Analytical transformation of the volume integral in the boundary integral equation for 3D anisotropic elastostatics involving body force

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Abstract

In the boundary element method (BEM), it is well known that the presence of body force shall give rise to an additional volume integral that conventionally requires domain discretization for numerical computations. To restore the BEM's distinctive notion of boundary discretization, the present work analytically transforms the volume integral to surface ones for the body-force effect in the 3D anisotropic elasticity. On applying Green's Theorem, new fundamental solutions with explicit forms of Fourier series are introduced to facilitate the volume-to-surface transformation. The coefficients of the Fourier-series representations are determined by solving a banded matrix formulated from integrations of the constrained equation. Of no doubt, such an approach has fully restored the boundary element method as a truly boundary solution technique for analyzing 3D anisotropic elasticity involving body force. At the end, numerical verifications of the volume-to-surface integral transformation are presented. Also, such an approach has been implemented in an existing BEM code. For demonstrating the implementation, numerical examples are presented with comparisons with ANSYS analysis. To the author's knowledge, this is the first work in the open literature that reports the successful transformation for 3D anisotropic elasticity.

Original languageEnglish
Pages (from-to)404-422
Number of pages19
JournalComputer Methods in Applied Mechanics and Engineering
Volume278
DOIs
Publication statusPublished - 2014 Aug 5

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elastostatics
Boundary integral equations
Boundary element method
integral equations
Elasticity
boundary element method
Fourier series
elastic properties
integral transformations
Green's functions
coefficients
matrices

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Cite this

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title = "Analytical transformation of the volume integral in the boundary integral equation for 3D anisotropic elastostatics involving body force",
abstract = "In the boundary element method (BEM), it is well known that the presence of body force shall give rise to an additional volume integral that conventionally requires domain discretization for numerical computations. To restore the BEM's distinctive notion of boundary discretization, the present work analytically transforms the volume integral to surface ones for the body-force effect in the 3D anisotropic elasticity. On applying Green's Theorem, new fundamental solutions with explicit forms of Fourier series are introduced to facilitate the volume-to-surface transformation. The coefficients of the Fourier-series representations are determined by solving a banded matrix formulated from integrations of the constrained equation. Of no doubt, such an approach has fully restored the boundary element method as a truly boundary solution technique for analyzing 3D anisotropic elasticity involving body force. At the end, numerical verifications of the volume-to-surface integral transformation are presented. Also, such an approach has been implemented in an existing BEM code. For demonstrating the implementation, numerical examples are presented with comparisons with ANSYS analysis. To the author's knowledge, this is the first work in the open literature that reports the successful transformation for 3D anisotropic elasticity.",
author = "Yui-Chuin Shiah",
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publisher = "Elsevier",

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T1 - Analytical transformation of the volume integral in the boundary integral equation for 3D anisotropic elastostatics involving body force

AU - Shiah, Yui-Chuin

PY - 2014/8/5

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N2 - In the boundary element method (BEM), it is well known that the presence of body force shall give rise to an additional volume integral that conventionally requires domain discretization for numerical computations. To restore the BEM's distinctive notion of boundary discretization, the present work analytically transforms the volume integral to surface ones for the body-force effect in the 3D anisotropic elasticity. On applying Green's Theorem, new fundamental solutions with explicit forms of Fourier series are introduced to facilitate the volume-to-surface transformation. The coefficients of the Fourier-series representations are determined by solving a banded matrix formulated from integrations of the constrained equation. Of no doubt, such an approach has fully restored the boundary element method as a truly boundary solution technique for analyzing 3D anisotropic elasticity involving body force. At the end, numerical verifications of the volume-to-surface integral transformation are presented. Also, such an approach has been implemented in an existing BEM code. For demonstrating the implementation, numerical examples are presented with comparisons with ANSYS analysis. To the author's knowledge, this is the first work in the open literature that reports the successful transformation for 3D anisotropic elasticity.

AB - In the boundary element method (BEM), it is well known that the presence of body force shall give rise to an additional volume integral that conventionally requires domain discretization for numerical computations. To restore the BEM's distinctive notion of boundary discretization, the present work analytically transforms the volume integral to surface ones for the body-force effect in the 3D anisotropic elasticity. On applying Green's Theorem, new fundamental solutions with explicit forms of Fourier series are introduced to facilitate the volume-to-surface transformation. The coefficients of the Fourier-series representations are determined by solving a banded matrix formulated from integrations of the constrained equation. Of no doubt, such an approach has fully restored the boundary element method as a truly boundary solution technique for analyzing 3D anisotropic elasticity involving body force. At the end, numerical verifications of the volume-to-surface integral transformation are presented. Also, such an approach has been implemented in an existing BEM code. For demonstrating the implementation, numerical examples are presented with comparisons with ANSYS analysis. To the author's knowledge, this is the first work in the open literature that reports the successful transformation for 3D anisotropic elasticity.

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