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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.

The load-penetration curve in elastic nanoindentation of an elastic micropolar flat by a diamond spherical punch is analyzed. The presented results are obtained by a specifically developed numerical tool based on a judicious combination of the conventional boundary element method and strong form local point interpolation method. The results show that the usual linear relationship between the material depression and the square of the radius of the contact area is also valid in this case of micropolar elastic material. It is also shown that the relation between the indentation stress (applied load over the contact surface) and the indentation strain (ratio of contact radius by the punch radius) is linear. The proportionality coefficient which is none other than the indentation stiffness varies with the coupling factor of the micropolar elastic medium. A relation between the indentation stiffness of a micropolar solid and that of a conventional solid with the same Young modulus and Poisson ratio is derived.

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.

Made available in DSpace on 2019-10-06T15:24:54Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-02-01 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) 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. Civil Engineering Department Federal University of Goiás (UFG) – Regional Catalão, Av. Dr. Lamartine Pinto de Avelar, 1120, Setor Universitário- CEP Civil Engineering Department São Paulo State University – UNESP, Al. Bahia, 550 Civil Engineering Department São Paulo State University – UNESP, Al. Bahia, 550 CNPq: 302841/2014-8

Made available in DSpace on 2020-12-12T01:30:39Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-10-01 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de Goiás 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. Civil Engineering Department Regional Catalão – Federal University of Goiás (UFG) Av. Dr. Lamartine Pinto de Avelar, 1120, Setor Universitário Civil Engineering Department of São Paulo State University – UNESP, Al. Bahia, 550 Civil Engineering Department of São Paulo State University – UNESP, Al. Bahia, 550

The aim of this study is to develop an efficient numerical technique using the non-hypersingular, traction boundary integral equation method (BIEM) for solving wave propagation problems in an anisotropic, viscoelastic plane with cracks. The methodology can be extended from the macro-scale with certain modifications to the nano-scale. Furthermore, the proposed approach can be applied to any type of anisotropic material insofar as the BIEM formulation is based on the fundamental solution of the governing wave equation derived for the case of general anisotropy. The following examples are solved: (i) a straight crack in a viscoelastic orthotropic plane, and (ii) a blunt nano-crack inside a material of the same type. The mathematical modelling effort starts from linear fracture mechanics, and adds the fractional derivative concept for viscoelastic wave propagation, plus the surface elasticity model of M. E. Gurtin and A. I. Murdoch, which leads to nonclassical boundary conditions at the nano-scale. Conditions of plane strain are assumed to hold. Following verification of the numerical scheme through comparison studies, further numerical simulations serve to investigate the dependence of the stress intensity factor (SIF) and of the stress concentration factor (SCF) that develop in a cracked inhomogeneous plane on (i) the degree of anisotropy, (ii) the presence of viscoelasticity, (iii) the size effect with the associated surface elasticity phenomena, and (iv) finally the type of the dynamic disturbance propagating through the bulk material.

Made available in DSpace on 2022-04-28T19:07:07Z (GMT). No. of bitstreams: 0 Previous issue date: 2018-02-01 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) 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. FEIS – Faculdade de Engenharia de Ilha Solteira, Av. Brasil Sul, 56 - Centro, Ilha Solteira - Civil Engineering Department Federal University of Goiás (UFG) – Regional Catalão, Av. Dr. Lamartine Pinto de Avelar, 1120, Setor Universitário CNPq: 302841/2014-8 CAPES: BEX 0602/11-6

The buckling of square perforated plates is analysed with the effect of shear deformation in the bending model. The relationship between the buckling load and the plate thickness is better assessed with this bending model instead of the classical model. The simply supported condition at all sides was adopted in the buckling problem such that opposite sides of the plates were uniformly compressed in one direction. The plates had a thickness to length ratio between 1/1000 and 1/5. This study adopted the dual reciprocity method (DRM) to obtain a formulation without domain integrals. The numerical results obtained were compared with those available in the literature.

Advances in Computational Mathematics, 37 (1), ISSN:1019-7168, ISSN:1572-9044

International audience; It is well known that the 2D Laplace Dirichlet problem has a degenerate scale for which the direct boundary integral equation has several solutions. We study here the case of mixed boundary condition, mainly for the exterior problem, and show that this problem has also a degenerate scale. The degenerate scale factor is a growing functionof the part of the boundary submitted to Neumann condition. Different special cases are then addressed: segment, circle and symmetric problems. Some exact values of the degenerate scale factor are given for equilateral triangle and square. The numerical procedure for determinig the degenerate scale factor for mixed BC is described. The comparison is made with other kinds of boundary conditions and the consequence of the choice of Green's function when using the Boundary Element Method is studied.

International audience; It is well known that the 2D Laplace Dirichlet boundary value problem with a specific contour has a degeneratescale for which the boundary integral equation (BIE) has several solutions. We study here the case of the Robincondition (i.e. convection condition for thermal conduction problems), and show that this problem has also onedegenerate scale. The cases of the interior problem and of the exterior problem are quite different. For the Robininterior 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. Thecases of several simple boundaries like ellipse, equilateral triangle, square and rectangle are numericallyinvestigated 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 assimply as in the case of Dirichlet boundary condition by introducing a large reference scale into the Green'sfunction.

The three-dimensional eddy current time-dependent problem is considered. We formulate it in terms of two variables, one lying only on the conducting domain and the other on its boundary. We combine finite elements (FEM) and boundary elements (BEM) to obtain a FEM–BEM coupled variational formulation. We establish the existence and uniqueness of the solution in the continuous and the fully discrete case. Finally, we investigate the convergence order of the fully discrete scheme.

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.

Analytical integrations, in the framework of linear elastic problems modelled by means of boundary integral equations, have been considered in a previous publication (Int. J. Numer. Methods Eng. 2002; 53(7):1695–1719): the present note aims at extending the subject to linear elastic fracture mechanics. In such a context, special shape functions have been recently proposed (SIAM J. Appl. Math. 1998; 58: 428–455) in order to increase accuracy in stress intensity factors approximation: the closed form solution for ‘integrals’ that arise from the boundary element method is a goal of the present work. Exploiting the analytical integrations, asymptotical analysis around the crack tip are made possible, with the purpose of formulating a coherent and accurate correlation between approximated stress intensity factors and crack opening displacements over the crack tip straight special elements. Copyright © 2006 John Wiley & Sons, Ltd.

We analyze a least squares formulation for the numerical solution of second-order lineartransmission problems in two and three dimensions, which allow jumps on the interface. In a bounded domain the second-order partial differential equation is rewritten as a first-order system; the part of the transmission problem which corresponds to the unbounded exterior domain is reformulated by means of boundary integral equations on the interface. The least squares functional is given in terms of Sobolev norms of order -1 and of order 1/2. These norms are computed by approximating the corresponding inner products using multilevel preconditioners for a second-order elliptic problem in a bounded domain @? and for the weakly singular integral operator of the single layer potential on its boundary @[email protected]?. As preconditioners we use both multigrid and BPX algorithms, and the preconditioned system has bounded or mildly growing condition number. Numerical experiments confirm our theoretical results.

The dual reciprocity method (DRM) is a technique to transform the domain integrals that appear in the boundary element method into equivalent boundary integrals. In this approach, the nonlinear terms are usually approximated by an interpolation applied to the convective terms of the Navier-Stokes equations. In this paper, we introduce a radial basis function interpolation scheme for the velocity field, that satisfies the continuity equation (mass conservative). The proposed method performs better than the classical interpolation used in the DRM approach to represent such a field. The new scheme together with a subdomain variation of the dual reciprocity method allows better approximation of the nonlinear terms in the Navier-Stokes equations.

In this paper, we review the main contributions developed by the authors to solve problems involving contact between bodies with a roughness covering several orders of magnitude. A periodic self-equilibrated formulation is introduced to avoid any border problem. Furthermore, when focusing on the steady-state rolling or sliding contact mechanics between viscoelastic materials, we develop a mathematical formulation, parametrically dependent on the rolling/sliding speed, which employs the same computational techniques introduced for elastic rough contacts. In particular, in both cases, we adopt an ad hoc discretization technique enabling us to reach the full convergence.

The publication is available http://dx.doi.org/10.1137/S0036142998335364 [Abstract] We use a version of the FEM--BEM method introduced by Costabel [ Boundary Elements IX, Vol. 1, C. A. Brebbia et al., eds., Springer-Verlag, 1987] and Han [ J. Comput. Math., 8 (1990), pp. 223--232] to discretize an exterior quasilinear problem. We provide error estimates for the Galerkin method and propose a fully discrete scheme based on simple quadrature formulas. Furthermore, we show that these numerical integration schemes preserve the optimal rates of convergence. Finally, we present results of numerical experiments involving our discretization method.

We consider the classical Fredholm linear integral equation of the first kind with logarithmic kernel on a smooth Jordan open arc. Applying the well-known cosine change of variable, the arc is reparametrized and the problem is transformed into a new integral equation. We investigate the existence of an asymptotic expansion for the error of the Galerkin method with splines on a uniform mesh as test-trial functions. We also analyse a full discretization of the method based on the Galerkin collocation method using high order integration formulae to keep the optimal error estimates of the Galerkin method in weak norms. Asymptotic expansions of the error for this method are provided. Finally, we show how these expansions extend to the computation of the potential. The expansions of the error in powers of the discretization parameter are useful to obtain a posteriori estimates of the error and to apply Richardson extrapolation for acceleration of convergence. © 1999 Elsevier Science Ltd. All rights reserved.

The paper deals with the frequency domain Galerkin-Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM) for the solution of the Pocklington integral equations for arbitrary thin wire configurations. The presence of a lossy media is taken into account by using both the reflection coefficient approximation and the rigorous Sommerfeld integral formulation. Some illustrative computational examples related to power line communication systems (PLC) and grounding systems are presented.

The paper deals with the space-time Galerkin-Bubnov scheme of the Indirect Boundary Element Method for the solution of time domain integral equations for thin wires in the presence of lossy media of the Pocklington and Hallen type, respectively. The presence of a dissipative half-space is taken into account via the corresponding space-time reflection coefficients. Some illustrative computational examples related to the overhead wires and grounding electrodes are presented.

A three-dimensional boundary element method (BEM) implementation of the interaction integral methodology for the numerical analysis of mixed-mode three-dimensional thermoelastic crack problems is presented in this paper. The interaction integral is evaluated from a domain representation naturally compatible with the BEM, since stresses, strains, temperatures and derivatives of displacements and temperatures at internal points can be evaluated using the appropriate boundary integral equations. Several examples are analysed and the results compared with those available in the literature to demonstrate the efficiency and accuracy of the implementation to solve straight and curved crack-front problems. Fil: Balderrama, R.. Universidad Central de Venezuela; Venezuela Fil: Cisilino, Adrian Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones en Ciencia y Tecnología de Materiales. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones en Ciencia y Tecnología de Materiales; Argentina Fil: Martinez, M.. Universidad Central de Venezuela; Venezuela

The paper deals with a frequency domain analysis of a log-periodic dipole array (LPDA) antenna using boundary element analysis. The mathematical model is based on the set of corresponding coupled Pocklington integro-differential equations. Once the current distribution along the wires is obtaining, it is possible to determine the radiation characteristics of LPDA. The set of coupled Pocklington integro-differential equations is handled via the Galerkin-Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM). The field irradiated by LPDA is also assessed using BEM formalism.

The present work deals with the application of the traction hypersingular boundary integral equation to approximate the stress tensor along the boundary, by making use of unit vectors that differ from the normal at the boundary. It is proved that special care is required in the evaluation of the free terms, in order to avoid insidious and unexpected errors. Copyright © 2007 John Wiley & Sons, Ltd.

28th World Conference on Boundary Elements and other Mesh Reduction Methods (from 5/10/2006 to 5/12/2006), Skiathos, Greece, available, unclassified, unlimited

We considered a nonlinear parabolic equation in a bounded domain of R 2 coupled with the Laplace equation in the corresponding exterior region. This kind of problems appears in the modelling of quasi-stationary electromagnetic fields. We chose a regular artificial boundary containing the nonlinear region in its interior. Then, we applied a symmetric FEM-BEM coupling procedure including a parameterization of the artificial boundary. We used the backward Euler method for the time discretization and an exact triangulation of the finite element domain. Assuming that the nonlinear operator is strongly monotone and Lipschitz-continuous, we proved convergence and obtained optimal error estimates for the solution of the discrete problem. Finally, we proposed a fully discrete scheme with quadrature formulas of low order and, under some additional conditions on the nonlinearity, proved that the order of convergence remains optimal.

Journal of Engineering Mathematics, 51 (3), ISSN:0022-0833, ISSN:1573-2703

A three-dimensional boundary element method (BEM) implementation of the interaction integral methodology for the numerical analysis of mixed-mode three-dimensional cracks is presented in this paper. The interaction integral is evaluated from a domain representation naturally compatible with the BEM, since stresses, strains and derivatives of displacements at internal points can be evaluated using their appropriate boundary integral equations. Special emphasis is put in the selection of the auxiliary function that represents the virtual crack advance in the domain integral. This is found to be a key feature to obtain reliable results at the intersection of crack fronts with free surfaces. Several examples are analysed to demonstrate the efficiency and accuracy of the implementation. Fil: Cisilino, Adrian Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones en Ciencia y Tecnología de Materiales. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones en Ciencia y Tecnología de Materiales; Argentina Fil: Ortiz, J.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones en Ciencia y Tecnología de Materiales. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones en Ciencia y Tecnología de Materiales; Argentina

We describe the simulation of an exterior problem using a magnetic field deriving from magnetostatics, with a numerical method mixing the approaches of C. I. Goldstein and L.-A. Ying. This method is based on the use of a graded mesh obtained by gluing homothetic layers in the exterior domain. On this mesh, we use an edge elements discretization and a recently proposed mixed formulation. In this paper, we provide both a theoretical and numerical study of the method. We establish an error estimate, describe the implementation, propose some preconditioning techniques and show the numerical results. We also compare these results with those obtained from an equivalent boundary elements approach. In this way, we retain that our method leads to a practical numerical implementation, a saving of storage, and turns out to be an alternative to the classical boundary elements method. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 595–637, 2003

The performance of the Boundary Element Method (BEM) depends on the size of the elements and the interpolation function used. However, improvements in accuracy and efficiency obtained with both expansion and grid refinement increases demand on the computational effort. This paper evaluates the performance of constant, linear and quadratic elements in the analysis of the three-dimensional scattering caused by a cylindrical cavity buried in an infinite homogeneous elastic medium subjected to a point load. A circular cylindrical cavity for which analytical solutions are known is used in the simulation analysis. First, the dominant BEM errors are identified in the frequency domain and related to the natural vibration modes of the inclusion. Comparisons of BEM errors are then made for different types of boundary elements, maintaining similar computational costs. Finally, the accuracy of the BEM solution is evaluated when the nodal points are moved inside linear and quadratic discontinuous elements. http://www.sciencedirect.com/science/article/B6V2N-3YN93TX-1/1/28e4a46d3da333118f419ca7b5266239

Singularity-reduced integral relations are developed for displacement discontinuities in three-dimensional, anisotropic linearly elastic media. An isolated displacement discontinuity is considered first, and a systematic procedure is followed to develop relations for the displacement and stress fields induced by the discontinuity. The singularity-reduced relation for the stress is particularly important since it is in a form which allows a weakly-singular, weak-form traction integral equation to be readily established. The integral relations obtained for a general displacement discontinuity are then specialized to an isolated crack and to dislocations; the relations for dislocations are introduced to emphasize their direct connection to corresponding results for cracks and to allow earlier independent findings for these two types of discontinuities to be put into proper context. Next, the singularity-reduced integral equations obtained for an isolated crack are extended to allow treatment of cracks in a finite domain, and a pair of weakly-singular, weak-form displacement and traction integral equations is established. These integral equations can be combined to obtain a final formulation which is in a symmetric form, and in this way they serve as the basis for a weakly-singular, symmetric Galerkin boundary element method suitable for analysis of cracks in anisotropic media.

This paper deals with the symmetric linear systems of equations arising in the Galerkin boundary element method. In particular, we consider the application of several variants of the conjugate-gradient method to these systems and present some numerical results which shows that a simple preconditioning strategy can lead to significant improvements in solution times.

In this work, a numerical method has been developed to investigate the adhesionless contact mechanics between rough surfaces. To solve the elastic problem a boundary elements approach is used with self-equilibrated square elements. The domain of integration is discretized developing an “intelligent” adaptive mesh and obtaining a considerable memory saving. The numerical convergence of the method has been verified by comparing the results with the Hertzian solution and by checking the stress probability distribution at the contact interface. The methodology has been then utilized to analyse the contact between an elastic flat substrate and a periodic numerically generated self-affine fractal rigid surface. The fractal surface has been generated by employing spectral methods. The results of our investigation supports the findings of some analytical theories ( Persson, 2001 ) and numerical findings ( Yang et al., 2006 , Hyun et al., 2004 , Carbone and Bottiglione, 2008 , Campana and Muser, 2007 ) in terms of linearity between contact area and load and stress probability distributions.

The present work shows the propagation of Scholte interface waves at the boundary of a fluid in contact with an elastic solid, for a broad range of solid materials. It has been demonstrated that by an analysis of diffracted waves in a fluid it is possible to infer the mechanical properties of the elastic solid medium, specifically, its propagation velocities. For this purpose, the diffracted wave field of pressures and displacements, due to an initial wave of pressure in the fluid, are expressed using boundary integral representations, which satisfy the equation of motion. The source in the fluid is represented by a Hankel’s function of second kind and zero order. The solution to this wave propagation problem is obtained by means of the Indirect Boundary Element Method, which is equivalent to the well-known Somigliana representation theorem. The validation of the results is carried out by using the Discrete Wave Number Method and the Spectral Element Method. Firstly, we show spectra of pressures that illustrate the behavior of the fluid for each solid material considered, then, we apply the Fast Fourier Transform to show results in time domain. Snapshots to exemplify the emergence of Scholte’s waves are also included.

A new technique for treating surface discontinuities within boundary element calculations is proposed. Multiple nodes are used to represent the geometry, and the necessary additional equations are obtained by differentiating the usual boundary element integral equation. In deriving expressions for the resulting singular integrals, it is found that constraints must be placed on the functional approximation at the discontinuity. An algorithm for incorporating these constraints is developed and numerical tests for an exactly solvable three-dimensional Laplace equation problem are presented.

An iterative variation of the linear-element complex variable boundary element method (CVBEM) is used to generate grid points in two-dimensional simply connected spatial domains. As in many grid generation techniques, the solution of Laplace's equation is involved; however, the boundary element formulation results in a much smaller set of simultaneous equations, and once the values of the complex potential at the boundaries are fully determined, the internal grid point distribution can be altered without resolving the elliptic system. The boundary conditions implemented produce grid line orthogonality at the domain boundaries. Additionally, by using complex variables in the formulation, numerical integration is avoided. The utility of the method is demonstrated by (1) generating grid systems for several irregular geometries and (2) obtaining a numerical solution for the flow field associated with one of the geometries.

A weak formulation for ‘direct’ boundary methods, deduced from distribution theory, is presented. The present approach seems particularly profitable when dealing with problems having non-integrable singularities. Numerical examples are also reported for plane elasticity.

This paper describes a method for the numerical solution of a Riabouchinsky cavity flow. Application of a boundary element method leads to a system of non‐linear equations. The mild singularity appearing at the separation point is treated with the introduction of a curved boundary element, which satisfies the exact behaviour of the free boundary in that neighbourhood. Copyright © 1988 John Wiley & Sons, Ltd 8 1 91 96 Cited By :8

In this paper an analytical integration scheme is described that is designed to reduce the errors resulting from the numerical evaluation of integrals with singular integrands. The analytical scheme can be applied to linear triangular elements for use in elastostatic problems and is particularly useful for predicting distortion, to high accuracy, close to surfaces. It is demonstrated that although the analytical scheme takes longer computationally than the usual quadrature approach it is quicker when element subdivision is required to achieve reasonable accuracy. Numerical tests are performed on a simple test problem to demonstrate the advantages of the analytical approach, which is shown to be orders of magnitude more accurate than standard quadrature techniques.

A weak form to computate the dipolar and monopolar surface gradients, related to a low order panel method, is shown. The flow problem is formulated by means of a three-dimensional potential model and the discretization is based on Morino´s formulation for the perturbation velocity potential. On the body surface this representation reduces to a boundary integral equation with the source (or monopolar) and the doublet (or dipolar) densities. The first of them is found by application of the boundary flow condition, and the second one is the unknown over the body surface. A lower panel method is used for the analytic integrations of both the monopolar and dipolar influence coefficients. The surface velocity field is computed after solving the linear system, with a strong and a weak form of the Stokes theorem, which is oriented to fairly non-structured panel meshes. The proposed method is validated by comparing the numerical results with analytical ones for an isolated sphere and includes a prediction over a car-like configuration. Fil: D'elia, Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina Fil: Storti, Mario Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina Fil: Idelsohn, Sergio Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina