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A theorem on the conformal mapping of the flow field with a continuous vorticity distribution is proved. An efficient algorithm of the boundary elements computing based on the theorem is applied in simulation of two-dimensional flow around an elliptic cylinder by the meshless method of Viscous Vortex Domains (VVD). The algorithm makes it possible to significantly reduce (orders of magnitude compared to conventional methods) the time spent on calculating boundary elements and multiply the number of calculation points on the body contour, which is necessary for high resolution of the boundary layer at high values of the Reynolds number. The algorithm can also be used to calculate boundary elements on cylindrical surfaces of arbitrary section and in combination with different vortex methods. The flow around an elliptical cylinder is simulated with a high resolution of the boundary layer for Re numbers from 102 to 105. [ABSTRACT FROM AUTHOR]

This study presents a BEM multi-scale modelling to analyse the bending problem of concrete plates. The concrete microstructure is represented by the Representative Volume Element (RVE), in which the mortar matrix behaviour is governed by the Mohr-Coulomb criterion, the aggregates are considered elastics and the mortar porosity is modelled by defining voids into its domain. Moreover, the microcracking process at ITZ (Interfacial Transition Zone) is modelled by defining additional cohesive-contact finite elements on interfaces between mortar and aggregates. To define the RVE microstructure and the parameters of its phases, we consider a concrete whose experimental curve in compression is known. We show that, for the same volume fraction of inclusions and voids, a RVE with reduced number of aggregates and voids can reproduce the experimental results for compression predominant regimes. But for plate bending analysis, the microstructure and mainly the modelling of the microcracking process at ITZ have enormous influence on the plate mechanical behaviour. The results are also compared to a multi-scale formulation considering the FEM (Finite Element Method) at micro-scale, showing that the proposed model is much faster than the coupled BEM/FEM model. [ABSTRACT FROM AUTHOR]

This paper presents static analysis of a double-plate system using the boundary element method. The system is composed of two parallel plates with an elastic layer in between. The plates are assumed to be represented by the Kirchhoff plate model and the elastic layer is treated as a Winkler elastic foundation. The mathematical steps required to establish a boundary element technique are adequately addressed: integral equations, fundamental solution; domain integral transformation into boundary integral, and formation of an algebraic system of the double-plate problem. Numerical examples of double plate problems with different mechanical properties, boundary conditions, and load types are presented. [ABSTRACT FROM AUTHOR]

In this paper a practical numerical method for calculating the settlement response of piles embedded in multilayered soils is presented. Finite beam elements are used for the discretization of piles. The soil mass, which is considered as a semi-infinite or finite medium with each layer being elastic, homogeneous and isotropic, is modeled with the boundary element method and the Steinbrenner's approximation. In addition, the critical case in which the elastic modulus is decreasing with depth is appropriately treated by considering the soil as a half space inhomogeneous medium. The present formulation, besides yielding fully adequate results for design purposes when compared with other approaches, presents a more practical problem modeling and data preparation. Results of numerical examples considering single piles and pile groups are compared with those of other formulations in order to demonstrate the efficiency and accuracy of the proposed formulations. [ABSTRACT FROM AUTHOR]

The paper presents some boundary element methods (BEM) applied to diffraction of the harmonic acoustic wave generated by a point source. The authors first consider a basic boundary integral equation (BIE). Its analytical analysis permits development of some explicit conclusions. Then, some boundary element methods arise as a result of the dicretization of the BIE by various quadrature formulas. The matrices of the arising systems of linear algebraic equations (SLAE) are studied in the aspect of the structure of their spectrum. It is shown that the spectrum of the matrices is located in the right half-plane, hence the matrices are positive-definite. This predetermines a rapid convergence of the iterative algorithms applied, to solve the SLAEs. [ABSTRACT FROM AUTHOR]

This article presents a model of the response of rigid circular plates supported by embedded elastic pile foundations under time-harmonic torsional excitation. The contact tractions at the pile-soil and plate-soil interfaces are resolved into circumferential components, which are then approximated by piece-wise constant distributions. The dynamic stress-displacement relation for the soil part, here modeled as a homogeneous, transversely isotropic half-space, is obtained by numerical integration of that medium's Green's functions. The pile is modeled as a series of interconnected one-dimensional circular shafts, and the plate is modeled by imposing rigid-body rotation conditions throughout the portion of the surface of the soil that it occupies. A tangential Winkler-type layer is incorporated between the plate and the soil, in order to represent potential imperfect bonding contact that may occur in engineering practice. This article presents an analysis of the influence of geometric and constitutive parameters of the system in its time-harmonic torsional response, as well as a study on the wave propagation from the piled plate system through the soil. [ABSTRACT FROM AUTHOR]

In this study, we propose a novel approach based on the dual reciprocity boundary element method (DRBEM) to approximate the solutions of various Steklov eigenvalue problems. The method consists in weighting the governing differential equation with the fundamental solutions of the Laplace equation where the definition of interior nodes is not necessary for the solution on the boundary. DRBEM constitutes a promising tool to characterize such problems due to the fact that the boundary conditions on part or all of the boundary of the given flow domain depend on the spectral parameter. The matrices resulting from the discretization are partitioned in a novel way to relate the eigenfunction with its flux on the boundary where the spectral parameter resides. The discretization is carried out with the use of constant boundary elements resulting in a generalized eigenvalue problem of moderate size that can be solved at a smaller expense compared to full domain discretization alternatives. We systematically investigate the convergence of the method by several experiments including cases with selfadjoint and non-selfadjoint operators. We present numerical results which demonstrate that the proposed approach is able to efficiently approximate the solutions of various mixed Steklov eigenvalue problems defined on arbitrary domains. [ABSTRACT FROM AUTHOR]

A full coupled multi-scale modelling using the Boundary Element Method for analysing the 2D problem of stretched plates composed of heterogeneous materials, where dissipative phenomena can be considered, is presented. Both the macro-scale and the micro-scale are modelled by BEM formulations where the consistent tangent operator (CTO) is used to achieve the equilibrium of the iterative procedures. The equilibrium equation of the plate (macro-continuum) is written in terms of in-plane strains while the equilibrium problem of the microstructure, which is defined by the RVE (Representative Volume Element), is solved in terms of displacements fluctuations. In this kind of modelling, the mechanical behaviour of the material is governed by the homogenized response of the RVE, obtained after solving its equilibrium problem. As this kind of modelling is expensive computationally, it is important to investigate other numerical methods to have faster formulations, but which are still accurate. To validate the presented model, the numerical results are compared to the ones where the material microstructure (RVE) is modelled by the FEM. [ABSTRACT FROM AUTHOR]

This work presents a novel formulation of the Boundary Element Method (BEM) with the Radial Integration Method (RIM) to calculate the critical loads of the plate buckling problem with shear deformation. An alternative formulation is adopted where the effect of the geometric non-linearity is described by using the first derivative of the function for the out-of-plane displacements. The RIM is developed for this problem and used to convert the resulting domain integrals into equivalent boundary integrals. The results are compared with other results available in the literature and with the results obtained with the Dual Reciprocity Method (DRM). The advantages of using the RIM are discussed at the end of this work. [ABSTRACT FROM AUTHOR]

• The lifting force of the upstream hydrofoil increases and that of downstream hydrofoil decreases when the longitudinal distance is limited in unbounded flow. • The lift augment mode is obtained when the downstream hydrofoil is placed below the zero crossings with an upwash wave flow. • The lift attenuation mode can be found when the downstream hydrofoil is placed below the zero crossings with a downwash wave flow. The hydrodynamics of two dimensional tandem hydrofoils travelling below the water surface has been investigated numerically through potential flow theory. The boundary element method is adopted to solve the boundary value problem. The nonlinear free surface and vortex wake are tracked through time stepping schemes. The downstream hydrofoil is moving in the wake flow of the upstream hydrofoil. The wave induced by the upstream hydrofoil causes the variation of the flow field around the downstream hydrofoil. For tandem hydrofoils with finite longitudinal distance, the effective attack angle and the lifting force of the downstream hydrofoil are affected significantly when there is upwash/downwash flow. The longitudinal distance between the two hydrofoils dominates the hydrodynamic forces of the downstream hydrofoil. The downstream hydrofoil obtains higher lifting force when it is placed below the zero crossing with an upwash flow; a lower lifting force is found when it is placed below the zero crossing with a downwash flow. [ABSTRACT FROM AUTHOR]

The paper illustrates the numerical procedure, based upon a Boundary Element (BE) approach, developed to efficiently evaluate the warping functions in the Saint Venant theory of beam-like solids having both compact and thin-walled sections. Specifically, Chebyshev nodes are selected as collocation points of the BE formulation associated with the relevant pure Neumann problem and the entries of the resulting linear system of equations are evaluated analytically by invoking recursive formulas. Assuming a polynomial interpolation for the unknown function over each boundary element, we show that a reduction in the numerical accuracy of the solution is achieved if the polynomial degree exceeds a given order strictly related to the strategy adopted to discretize the boundary. For this reason, in order to automatically cope both with compact and thin-walled domains, a general criterion has been established for properly selecting the best combination of polynomial degree and edge discretization capable of reducing the numerical error of the procedure below a given tolerance. [ABSTRACT FROM AUTHOR]

The buckling problem represents a way to evaluate the effect of in-plane forces in the behaviour of plates. The effect is distributed along the plate domain, and thus the Boundary Element Method (BEM) formulation of the problem requires domain integration. Several techniques can be used in the numerical implementation of the BEM to replace the domain integral with equivalent boundary integrals. This study adopted the Dual Reciprocity Method (DRM) to obtain a formulation without domain integrals. The bending model considered the effect of the shear deformation for better assessment of the relationship between the buckling load and the plate thickness. The analyses considered in-plane forces distributed in one or in both directions of the plate (normal forces), as well as in the tangential direction to the plate side (shear forces). The numerical results obtained for square and rectangular plates are compared with those available in the literature. [ABSTRACT FROM AUTHOR]

A boundary element model of a piled raft foundation under horizontal and rocking excitations is presented. Excitations are time-harmonic and can be either horizontal loads and rocking moments applied to the raft, or a vertically-propagating seismic shear wave. The raft is modeled as a rigid circular plate bonded to the surface of the soil, and the pile is an elastic body embedded in the soil. The soil is a three-dimensional, transversely isotropic half-space. Contact tractions at the plate–soil and pile–soil interfaces are obtained by a numerical integration of Green's functions for the aforementioned half-space at discrete points. The equation of motion for the discretized piled raft is obtained upon establishing equilibrium and continuity conditions between foundation and soil throughout those interfaces. The paper investigates the effect of foundation and soil parameters in the response of the system to both external and seismic excitations. [ABSTRACT FROM AUTHOR]

In this work, we attempt to collect all available fundamental solutions in 3D elastodynamics that would be suitable for use in Boundary Element Method (BEM) formulations. Given that research on transient and steady state cases involving the elastic, homogeneous and isotropic continuum commenced in the 1950′s, it is practically impossible to reference all work done since then, so we apologize a priori for any omissions on our part. When we use the term fundamental solution, what comes to mind is the elastic full space under a point load in space and time and with the radiation condition arising because the medium has no boundaries, i.e. it extends to infinity. However, this is far from being the end: If the full space becomes a half-space, then boundary conditions enter the picture and now we are talking about Green's functions. These are more desirable for BEM formulations because it now becomes unnecessary to discretize the free surface. In general, the more particular features of the problem at hand are included in the Green's function, the less discretization is necessary in the BEM formulation. What we aim for in this review is to present and briefly discuss the basic fundamental solutions and more specialized Green's functions in a 3D elastic continuum, in either the frequency or the time domain, for the following type of materials: (1) Isotropic and homogeneous; (2) isotropic and inhomogeneous; (3) anisotropic and homogeneous; (4) anisotropic and inhomogeneous. We also look at poroelastic materials with all above possible combinations. We note at this point that the continuously inhomogeneous (e.g., functionally graded) material is understood as one having its material parameters as functions of position. There is, of course, the category of layered media, considered here as discretely inhomogeneous materials. One final note of caution has to do with the numerical implementation of these solutions: Some are very difficult to program, despite the fact that they come in closed form, because they may involve integrals, or there may be turning points in the solution where the form available depends on the frequency, or because of round-off errors in computing special functions. In closing, there is a trade-off between easy to implement fundamental solutions that require substantial spatial discretization effort and advanced ones based on Green's functions that are difficult to implement but require minimal discretization effort. This points out the relevance of speeding up BEM computations, a subject that is treated in the Appendix. [ABSTRACT FROM AUTHOR]

A 2D Boundary Element Method (BEM) Formulation to obtain the constitutive response of heterogeneous materials based on the Representative Volume Element (RVE) concept is developed to deal with dissipative phenomena over the domain and the phase debonding on the interface zone. Despite the formulation is written within a multiscale framework, in this work the analyses are performed only at microstructure level, but if a full coupled multiscale analysis is performed the computational cost becomes very expensive. Usually this kind of modelling is performed considering the Finite Element Method (FEM), but it is important to find other numerical solutions which are less expensive, but still accurate. To analyse metal matrix composites the RVEs are assumed to contain a ductile matrix, rigid inclusions and an interface zone where the phase debonding is modelled by a cohesive fracture model using embedded cohesive contact finite elements into the boundary element mesh. The RVE domain is discretized into cells to compute the domain integral written in terms of the inelastic forces, which have a part related to the plasticity phenomenon and another one referred to the cohesive-contact problem. The homogenized results are compared to a FEM model in order to validate the proposed formulation. [ABSTRACT FROM AUTHOR]

In this work, an explicit direct FEM–BEM coupling procedure is proposed for nonlinear dynamics. In this procedure, each subdomain of the model is analysed separately taking into account proper interface conditions, allowing optimized solver procedures to be applied within each subdomain. In addition, the solution procedure is carried out directly (i.e., without any iterative process), since an explicit time-marching technique is employed within the FEM subdomains. In this context, a locally stabilized central difference approach is utilized, ensuring stability for the FEM analyses, as well as enhanced accuracy. Thus, a very efficient and versatile coupled solution takes place, allowing the direct and independent solution of the subdomains of the model, without regarding critical time-steps limitations within the explicit subdomains. A multi-level time-step algorithm is also considered here, enabling different time-steps to be applied to each subdomain of the model, further improving the flexibility of the coupled analyses. At the end of the paper, numerical applications are presented, illustrating the effectiveness and versatility of the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper, soil-structure interaction problems are analysed using a three-dimensional formulation obtained by combining the Boundary Element Method (BEM) and the Finite Element Method (FEM). Structural elements that interact with the soil are modelled with the FEM. Soil, which is considered as a semi-infinite, homogeneous, linear elastic and isotropic medium, is modelled with the BEM using Mindlin's fundamental solution. A pile is discretized by several three-dimensional finite beam elements. A plate is discretized by finite flat shell elements, making it possible to consider the bending and membrane effects. The vertical and horizontal loads in the plate-pile-soil system are directly applied to the plate. This approach allows for a static analysis of the full interaction between capped pile groups or piled rafts and the soil. The developed formulations can also be extended to dynamic or non-linear analyses. Coupling between the BEM and FEM is performed through a mixed formulation in which the matrix of the soil's influence coefficients obtained by BEM is added to the stiffness matrix of the structural elements obtained by FEM, resulting in an equivalent stiffness matrix. Numerical examples of the plate-pile-soil interactions are solved, and their results are compared with those of other formulations. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a numerical model of the vertical time-harmonic response of a piled-raft foundation under external and seismic excitations. The surface raft is a circular, rigid plate on the surface of the soil, while the pile is represented by a classical finite element bar model embedded within the soil. The soil is modeled as a homogeneous, transversely isotropic, viscoelastic half-space. The fully coupled response of the plate–pile–half-space system is modeled through a superposition of Green's functions, in the framework of the indirect boundary element method. The article investigates the response of the coupled system for different sets of constitutive parameters, especially with regards to the effectiveness of the pile in reducing vibration amplitudes of the surface plate. [ABSTRACT FROM AUTHOR]

Abstract A boundary element formulation to obtain the constitutive response of heterogeneous microstructures is proposed, considering a RVE-based multiscale theory. The sub-region technique is adopted to model the RVE (Representative Volume Element), where voids and inclusions can be defined inside the matrix and different elastic properties and constitutive models can be assumed for each phase. Triangular cells are adopted to approximate the dissipative forces over the RVE domain, where they are assumed constant. After a strain vector is imposed to the microstructure boundary, its elastic forces field is obtained and the respective strain field computed. Then, according to the RVE-based multiscale theory, the RVE equilibrium problem must be solved what requires an iterative procedure to find the displacement fluctuations field that auto-equilibrates the microstructure stress field. After the RVE solution, the boundary tractions must be recalculated to consider the displacement fluctuations field as well as the dissipative forces. Then, from the boundary tractions the homogenized stress vector can be computed. The homogenized constitutive tensor is evaluated considering the constitutive tensors of all cell nodes and also the consistent tangent operator. To validate the proposed model, the homogenized responses of different microstructures are compared to the responses obtained via finite element model. [ABSTRACT FROM AUTHOR]

A BEM formulation to perform elastic analysis of heterogeneous microstructures is proposed in the context of multi-scale analysis. The microstructure, also denoted as RVE (Representative Volume Element), is modeled as a zoned plate where voids or inclusions can be considered inside a matrix. Thus, each sub-region represents either the matrix or an inclusion, where different values of Poisson's ratio and Young's modulus can be defined. The RVE equilibrium equation is solved in terms of displacement fluctuations according to the formulation proposed in de Souza Neto and Feijóo (2006). Only elastic behavior is considered for matrix and inclusions, although the proposed model can be extended to consider dissipative phenomena. To make the micro-to-macro transition necessary in a multi-scale analysis, the homogenized values for stress and constitutive tensor have to be computed adopting homogenization techniques. Some numerical examples of heterogeneous microstructures are presented and compared to a FEM model to show the accuracy of the proposed model. [ABSTRACT FROM AUTHOR]

The paper deals with the direct time domain calculation of a transient electric field generated by a ground penetrating radar (GPR) dipole antenna and transmitted into the lossy half-space. The space–time dependent current along the dipole is governed by the Hallen integral equation which is numerically solved by means of the Galerkin–Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM). Provided that the current distribution along the GPR antenna is determined, one may compute the related electromagnetic field transmitted into the lossy ground by solving the field integral formulas. Some illustrative computational examples related to the transmitted field into the lower half-space are reported in this paper. [ABSTRACT FROM AUTHOR]

It is well known that the 2D Laplace Dirichlet boundary value problem with a specific contour has a degenerate scale for which the boundary integral equation (BIE) has several solutions. We study here the case of the Robin condition (i.e. convection condition for thermal conduction problems), and show that this problem has also one degenerate scale. The cases of the interior problem and of the exterior problem are quite different. For the Robin interior problem, the degenerate scale is the same as for the Dirichlet problem. For the Robin exterior problem, the degenerate scale is always larger than for the Dirichlet problem and has some asymptotic properties. The cases of several simple boundaries like ellipse, equilateral triangle, square and rectangle are numerically investigated and the results are compared with the analytically predicted asymptotic behavior. An important result is that avoiding a contour leading to a degenerate Robin problem cannot be achieved as simply as in the case of Dirichlet boundary condition by introducing a large reference scale into the Green's function. [ABSTRACT FROM AUTHOR]

This work explores the application of coupled numerical models in thermal conduction analysis, taking into account frequency domain formulations. For this purpose, iterative coupling techniques between the Boundary Element Method (BEM) and the Finite Element Method (FEM) are discussed, also considering adaptive discretization procedures. Two coupling approaches are studied here, both using optimal relaxation parameters to ensure and/or to speed up the convergence of the iterative analysis. Non-matching discretizations on the common interfaces of the different subdomains of the model are allowed, and a single iterative cycle is adopted, incorporating both the adaptive and the coupling processes simultaneously. The methodology is quite flexible, and the possibility of using independent discretizations on each subdomain greatly facilitates the use of enhanced adaptive remeshing; in this context, specialized adaptive techniques for each subdomain/methodology may be applied. The adoption of a single iterative loop also renders a very efficient methodology, avoiding the excessive computational costs of sequentially chained iterative cycles. Numerical examples are presented in the end of the paper, illustrating the good performance of the proposed techniques, as well as their potentialities in engineering applications. [ABSTRACT FROM AUTHOR]

A weighting-iteration method in the time domain is developed to calculate the scattered waves from a complex-shaped scatterer. The incident waves can be mono-frequency or multi-frequency, and the complex object includes sharp edges and dramatic variations in geometry. The solid angles on the boundary elements of a complex-shaped scatterer are generally reduced to below the standard value of 0.5 for points on a smooth part of the boundary. These reduced solid angles destroy the convergence history during the iteration process in the time domain. A weighting function associated with the variation of solid angles is introduced to robust and rapid convergence in the time domain. The new method is used to calculate the scattering from a cube with sharp edges and an indented surface. The weighting function speeds up the convergence history to reach a robust convergence for both mono- and multiple-frequency incident waves. [ABSTRACT FROM AUTHOR]

In this paper, new boundary-domain integral equations are derived for solving two- and three-dimensional elastoplastic problems. In the derived formulations, domain integrals associated with initial stresses (strains) are avoided to use, and material nonlinearities are implicitly embodied in the integrand kernels associated with the constitutive tensor. As a result, only displacements and tractions are explicitly involved in the ultimate integral equations which are easily solved by employing a mature efficient non-linear equation solver. When materials yield in response to applied forces, the constitutive tensor (slope of the stress–strain curve for a uniaxial stress state) becomes discontinuous between the elastic and plastic states, and the effect of this non-homogeneity of constitutive tensor is embodied by an additional interface integral appearing in the integral equations which include the differences of elastic and plastic constitutive tensors. The domain is discretized into internal cells to evaluate the resulted domain integrals. An incremental variable stiffness iterative algorithm is developed for solving the system of equations. Numerical examples are given to verify the correctness of the proposed BEM formulations. [ABSTRACT FROM AUTHOR]

An augmented Lagrangian method, based on the fixed point method and boundary variational formulations, is designed and analysed for frictionless contact problems in linear elasticity. Using the equivalence between the contact boundary condition and a fixed point problem, we develop a new iterative algorithm that formulates the contact problem into a sequence of corresponding linear variational equations with the Steklov–Poincaré operator. Both theoretical results and numerical experiments show that the method presented is efficient. [ABSTRACT FROM AUTHOR]

In this work, we study elastic wave scattering and diffraction at the nanoscale by multiple heterogeneities such as cavities and inclusions embedded in an otherwise homogeneous elastic matrix. The dynamic loads are the result of pressure and shear waves propagating through the heterogeneous continuum under two-dimensional conditions. The mathematical model used here combines (a) classical elastodynamic theory for the bulk solid, where the total elastic wave field comprises both incident and scattered wave fields, with (b) non-classical boundary conditions and a localized constitutive equation for the matrix–inclusion interfaces within the framework of the Gurtin–Murdoch surface elasticity theory. The computational platform used is the boundary element method (BEM) defined in terms of the frequency-dependent fundamental solution of the governing equations of motion for the bulk solid under time-harmonic conditions. Following development of the BEM for this category of problems, a verification study is conducted to establish its accuracy with the help of benchmark-type examples. Subsequent numerical simulations for the case of multiple cavities and inclusions embedded in an elastic matrix examine the development of the wave fields in the bulk solid, as well as of the dynamic stress concentration factor (DSCF) at the solid-inclusion interfaces, in terms of the following parameters: (a) nanoheterogeneity shape, which directly influences the surface energy; (b) nanoheterogeneity size; (c) ratio of the bulk material properties of the matrix to those of the inclusion; (d) surface properties such as the interfacial constants and the residual interface tension; (e) dynamic interaction between multiple nanoheterogeneities and (f) direction of propagation and frequency content of the incident wave. [ABSTRACT FROM AUTHOR]

In this paper a boundary element method for analysis of fractured stiffened panels repaired with riveted or adhesively bonded patches is presented. In order to achieve such a formulation, several boundary element formulations involving the membrane and bending of displacement, and, stress resultants are coupled together to analyse the model. The multi-region formulation is used to simulate the stiffeners, which are modelled as an assembly. They are then connected to the sheets to form the stiffened panels by means of a rivet formulation. The dual boundary element method is used to simulate the presence of cracks, and the patches, treated as independent plates, are joined to the panel either with rivets or adhesive. A boundary element formulation for adhesive bonding is implemented to model the adhesively bonded patches. The Crack Opening Displacements (COD) method and the J-integral are implemented to evaluate the required fracture parameters. Examples presented include a wing box with a three spar section, with fully stiffened skin, and, the skin is considered to have a crack and a repair patch is used on top of the crack to stop its growth. [ABSTRACT FROM AUTHOR]

A multi-scale modelling for analysing the stretching problem of plates composed of heterogeneous materials is presented. The BEM (Boundary Element Method) is adopted to model the macro-continuum (represented by the plate) while the equilibrium problem at micro-scale (represented by the Representative Volume Element – RVE) is solved by a FEM (Finite Element Method) formulation that takes into account the Hill–Mandel Principle of Macro-Homogeneity. After solving the equilibrium problem of the RVE, the micro-to-macro transition is made by applying the volume averaging hypothesis of strain and stress tensors. Some numerical examples are then analysed to show that the proposed formulation is a suitable tool for the analysis of stretched of plates composed of heterogeneous materials. To define the microstructure, different RVEs composed of an elasto-plastic matrix with inclusions or voids are considered. Besides, a quadratic rate of asymptotic convergence of the Newton–Raphson scheme has been achieved during the iterative procedure. [ABSTRACT FROM AUTHOR]

A multi-scale modelling for analyzing the bending problem of plates composed of heterogeneous materials is presented. The macro-continuum is modelled by a non-linear formulation of the boundary element method (BEM) taking into account the consistent tangent operator (CTO). The micro-scale is represented by the RVE (representative volume element) being its equilibrium problem solved by a finite element formulation that takes into account the Hill-Mandel Principle of Macro-Homogeneity while the volume averaging hypothesis of the strain and stress tensors is used to make the micro-to-macro transition. Three different boundary conditions are imposed over the RVE: (i) linear displacements, (ii) periodic displacement fluctuation and (iii) uniform boundary tractions. The material behaviour is governed by the Von Mises elasto-plastic criterion although the proposed multi-scale model can be used with any other non-linear model. Numerical examples are presented to illustrate the main features and scope of the proposed formulation. [ABSTRACT FROM AUTHOR]

In the present study, a nonlinear joint element model with a coupled shear-tensile behavior for multi body boundary element frictional contact problems is presented. The analysis is carried out by discrete crack model using the multi-region 3D boundary element method including material damping. To account for the decay of joint strength parameters at intermediate courses of deformation, the simplified discrete crack joint model (SDCJ) has been used. The nonlinear nature of contact problems demands an iterative technique development to determine the actual contact conditions (opening and sliding with bonding and friction) at arbitrary points of the contact boundaries. Through several analyses, it is demonstrated that the proposed method is robust, as it does not require to solve the whole system simultaneously. As a particular case, the influence of foundation inhomogeneity on the seismic response of concrete arch dam has been studied in order to illustrate the accuracy and efficiency of the present approach in a complicated case. [ABSTRACT FROM AUTHOR]

Abstract: A technique that couples the boundary element method (BEM) with the meshless local Petrov–Galerkin (MLPG) method is proposed to simulate the 2-D acoustic wave propagation in an unbounded fluid domain containing confined subdomains where the material properties vary from point to point. The non-homogeneous confined subdomains are only discretized with nodal points and treated by the MLPG. The nodal points, which are placed at the interface between the confined subdomains and the unbounded homogenous acoustic fluid, are used to couple the BEM and the MPLG. The moving least-squares (MLS) approximation scheme is used to provide the approximation of field quantities. The proposed BEM–MLPG coupled approach is verified against the results provided by an analytical solution developed for a circular confined subdomain, in which the velocity variation within the circular non-homogeneous region only occurs in the radial direction. A numerical example illustrates the application of the proposed approach to solve the case of a pair of non-homogeneous confined subdomains, for which analytical solutions are not known. [Copyright &y& Elsevier]

Abstract: This work presents a methodology for identifying inclusions in a conductor domain. The methodology is based on electrical potential measurements on the external boundary of a conductor body subjected to a prescribed set of electrical current injections. The boundary of each inclusion is approximated by a special kind of spline, whose control points have an extra parameter related to the distance between the control point and the curve. Such special feature allows identification of smooth or sharp inclusions with the same initial guess. The identification is an inverse problem that, in this work, is solved by the Levenberg–Marquardt Method. This iterative method tries to locate the minimum of an objective function, the square of the norm of a residual vector function, given by the differences between electrical potential measurements and the computed ones. The computation of the electrical potential is called forward problem and it is solved by an implementation of the direct formulation of the Boundary Element Method (BEM). The present paper addresses two approaches for computing the derivatives of the residual function with respect to the minimization parameters, required by the Levenberg–Marquardt Method. The first one is based on finite differences and the second one is based on the direct differentiation of the integral equation of the BEM for potential problems. Performance comparisons of these two approaches are presented, based on numerical experiments of identification of inclusions with noisy datasets computationally obtained. [Copyright &y& Elsevier]

Abstract: In this paper the inverse problem of electrical impedance tomography (EIT) in a three dimensional environment is considered. In this technique, electrodes are placed on the external boundary of the body and electrical current is injected by sequentially activating pairs of them while the corresponding potentials are measured. Usually such measures are used in order to solve the nonlinear inverse problem of achieving a two-dimensional image of the conductivity distribution over the cross section of the body. In the problem studied here the goal is to determine the size and position of an existing cavity within a homogeneous medium. The geometrical parameters that describe the cavities are the unknowns of the resulting 3D inverse problem, which is solved by the Levenberg–Marquardt method. Two shapes of geometrical cavities are here considered: spherical and spheroidal. Due to its accuracy and simplicity of mesh generation, the Boundary Element Method (BEM) is used in the solution of the direct problem. In order to evaluate the proposed strategy, numerical experiments are presented varying the position and the shape of the cavity and also the injection-measure protocol used. Since measured data are not currently available, boundary potential measurements have been obtained computationally also using BEM. The sensitivity of the present method in the presence of measurement noise has also been estimated through numerical experiments. [Copyright &y& Elsevier]

Abstract: In this work, interacting acoustic–elastodynamic models are analyzed by means of an optimized iterative coupling algorithm. In this iterative coupling procedure, each acoustic/elastodynamic sub-domain of the model is solved independently, and the variables at the common interfaces of the sub-domains are successively renewed, until convergence is achieved. A relaxation parameter is introduced in order to ensure and/or speed up the convergence of the iterative analysis, and an expression to compute optimal values for the relaxation parameter is presented. Several numerical methods are considered to discretize the acoustic and elastodynamic sub-domains of the coupled model, and the performance of these different methodologies, in the coupled analysis, is discussed. In this context, the boundary element method and the method of fundamental solutions are applied to model the acoustic sub-domains, whereas the finite element method, the collocation method and the meshless local Petrov–Galerkin method are applied to model the elastodynamic sub-domains. Independent discretizations of the acoustic/elastodynamic sub-domains are allowed, being no matching nodes required along the common interfaces. At the end of the paper, numerical examples are presented, illustrating the performance and potentialities of the adopted procedures. [Copyright &y& Elsevier]

Abstract: In this work, a plate bending formulation of the boundary element method (BEM) based on the Reissner''s hypothesis to perform linear analysis of plates reinforced by rectangular beams is extended to consider the beams not displayed over their middle surface. Therefore eccentricity effects are taken into account. The building floor structure is modelled as a stiffened plate which is treated as a single body without dividing it into beam and plate elements. Moreover the equilibrium and compatibility conditions are automatically imposed by the integral equations. In the proposed model the final system of equation is obtained by coupling the bending problem to the stretching problem. Besides, in order to reduce the number of degrees of freedom, both the displacements and tractions are approximated along the beam width, leading to a model where the values are defined on the beams axis. In order to validate the proposed formulation, the numerical results are compared to a well know finite element code. [Copyright &y& Elsevier]

Abstract: This work describes a numerical frequency domain model, based on the joint use of the BEM and the radial basis function collocation method (also known as Kansa''s Method), which is used to model acoustic systems containing a heterogeneous portion. The model makes use of the BEM to model the homogeneous part of the propagation domain, while Kansa''s method is used to model a heterogeneity, with smooth velocity variations from point to point. Continuity of velocities and pressures is imposed in the interface between the two parts of the domain. Kansa''s Method is applied here, making use of multiquadric (MQ) RBFs, which incorporate a shape parameter that strongly influences the quality of the results. To overcome this problem, a general strategy based on the assessment of the domain residual error in the enforcement of the governing PDE is used to define adequate values of this shape parameter. The proposed method is verified and tested against solutions that have been developed analytically for simple geometries. Its application is then illustrated with an example. [Copyright &y& Elsevier]

Abstract: An algorithm for a parallelized coupled model based on finite element method (FEM), boundary element method (BEM), and scaled boundary FEM (SBFEM) for harmonic and transient dynamic response of large-scale 2D structures embedded in or on layered soil media is presented. The BEM and SBFEM are used for modelling the dynamic response of the unbounded media. The standard FEM is used for modelling the finite region and the embedded structure. The objective of the development of this parallelized coupled model is to use the power of high performance computing, and to take into account the advantages and evade the disadvantages of the above mentioned numerical methods for modelling of the unbounded media in soil-structure interaction (SSI) systems. The development of the parallel algorithm for this model is essential for solving arbitrarily shaped large-scale SSI problems, which cannot be solved within reasonable elapsed times by a serial algorithm. The efficiency of the proposed parallel algorithm and the validity of the coupled model are shown by means of three numerical examples, indicating the excellent accuracy and applicability of the parallel algorithm with considerable time-savings in large-scale problems. [Copyright &y& Elsevier]

Abstract: In this paper a solution method is presented for the coupled problem of elastic flat or space membranes supported by elastic flexible cables. Both membrane and cable undergo large deflections. Starting from the minimal surface the membrane is prestressed by imposed boundary displacements under the self-weight. Then an iterative procedure is employed, which consists in solving the membrane and the cable large deflection problems separately in each iteration step and checking the continuity of displacements and forces between membrane and cable. The procedure is repeated until convergence is achieved. Both membrane and cable problems are solved using the analog equation method (AEM). The displacements as well as the stress resultants are evaluated at any point of the membrane and the cable from the integral representations of the solution of the analog equations, which are used as mathematical formulae. Example problems are presented, for both flat and space membranes, which illustrate the method and demonstrate its efficiency and accuracy. [Copyright &y& Elsevier]

Abstract: In this work a general and concise two-dimensional fundamental solution is obtained for quasi-static linear viscoelastic problems using the boundary element method. For this purpose, the three-dimensional fundamental displacement, derived by Sternberg and Al-Khozaie from the generalization of Navier equation, is integrated with respect to z-coordinate. A time formulation is constructed from the viscoelastic Reciprocity Principle, defined in terms of the Stieltjes integral and the material functions are acquired by means of Boltzmann''s rheological model. The collocation method and a semi-analytical procedure for the singular boundary integral are employed to the numerical analysis of the boundary integral. The Gaussian quadrature, the analytical method and an incremental approach are used to deal with the convolution integral. As the latter has presented the best performance, it is employed in most analyses of the examples. Finally, numerical results of problems, found in the literature, are presented in order to validate the formulation and the two-dimensional fundamental solution. [Copyright &y& Elsevier]

Abstract: The conventional way for formulating a time domain boundary element method (TD-BEM) in linear elastodynamics is to utilize Graffi''s reciprocal theorem. This theorem may either be the starting point in formulating a numerical methodology or the endpoint, if one starts directly from the governing equations of motion and follows various manipulations. The literature abounds with evidence of serious instability problems that accompany these formulations. Thus, research effort has been devoted on reducing this undesirable behavior. In this paper, we utilize a reciprocal theorem that relates velocities and tractions of two different elastodynamic states of the same body, in order to establish a well behaved TD-BEM formulation for 3D transient problems. It is shown that regarding stability, this straightforward formulation is capable of not only reducing instabilities compared to the conventional formulation, but also seems to eliminate the “intermittent” as well as the “sudden” instability problem. [Copyright &y& Elsevier]

Abstract: A total BETI (TBETI) based domain decomposition algorithm with the preconditioning by a natural coarse grid of the rigid body motions is adapted for the solution of multibody frictionless contact problems of linear elastostatics and proved to be scalable, i.e., the cost of the solution is asymptotically proportional to the number of variables. The analysis admits floating bodies. The proofs combine the original results by Langer and Steinbach on the scalability of BETI for linear problems and our development of optimal quadratic programming algorithms for bound and equality constrained problems. The theoretical results are verified by numerical experiments. The power of the method is demonstrated on the analysis of ball bearings. [ABSTRACT FROM AUTHOR]

Abstract: The paper deals with two different approaches to the assessment of the transient impedance of a horizontal grounding electrode: frequency domain boundary element analysis, based on the straight thin wire antenna model (AM) and generalized telegrapher’s equations combined with inverse Fast Fourier Transform (FFT); and time domain finite element analysis based on the transmission line model (TLM) and standard telegrapher’s equations. Extensive numerical experiments have been undertaken and some of illustrative numerical results are presented in this paper. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a BE-based shape optimization method for acoustic problems in the context of shape design of sound insulating walls. In order to avoid the convergence to a local minimal solution around an initial shape, the topological derivative is introduced. Based on the global distribution of the topological derivative, new shape or topology are attained by nucleating small scattering bodies. Evaluation of the topological derivative is achieved within the framework of the boundary element analysis. To cope with the topological change due to the nucleation and cutting of thin branches, shape is updated by the aid of the level set approach during the optimization process. Through numerical examples, it is proved that the developed method can find a shape with good performance irrespective of its initial shape. [ABSTRACT FROM AUTHOR]

Abstract: A comparison of two approaches for solving time dependence in an unsteady heat conduction problem with a material or other interface, based on a boundary element technique is presented. A quadrature algorithm is used in the first approach for calculating convolutional integrals, which leads directly to the time-domain solution of the problem; the other approach uses the Laplace transform and a numerical inversion of the Laplace domain solution. The new numerical techniques lead together with the Symmetric Galerkin Boundary Element Method applied for space variables and a weak formulation of interface conditions to an interface problem with generally curved interfaces and to independent meshing of each side of the interface. The discussion on numerical results is focused on the non-matching discretization of the interface. The obtained data are also compared with known analytical solutions, if available, and discussed in the cases of different material properties pertinent to substructures on both sides of the interface. [Copyright &y& Elsevier]

Abstract: Large scale changes in geometry due to corrosion of polycrystalline pure copper are modeled using the Boundary Element Method. Axisymmetric geometries are considered. A quasi-static analysis is performed and a nonlinear polarization curve is determined from experiments to impose third kind boundary conditions. Super-elements, based on a cubic spline fit interpolation, are introduced to model the motion of the boundaries. Faraday''s law is used to relate boundary motion to the surface flux. An set of controlled experiments using nearly pure (99.99% and 99.9%) copper with aerated NH4OH electrolyte was used to test the experimental methods developed for this study and to verify the functionality of the numerical code in predicting large changes in geometry due to long duration dissolution. Polarization curves were measured and input into the BEM code and recession profiles were predicted. Comparison between experiment and predictions reveal that, given the polarization curves measured in the lab, the BEM code predicts accurate recession profiles. [Copyright &y& Elsevier]

Abstract: This work deals with analysis of cracked structures using BEM. Two formulations to analyse the crack growth process in quasi-brittle materials are discussed. They are based on the dual formulation of BEM where two different integral equations are employed along the opposite sides of the crack surface. The first presented formulation uses the concept of constant operator, in which the corrections of the non-linear process are made only by applying appropriate tractions along the crack surfaces. The second presented BEM formulation to analyse crack growth problems is an implicit technique based on the use of a consistent tangent operator. This formulation is accurate, stable and always requires much less iterations to reach the equilibrium within a given load increment in comparison with the classical approach. Comparison examples of classical problem of crack growth are shown to illustrate the performance of the two formulations. [Copyright &y& Elsevier]

Abstract: In this work, a boundary element method (BEM) formulation to perform linear bending analysis of building floor structures where slabs and beams can be defined with different materials is presented. The proposed formulation is based on Kirchhoff''s hypothesis, the building floor being modelled by a zoned plate, where the beams are treated as thin sub-regions with larger rigidities. This composed structure is treated as a single body, the equilibrium and compatibility conditions being automatically taken into account. In the final integral equation, the tractions are eliminated along the interfaces, therefore reducing the number of degrees of freedom. The displacements are approximated along the beam cross-section, leading to a model where the values remain defined on the beam skeleton line instead of their boundaries. The accuracy of the proposed model is shown by comparing the numerical results with a well-known finite element code. [Copyright &y& Elsevier]

Abstract: In this paper a novel numerical approach is presented for the simulation of solids containing thin linear inclusions with the boundary element method (BEM). Assumptions are that the inclusions are in continuous contact with the surrounding solid and that they are only able to carry axial stresses, their bending stiffness is neglected. A practical application is the simulation of underground openings such as tunnels supported by rock bolts. To avoid an increase in the number of unknowns in the system of equations, the problem is solved iteratively. The iterative solution procedure is particularly suitable for solving problems containing a high number of inclusions and involving nonlinear material behaviour, where an iterative solution procedure has to be used anyway. The approach has been implemented into the boundary element program . To verify the method a test example is presented, considering elastic and plastic material behaviour. The results are compared with those calculated by finite elements. [Copyright &y& Elsevier]

Abstract: This work presents an application of a direct boundary element method (BEM) formulation for drop deformation and interaction in Stokes flows through converging channels. Parametric studies are conducted to investigate the effect, on drop deformation, of the channel''s convergence ratio, the drop-fluid viscosity ratio, the interfacial tension and the initial relative position of the drops. [Copyright &y& Elsevier]