# Temperature and Displacement Discontinuity Boundary Element Method for Analysis of Cracks in Three-Dimensional Isotropic Thermoelastic Media

Temperature and Displacement Discontinuity Boundary Element Method for Analysis of Cracks in Three-Dimensional Isotropic Thermoelastic Media

Zhao, M.H. Dang, H.Y. Li, Y. Fan, C.Y. Xu, G.T.

School of Mechanical Engineering, Zhengzhou University, Zhengzhou, Henan 450001, China

School of Mechanics and Engineering Science, Zhengzhou University, Zhengzhou, Henan 450001, China

Page:
241-249
|
DOI:
https://doi.org/10.2495/CMEM-V5-N3-241-249
N/A
| |
Accepted:
N/A
| | Citation

OPEN ACCESS

Abstract:

For the analysis of cracks in three-dimensional isotropic thermoelastic media, a temperature and displacement discontinuity boundary element method is developed. The Green functions for unit-point temperature and displacement discontinuities are derived, and the temperature and displacement discontinuity boundary integral equations are obtained for an arbitrarily shaped planar crack. Our boundary element method is based on the Green functions for a triangular element. As an application, elliptical cracks are analyzed to validate the developed method. The influence of various thermal boundary conditions is studied.

Keywords:

boundary element method, boundary integral equation method, displacement and temperature discontinuity, Green function, isotropic thermoelastic medium, planar crack, stress intensity factor, thermal boundary condition, triangular element

References

[1] Florence, A.L. & Goodier, J.N., The linear thermoelastic problem of uniform heat flow disturbed by a penny-shaped insulated crack. International Journal of Engineering  Science, 1, pp. 533–540, 1963.

http://dx.doi.org/10.1016/0020-7225(63)90008-9

[2] Rizzo, F.J. & Shippy, D.J., An advanced boundary integral equation method for three-dimensional thermoelasticity. International Journal for Numerical Methods in  Engineering, 11, pp. 1753–1768, 1977. http://dx.doi.org/10.1002/nme.1620111109

[3] Dell’Erba, D.N. & Aliabadi, M.H., On the solution of three-dimensional thermoelastic mix- mode edge crack problems by the dual boundary element method. International Journal of Fracture, 66, pp. 269–285, 2000.

[4] Mukherjee, Y.X., Shah, K. & Mukherjee, S., Thermoelastic fracture mechanics with regularized hypersingular boundary integral equations. Engineering Analysis with Boundary elements, 23, pp. 89–96, 1999.

http://dx.doi.org/10.1016/S0955-7997(98)00064-2

[5] Crouch, S.L., Solution of plane elasticity problems by the displacement discontinuity method. International Journal for Numerical Methods in Engineering, 10, pp. 301–343, 1976.

http://dx.doi.org/10.1002/nme.1620100206

[6] Zhao, M.H., Shen, Y.P., Liu, Y.J. & Liu, G.N., The method of analysis of cracks in three-dimensional transversely isotropic media: boundary integral equation approach. Engineering Analysis with Boundary elements, 21, pp. 169–178, 1998.

http://dx.doi.org/10.1016/S0955-7997(98)00033-2

[7] Zhao, M.H., Fan, C.Y., Liu, T. & Yang, F., Extended displacement discontinuity Green functions for three-dimensional transversely isotropic magneto-electro-elastic media and applications. Engineering Analysis with Boundary Elements, 31, pp. 547–558, 2007. http://dx.doi.org/10.1016/j.enganabound.2006.11.002

[8] Zhao, M.H., Dang, H.Y., Li, Y., Fan, C.Y. & Xu, G.T., Displacement and temperature discontinuity boundary integral equation and boundary element method for analysis of cracks in three-dimensional isotropic thermoelastic media. International Journal of Solids and Structure, 81, pp. 179–187, 2016. http://dx.doi.org/10.1016/j.ijsolstr.2015.11.024

[9] Fan, C.Y., Dang, H.Y. & Zhao, M.H., Nonlinear solution of the PS model for a semi-permeable crack in a 3D piezoelectric medium. Engineering Analysis with Boundary Elements, 46, pp. 23–29, 2014.

http://dx.doi.org/10.1016/j.enganabound.2014.05.003