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Interface Crack Problems in Anisotropic Solids Analyzed by the MLPG

J. Sladek1, V. Sladek1, M. Wünsche2, Ch. Zhang2
Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia, sladek@savba.sk
Department of Civil Engineering, University of Siegen, D-57068 Siegen, Germany

Computer Modeling in Engineering & Sciences 2009, 54(2), 223-252. https://doi.org/10.3970/cmes.2009.054.223

Abstract

A meshless method based on the local Petrov-Galerkin approach is proposed, to solve the interface crack problem between two dissimilar anisotropic elastic solids. Both stationary and transient mechanical and thermal loads are considered for two-dimensional (2-D) problems in this paper. A Heaviside step function as the test functions is applied in the weak-form to derive local integral equations. Nodal points are spread on the analyzed domain, and each node is surrounded by a small circle for simplicity. The spatial variations of the displacements and temperature are approximated by the Moving Least-Squares (MLS) scheme. After performing the spatial integrations, one obtains a system of ordinary differential equations for certain nodal unknowns. The backward finite difference method is applied for the approximation of the diffusive term in the heat conduction equation. Then, the system of the ordinary differential equations of the second order resulting from the equations of motion is solved by the Houbolt finite-difference scheme as a time-stepping method.

Keywords

Meshless local Petrov-Galerkin method (MLPG), moving least-squares approximation, anisotropic materials, Houbolt method, backward finite difference method

Cite This Article

Sladek, J., Sladek, V., Wünsche, M., Zhang, C. (2009). Interface Crack Problems in Anisotropic Solids Analyzed by the MLPG. CMES-Computer Modeling in Engineering & Sciences, 54(2), 223–252.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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