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Meshless Local Petrov-Galerkin Method in Anisotropic Elasticity

J. Sladek1, V. Sladek1, S.N. Atluri2
Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia
Center of Aerospace Education & Research University of California, 5251 California Ave., Irvine, CA 92612, USA

Computer Modeling in Engineering & Sciences 2004, 6(5), 477-490. https://doi.org/10.3970/cmes.2004.006.477

Abstract

A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in a homogeneous anisotropic medium. The Heaviside step function is used as the test functions in the local weak form. It is leading to derive local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace transfor technique is applied and the LBIEs are given in the Laplace transform domain. The analyzed domain is covered by small subdomains with a simple geometry such as circles in 2-d problems. The final form of local integral equations has a pure contour character only in elastostatics. In elastodynamics an additional domain integral is involved due to inertia terms. The moving least square (MLS) method is used for approximation of physical quantities in LBIEs.

Keywords

meshless method, local weak form, Heaviside step function, moving least squares interpolation, Laplace transform

Cite This Article

Sladek, J., Sladek, V., Atluri, S. (2004). Meshless Local Petrov-Galerkin Method in Anisotropic Elasticity. CMES-Computer Modeling in Engineering & Sciences, 6(5), 477–490.



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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