problems. The formulation presented here employs the so-called Operational Quadrature Method, by means of which the convolution integral, presented in time-domain BEM formulations, is substituted by a quadrature formula, whose weights are computed by using the Laplace transform of the fundamental solution and a linear multistep method. Two examples are presented at the end of the article with the aim of validating the formulation.

We calculate the pressure in a box with different complex impedances on its walls. The frequency response of a point source is calculated using both Boundary Element Method and analytical calculations combined with Newton iteration to calculate the modes.

The methods of inverse problems solution appearing in the domain of steady heat transfer are discussed. In particular, the inverse boundary problems (the identification of the boundary values on the part of the surface limiting the system analyzed) and the inverse parametric problems (reconstruction of the thermophysical parameters of the material) are considered. Such problems have been solved using (on the stage of numerical computations) the boundary element method. The different methods of inverse problems solution have been applied. So, the direct method, the least squares method in the basic version, the same method supplemented by the regularization terms, the method of the energy minimization and also the algorithm basing on the sensitivity coefficients have been taken into account. The computations can been realized for different numbers and positions of the control points, the possible disturbances of 'measured' temperatures have been also taken into account. The remarks concerning the exactness and effectiveness of successive methods of the inverse problem solution have been formulated. The theoretical considerations are supplemented by the examples of computations verifying the correctness of the algorithms proposed.

Acoustic radiation efficiency is a parameter which characterizes the sound radiation effectiveness of a vibrating surface. It can be useful in describing the coupling between a vibrating element and the origin of its structure-borne noise. This paper discusses the possibilities of using acoustic radiation efficiency parameter as an indicator applied to assess the noise emitted by power machinery. Acoustic methods, including intensity scanning, Laser Doppler Vibrometry (LDV) and numerical analyses, were used to determine the vibration velocity and, subsequently, calculate and evaluate the radiation efficiency values. Results of measurements and FEM simulations are presented along with comparison of the methods.

PurposeThe purpose of this paper is to present the extension of plane wave based method.Design/methodology/approachThe mixed functional are discretized using enriched finite elements. The fluid is discretized by enriched acoustic element, the structure by enriched structural finite element and the interface fluid‐structure by fluid‐structure interaction element.FindingsResults obtained show the potentialities of the proposed method to solve a much larger class of wave problems in mid‐ and high‐frequency ranges.Originality/valueThe plane wave based method has previously been applied successfully to finite element and boundary element models for the Helmholtz equation and elastodynamic problems. This paper describes the extension of this method to the vibro‐acoustic problem.

Flows in nature are very complex and express different behaviour under different conditions. Therefore we are interested in using proper numerical models to describe the physical behaviour of such fluid flows. The micropolar fluid flow theory enables accurate computation of flows in a scale, where questions arise on the accuracy of the Navier-Stokes equation. In the present paper, the micropolar fluid flow theory is incorporated into the framework of velocity-vorticity formulation of Navier-Stokes equations. Governing equations are derived in differential as well as integral form, resulting from the application of boundary element method (BEM).

The contribution deals with numerical simulation of natural convection in micropolar fluids, describing flow of suspensions with rigid and underformable particles with own rotation. The micropolar fluid flow theory is incorporated into the framework of a velocity-vorticity formulation of Navier-Stokes equations. The governing equations are derived in differential and integral form, resulting from the application of a boundary element method (BEM). In integral transformations, the diffusion-convection fundamental solution for flow kinetics, including vorticity transport, heat transport and microrotation transport, is implemented. The natural convection test case is the benchmark case of natural convection in a square cavity, and computations are performed for Rayleigh number values up to 10 7 . The results show, which microrotation of particles in suspension in general decreases overall heat transfer from the heated wall and should not therefore be neglected when computing heat and fluid flow of micropolar fluids.

An approach combining the method of fundamental solutions (MFS) in conjunction with the normal modes technique (NMT) is proposed to simulate the acoustic wave propagation over the shallow water region. It is assumed that the sound-speed of considered model is the isovelocity profile, the free surface is quiescent and the seabed is rugged. The seabed, ranging from smooth to abrupt variation, is discretized into simple rectangular geometry and tunnel-shape deformation at the seabed in terms of the irregular topography. Mathematical formulations of the eigenfunction expansion, in point of NMT, are implemented clearly to describe the radiation conditions on the open boundaries. Effects of node resolution, numbers of modes on open boundaries and small aspect ratios over the computational domain are discussed. Accuracy of the results by the proposed method is assessed and verified by comparison with analytic solution and the boundary element method (BEM). Through the study, the dominant of transmission of energy under sources excitation beyond the underwater acoustic model is analyzed. It appears that the MFS is very effective for acoustic wave propagation problem.

An approach combining the method of fundamental solutions (MFS) in conjunction with the normal modes technique (NMT) is proposed to simulate the acoustic wave propagation over the shallow water region. It is assumed that the sound-speed is the isovelocity profile, the free surface is quiescent and the topography of seabed is rugged. The considered model, ranging from smooth to abrupt variation, is descritized into simple rectangular geometry and cosine bell deformation at the bottom in terms of the irregular topography. Mathematical formulations of the eigenfunction expansion, in point of NMT, are implemented clearly to describe the radiation conditions on the open boundaries. Effects of node resolution and small aspect ratios over the computational domain are discussed. Accuracy of the results by the proposed approach is assessed and verified by comparison with analytic solution and the boundary element method (BEM).

The unhomogeneous problem which has been found in mining is the case that the mediums of orebody of hanging walls and of foot walls are not the same. In this paper, the singular solution for a bonded tri-layer plane has been composed, deduced and resolved by Fourier transformation. First, the solution is transformed from original space to image space, and after its parameters have been obtained, it is transformed back to original space. Many kinds of unhomogeneous problems in mining engineering and rock mechanics can be solved using the boundary element method (BEM) which is composed of our singular solution. In this paper, the deducing process of the singular solution has been given. Then the results from the BEM for bonded tri-layer planes are compared with the existing analytic solution and the result from super VI program of FEM. Finally, the example of application for bonded tri-layer planes is presented. The advantages of the BEM for bonded tri-layer planes in numerical modelling for mining engineering and rock mechanics are obvious.

The method of fundamental solutions ͑MFS͒ is applied to acoustic scattering and radiation for axisymmetric bodies and boundary conditions. The fundamental solution of the governing equation and its normal derivative, which are required in the formulation of the MFS, can be expressed in terms of complete elliptic integrals, which are evaluated using library software. The method is tested on several problems from the literature and the results compared with existing solutions. Numerical experiments demonstrate that the fictitious eigenfrequency problem which is encountered with the boundary element method is not present in the MFS.

The generation of ground-borne noise inside receiver buildings due to nearby construction works can cause significant community impact and impose difficult constraints on construction activities. Several methods exist to predict ground vibration from permanent operational sources; however the suitability of some of these methods to predict ground-borne noise from construction activities are not well known and have not yet been thoroughly tested. This paper presents an overview of some of the various methods available to estimate ground-borne noise levels from construction activities and discusses the advantages and limitations of each.

Outdoor noise propagation with complex geometries A hybrid method that combines a noise engineering method and the 2.5D boundary element method approximates outdoor sound propagation in large domains with complex objects more accurately than noise engineering methods alone and more efficiently than reference methods alone. Noise engineering methods (e.g. ISO 9613-2 or CNOSSOS-EU) efficiently approximate sound levels from roads, railways, and industrial sources in cities for simple, box-shaped geometries by first finding the propagation paths between the source and receiver, then applying attenuations (e.g. geometrical divergence and atmospheric absorption) to each path, and finally incoherently summing all of the path contributions. Standard engineering methods cannot model more complicated geometries, but introducing an additional attenuation term quantifies the influence of complex objects. Calculating this extra attenuation term requires reference calculations, but performing reference computations for each path is too computationally expensive. Thus, the extra attenuation term is linearly interpolated from a data table containing the corrections for many source/receiver positions and frequencies. The 2.5D boundary element method produces the levels for the real and simplified geometries, and subtracting them yields a table of corrections. For a T-shaped barrier with two buildings, this approach reduces the mean error by approximately 2 dBA compared to a standard engineering method. a Portions of this work were presented in "The initial development of a hybrid method for modeling outdoor sound propagation in urban areas," 170th Meeting of the

The alpha magnetic spectrometer (AMS) is a sophisticated instrument developed for the determination of anti-matter nuclei in the outer space. Following specific requirements the silicon sensors are included in an array of several thin carbon fiber composite tubes of different length in various horizontal layers, which will be supported by an outcr vertical cylindrical structure also made in composite. A structural analysis of single tubes and of the complete structure has been performed using a fine element code. The main results of this study are reported in terms of maximum lateral displacement of tubes, suggesting the necessity to use shock absorbers between them; and in terms of vibration behavior expressed as the equivalent Von Misses stresses. The analysis shows that the designed structure accomplish with NASA specifications. where triangular elements were considered. The weight of electronic was considered increasing the density of the outer structure, where it is glued.

A boundary element method is utilized to find numerical solutions to boundary value problems of exponentially graded media governed by a spatially varying coefficients anisotropic-diffusion convection equation. The variable coefficients equation is firstly transformed into a constant coefficients equation for which a boundary integral equation can be formulated. A boundary element method (BEM) is then derived from the boundary integral equation. Some problems are considered. The numerical solutions justify the validity of the analysis used to derive the boundary element method with accurate and consistent solutions. A FORTRAN script is developed for the computation of the solutions. The computation shows that the BEM procedure elapses very efficient time in producing the solutions. In addition, results obtained from the considered examples show the effect of the anisotropy of the media on the solutions. An example of a layered material is presented as an illustration of the applicat...

The present paper deals with very important practical problems of wide range of applications. The main target of the present paper is to track all moving boundaries that appear throughout the whole process when dealing with multi-moving boundary problems continuously with time up to the end of the process with high accuracy and minimum number of iterations. A new numerical iterative scheme based the boundary integral equation method is developed to track the moving boundaries as well as compute all unknowns in the problem. Three practical applications, one for vaporization and two for ablation were solved and their results were compared with finite element, heat balance integral and the source and sink results and a good agreement were obtained.

Abstract. Composite materials are mixtures of two or more different materials, in order to improve the mechanicals properties. Mixtures of different materials can provide the appropriate behavior for a given solicitation. This behavior can be verified by the means of homogenization techniques. In this sense, the main goal of this work relies on establishing a homogenization methodology for viscoelastic composites using boundary elements method (BEM). For the homogenization process, was considered the average strain in each stressstrain curve. The experimental data were obtained from the literature. The representative volume element (RVE) was defined based on the calculated mean strains. For each volume element (EV) a twenty creep tests were conducted varying the positions of the microstructural heterogeneities. Mean, standard deviation and coefficient of variation (CV) were estimated for each EV. Finally, a graph of the number of inclusions x coefficient of variation is presented fo...

The model by Grilli eta/., 5,s based on fully nonlinear potential flow equations, is used to study propagation of water waves over arbitrary bottom topography. The model combines a higher-order boundary element method for the solution of Laplace's equation at a given time, and Lagrangian Taylor expansions for the time updating of the free surface position and potential. In this paper, both the accuracy and the efficiency of computations are improved, for wave shoaling and breaking over gentle slopes, in domains with very sharp geometry and large aspect ratio, by using quasi-singular integration techniques based on modified Telles 17 and Lutz H methods. Appfcations are presented that demonstrate the accuracy and the efllciency of the new approaches.

Optimal prestress of cracked structures with given frictionless and frictional crack interfaces is studied in this paper. The externally placed prestressing cables are modelled by the pin-load method. The static analysis (state) problem is a symmetric or nonsymmetric variational inequality. The arising nonsmooth and nonconvex optimal control problem is solved by a two level combination of nonsmooth optimization with structural analysis and sensitivity techniques. * on leave from Lehr-und Forschungsgebiet fur Mechanik, RWTH Aachen,

Computer programs have been developed or are under development for the IBM personal computer that enable their users to get information on atomic charges, electrostatic potentials, conformational and other properties of molecular systems containing H, C, N, O, F, Si, P, S, or Cl atoms. The zero‐order wavefunction is constructed of strictly localized molecular orbitals with fixed atomic orbital coefficients. The wave function can be refined by optimizing these coefficients, i.e., considering inductive effects via a coupled set of 2 × 2 secular equations within the CNDO/2 approximation. Delocalization and exchange effects are accounted for by expanding the wavefunction on a basis of the aforementioned strictly localized orbitals, instead of conventional atomic orbitals, and solving the corresponding SCF equations. Our method has been applied to the study of large systems. We calculated the electrostatic field of the complex of β‐trypsin and basic pancreatic trypsin inhibitor and it ha...

In this paper, we propose an analytical approach to characterize a transmission line bend. First, an electric field integral equation is derived under the thin wire assumption. The equation is solved using perturbation theory and analytical expressions are derived for the reflection and transmission coefficients associated with the line bend. The derived analytical expressions are compared with ‘exact’ numerical results published by other authors and a very good agreement is found. The developed analytical expressions can also be used to evaluate the radiated power associated with the line bend.

of motivation, accomplishments, and future plans This two-month visit at CTR was devoted to investigating possibilities in LES modeling in the context of the 3-D vortex particle method (=vortex element method, VEM) for unbounded flows. A dedicated code was developed for that purpose. Although O(N _) and thus slow, it offers the advantage that it can easily be modified to try out many ideas on problems involving up to N ,_ 104 particles. Energy spectrums (which require O(N 2) operations per wavenumber) are also computed. Progress was realized in the following areas: particle redistribution schemes, relaxation schemes to maintain the solenoidal condition on the particle vorticity field, simple LES models and their VEM extension, possible new avenues in LES. Model problems that involve strong interaction between vortex tubes were computed, together with diagnostics: total vorticity, linear and angular impulse, energy and energy spectrum, enstrophy. More work is needed, however, especially regarding relaxation schemes and further validation and development of LES models for VEM. + :: ()) vol',,_t__ V' ¢ ' (7)

Boundary element method has been widely used as a design tool in the offshore and ship building industry for more than 30 years. Its application to wave energy conversion is however more recent. This paper deals with the numerical modelling of a free-floating sloped wave energy device. The power take-off mechanism of the device consists of an immersed tube with a piston sliding inside. The modelling is done using the boundary-element method package WAMIT. The model is first worked out for the case where the axis of the tube is vertical. It is then derived for the tube inclined and successfully verified against numerical benchmark data. A companion paper presents results of a detailed comparison with a physical model study.

High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

The primary goal of this study is to create a nonlinear fractional boundary element method (BEM) model for magneto-thermo-visco-elastic ultrasound wave problems in temperature-dependent functionally graded anisotropic (FGA) rotating granular plates in a constant primary magnetic field. Classical analytical methods are frequently insufficient to solve the governing equation system of such problems due to nonlinearity, fractional order heat conduction, and strong anisotropy of mechanical properties. To address this challenge, a BEM-based coupling scheme that is both reliable and efficient was proposed, with the Cartesian transformation method (CTM) used to compute domain integrals and the generalized modified shift-splitting (GMSS) method was used to solve the BEM-derived linear systems. The calculation results are graphed to show the effects of temperature dependence, anisotropy, graded parameter, and fractional parameter on nonlinear thermal stress in the investigated plates. The numerical results validate the consistency and effectiveness of the developed modeling methodology.

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 threedimensional 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.

The paper is devoted to the theoretical analysis of interactions between a receiving array and a neighbouring structure as well as their consequences on the sonar function. The boundary element method is applied to solve the scattering problem for two bodies. Two configurations are considered: a cylindrical array placed in front of a thin rigid panel, both considered as two-dimensional bodies and the association of a spherical array and a thin soft disc. In both examples, the support of the sensors of the arrays are assumed perfectly rigid. The two-dimensional problem is solved using the Helmholtz integral representation; the threedimensional scattering problem using the axisymmetric formulation of the previous representation. Numerical results are used to compute directivity patterns as a function of the steering direction. Degradations produced by shielding and scattering phenomena such as the shift of the maximum level or the increase of the side lobe level are illustrated with d...