### Abstract

Green's functions, or fundamental solutions, are necessary items in the formulation of the boundary integral equation (BIE), the analytical basis of the boundary element method (BEM). In the formulation of the BEM for 3D general anisotropic elasticity, considerable attention has been devoted to developing efficient algorithms for computing these quantities over the years. The mathematical complexity of this Green's function has also posed an obstacle in the development of this numerical method to treat problems of 3D anisotropic thermoelasticity. This is because thermal effects manifest themselves as an additional domain integral in the integral equation; this has implications for the numerical modeling in BEM. Difficulties in deriving a true BIE arise, unless some simple representations of the thermal effects are used, such as in the dual reciprocity approach. These approximation schemes, however, have some serious limitations. An integral transformation method to obtain an exact BIE has been successfully employed, but only for isotropy and two-dimensional (2D) general anisotropy. The extension of this scheme to three-dimensional (3D) general anisotropy has remained a very serious challenge. This paper reports on the progress towards this end. By following the same steps as for 2D general anisotropy, and using a double-Fourier series representation of the Green's function first proposed by the authors recently, a true BIE is derived for 3D general anisotropic thermoelasticity. Some numerical results are presented to demonstrate the success of this derivation.

Original language | English |
---|---|

Pages (from-to) | 425-447 |

Number of pages | 23 |

Journal | CMES - Computer Modeling in Engineering and Sciences |

Volume | 102 |

Issue number | 6 |

Publication status | Published - 2014 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Software
- Modelling and Simulation
- Computer Science Applications

### Cite this

*CMES - Computer Modeling in Engineering and Sciences*,

*102*(6), 425-447.

}

*CMES - Computer Modeling in Engineering and Sciences*, vol. 102, no. 6, pp. 425-447.

**The boundary integral equation for 3D general anisotropic thermoelasticity.** / Shiah, Yui-Chuin; Tan, C. L.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The boundary integral equation for 3D general anisotropic thermoelasticity

AU - Shiah, Yui-Chuin

AU - Tan, C. L.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Green's functions, or fundamental solutions, are necessary items in the formulation of the boundary integral equation (BIE), the analytical basis of the boundary element method (BEM). In the formulation of the BEM for 3D general anisotropic elasticity, considerable attention has been devoted to developing efficient algorithms for computing these quantities over the years. The mathematical complexity of this Green's function has also posed an obstacle in the development of this numerical method to treat problems of 3D anisotropic thermoelasticity. This is because thermal effects manifest themselves as an additional domain integral in the integral equation; this has implications for the numerical modeling in BEM. Difficulties in deriving a true BIE arise, unless some simple representations of the thermal effects are used, such as in the dual reciprocity approach. These approximation schemes, however, have some serious limitations. An integral transformation method to obtain an exact BIE has been successfully employed, but only for isotropy and two-dimensional (2D) general anisotropy. The extension of this scheme to three-dimensional (3D) general anisotropy has remained a very serious challenge. This paper reports on the progress towards this end. By following the same steps as for 2D general anisotropy, and using a double-Fourier series representation of the Green's function first proposed by the authors recently, a true BIE is derived for 3D general anisotropic thermoelasticity. Some numerical results are presented to demonstrate the success of this derivation.

AB - Green's functions, or fundamental solutions, are necessary items in the formulation of the boundary integral equation (BIE), the analytical basis of the boundary element method (BEM). In the formulation of the BEM for 3D general anisotropic elasticity, considerable attention has been devoted to developing efficient algorithms for computing these quantities over the years. The mathematical complexity of this Green's function has also posed an obstacle in the development of this numerical method to treat problems of 3D anisotropic thermoelasticity. This is because thermal effects manifest themselves as an additional domain integral in the integral equation; this has implications for the numerical modeling in BEM. Difficulties in deriving a true BIE arise, unless some simple representations of the thermal effects are used, such as in the dual reciprocity approach. These approximation schemes, however, have some serious limitations. An integral transformation method to obtain an exact BIE has been successfully employed, but only for isotropy and two-dimensional (2D) general anisotropy. The extension of this scheme to three-dimensional (3D) general anisotropy has remained a very serious challenge. This paper reports on the progress towards this end. By following the same steps as for 2D general anisotropy, and using a double-Fourier series representation of the Green's function first proposed by the authors recently, a true BIE is derived for 3D general anisotropic thermoelasticity. Some numerical results are presented to demonstrate the success of this derivation.

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M3 - Article

AN - SCOPUS:84920509483

VL - 102

SP - 425

EP - 447

JO - CMES - Computer Modeling in Engineering and Sciences

JF - CMES - Computer Modeling in Engineering and Sciences

SN - 1526-1492

IS - 6

ER -