TY - JOUR

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

AU - Shiah, Y. C.

N1 - Funding Information:
The author gratefully acknowledges the financial support for this work from the National Science Council of Taiwan ( NSC 102-2221-E-006-290-MY3 ).

PY - 2014/8/5

Y1 - 2014/8/5

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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U2 - 10.1016/j.cma.2014.05.013

DO - 10.1016/j.cma.2014.05.013

M3 - Article

AN - SCOPUS:84944868344

VL - 278

SP - 404

EP - 422

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

ER -