Efficient analytical integration of symmetric Galerkin boundary integrals over curved elements; elasticity formulation

Balakrishna, C.; Gray, L. J.; Kane, J. H.

doi:10.1016/0045-7825(94)90081-7

Cited by 28 publications

(29 citation statements)

References 9 publications

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“…In fact, one has E (y, ε) = E in the disjoint case (17) and for sufficiently small ε, which is thus included in this setting.…”

Section: Double Integration: Preliminary Definitionsmentioning

confidence: 99%

“…All formulations of SGBEM based on regularization of the kernels before performing the limit, like in [11,12,13,14,15], do not provide free terms at all (and this is indeed one of their advantages). The same is true for the limit to the boundary method [16,17,18]. On the other hand, techniques based on the finite part idea [19,20,21] completely overlook the free term evaluation, as the 'bump' associated to the vanishing neighbourhood is never taken into account.…”

Section: Hypersingular Free Term Final Expressionmentioning

confidence: 99%

“…Regularization via integration by parts has been also presented in [15] for Kirchhoff plates. Another approach for the evaluation of singular integrals, often called limit to the boundary, was presented for SGBEM by Balakrishna et al in [16,17]. Recent developments on this technique can be found in [18].…”

Section: Introductionmentioning

confidence: 99%

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Galerkin BEM with Direct Evaluation of Hypersingular Integrals

Bonnet

Guiggiani

2007

EJBE

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In this paper a new general algorithm is presented for the direct evaluation of all singular double integrals arising in the 2D Galerkin BEM, including those with hypersingular kernels. A distinguishing feature of the proposed method is that double singular integrals are treated as a whole, that is not as inner integrals followed by outer ones. Therefore, when applied to the symmetric Galerkin BEM, the proposed technique is strictly symmetry preserving. Moreover, a careful analysis of the limiting process is performed which shows that some new free terms may arise.

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“…In fact, one has E (y, ε) = E in the disjoint case (17) and for sufficiently small ε, which is thus included in this setting.…”

Section: Double Integration: Preliminary Definitionsmentioning

confidence: 99%

Section: Hypersingular Free Term Final Expressionmentioning

confidence: 99%

See 1 more Smart Citation

Galerkin BEM with Direct Evaluation of Hypersingular Integrals

Bonnet

Guiggiani

2007

EJBE

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“…Let ∆u = u E − u I and ∆t = −t E − t I denote respectively the displacement and traction jumps accross ∂Ω (note that t I and t E are defined in terms of the opposite normals n and n, and also that ∆u should be continuous over ∂Ω and satisfy (12)). Thus, due to the linearity of B uu , etc.…”

Section: Indirect Variational Bie Formulationmentioning

confidence: 99%

“…One possibility is a proper direct handling of the strongly singular and hypersingular simple surface integrals that appear, using either a numerical method (Guiggiani et al [9]) or analytical integration of the singularity (Sirtori et al [21], Balakrishna et al [12]; the latter used symbolic computation). Another possibility is to perform, as is done here, an analytical regularization before any discretization.…”

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confidence: 99%

Regularized direct and indirect symmetric variational BIE formulations for three-dimensional elasticity

Bonnet

1995

Engineering Analysis with Boundary Elements

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A symmetric Galerkin multi-zone boundary element formulation

Layton

Ganguly

Balakrishna

et al. 1997

Int. J. Numer. Meth. Engng.

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The recent development of the symmetric Galerkin approach to boundary element analysis (BEA) has been demonstrated to be superior to the collocation method for medium to large problems. This fact has been shown in both heat conduction and elasticity. Accounts of collocation multi‐zone analysis techniques have also been prevalent in the literature, dealing with multiple boundary integral relations associated with portions of overall objects. This technique results in overall system matrices with a blocked, sparse, but unsymmetric character. It has been shown that multi‐zone techniques can produce smaller solution times than a single zone analysis for large problems. These techniques are useful for multi‐material problems as well. This paper presents an approach for combining the benefits of both techniques resulting in a Galerkin multi‐zone method, that is overall unsymmetric but contains a significant amount of block symmetry. A condensation technique in the multi‐zone solver is shown to exploit the symmetry of the Galerkin formulation as well as the blocked sparsity of the multi‐zone technique. This method is compared to collocation multi‐zone on two elasticity problems from the literature. It is concluded that an appropriate implementation of the symmetric Galerkin multi‐zone BEA indeed has the potential to be superior to the collocation based multi‐zone BEA, for medium to large‐scale elasticity problems. © 1997 John Wiley & Sons, Ltd.

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Efficient analytical integration of symmetric Galerkin boundary integrals over curved elements; elasticity formulation

Cited by 28 publications

References 9 publications

Galerkin BEM with Direct Evaluation of Hypersingular Integrals

Galerkin BEM with Direct Evaluation of Hypersingular Integrals

Regularized direct and indirect symmetric variational BIE formulations for three-dimensional elasticity

A symmetric Galerkin multi-zone boundary element formulation

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