A New Regularized Boundary Integral Formulation for Thin Elastic Plate Bending Analysis

Matsumoto, Toshiro; Tanaka, Masataka; Hondoh, Koji

doi:10.1007/978-94-011-3696-9_42

Cited by 3 publications

(1 citation statement)

References 3 publications

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“…The remaining equation after the limiting process, i.e. equation (8), is insufficient in determining all the unknowns ( u and u across the crack, or u on the two surfaces). The remedy to this degeneracy is either to avoid it by using the multi-region BIE approach in some cases or to employ the hypersingular BIEs.\…”

Section: D> \ U\p ( I!d>)u\mentioning

confidence: 99%

Analysis of shell-like structures by the Boundary Element Method based on 3-D elasticity: formulation and verification

Liu

1998

Int. J. Numer. Meth. Engng.

148

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In this paper, the Boundary Element Method (BEM) for 3-D elastostatic problems is studied for the analysis of shell or shell-like structures. It is shown that the conventional boundary integral equation (CBIE) for 3-D elasticity does not degenerate when applied to shell-like structures, contrary to the case when it is applied to crack-like problems where it does degenerate due to the closeness of the two crack surfaces. The treatment of the nearly singular integrals, which is a crucial step in the applications of BIEs to thin shapes, is presented in detail. To verify the theory, numerical examples of spherical and ellipsoidal vessels are presented using the BEM approach developed in this paper. It is found that the system of equations using the CBIE is well conditioned for all the thickness studied for the vessels. The advantages, disadvantages and potential applications of the proposed BEM approach to shell-like structures, as compared with the FEM regarding modelling and accuracy, are discussed in the last section. Applications of this BEM approach to shell-like structures with non-uniform thickness, stiffeners and layers will be reported in a subsequent paper.

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Section: D> \ U\p ( I!d>)u\mentioning

confidence: 99%

Analysis of shell-like structures by the Boundary Element Method based on 3-D elasticity: formulation and verification

Liu

1998

Int. J. Numer. Meth. Engng.

148

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Regularization of hypersingular and nearly singular integrals in the potential theory and elasticity

Sládek

Tanaka

1993

Numerical Meth Engineering

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107

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SUMMARYBoth the hypersingular and nearly singular integrals, which appear in the hypersingular boundary integral equations and integral representations of the secondary fields, respectively, are regularized by the application of the superposition principle. Two kinds of the non-singular formulations, namely, those with the strongly singular and weakly singular kernels, are presented in this paper. The formulations are given in terms of the relevant boundary quantities and the collocation at element junctions is possible. Two-and three-dimensional problems are analysed simultaneously in a unique way for either internal or external problems of the potential theory and elasticity.

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A boundary element method applied to the elastostatic bending problem of beam-stiffened plates

Tanaka¹,

Matsumoto²,

Oida³

2000

Engineering Analysis with Boundary Elements

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A New Regularized Boundary Integral Formulation for Thin Elastic Plate Bending Analysis

Cited by 3 publications

References 3 publications

Analysis of shell-like structures by the Boundary Element Method based on 3-D elasticity: formulation and verification

Analysis of shell-like structures by the Boundary Element Method based on 3-D elasticity: formulation and verification

Regularization of hypersingular and nearly singular integrals in the potential theory and elasticity

A boundary element method applied to the elastostatic bending problem of beam-stiffened plates

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