Open Access

ARTICLE

Elastic analysis in 3D anisotropic functionally graded solids by the MLPG

J. Sladek¹, V. Sladek¹, P. Solek²

1 Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia
2 Department of Mechanics, Slovak Technical University, 81243 Bratislava, Slovakia

Computer Modeling in Engineering & Sciences 2009, 43(3), 223-252. https://doi.org/10.3970/cmes.2009.043.223

Abstract

A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in 3-D continuously non-homogeneous anisotropic bodies. Functionally graded materials (FGM) are multi-phase materials with the phase volume fractions varying gradually in space, in a pre-determined profile. The Heaviside step function is used as the test functions in the local weak form resulting into the derived local integral equations (LIEs). For transient elastodynamic problems either the Laplace transform or the time difference techniques are applied. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by a spherical subdomain to which a local integral equation is applied. The final form of the local integral equations has a pure contour character only in elastostatics. In elastodynamics an additional domain integral is involved due to inertia terms. The spatial variation of the displacement is approximated by the moving least-square (MLS) scheme.

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Keywords

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