Open Access

ARTICLE

Meshless Local Petrov-Galerkin Method for Stress and Crack Analysis in 3-D Axisymmetric FGM Bodies

by J. Sladek¹, V. Sladek¹, J. Krivacek¹, Ch. Zhang²

1 Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia
2 Department of Civil Engineering, University of Siegen, D-57068 Siegen, Germany

Computer Modeling in Engineering & Sciences 2005, 8(3), 259-270. https://doi.org/10.3970/cmes.2005.008.259

Abstract

A meshless method based on the local Petrov-Galerkin approach is presented for stress analysis in three-dimensional (3-d) axisymmetric linear elastic solids with continuously varying material properties. The inertial effects are considered in dynamic problems. A unit step function is used as the test functions in the local weak-form. It is leading to local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace-transform technique is applied and the LBIEs are given in the Laplace-transformed domain. Axial symmetry of the geometry and the boundary conditions for a 3-d linear elastic solid reduces the original 3-d boundary value problem into a 2-d problem. The geometry of subdomains is selected as a toroid with a circular cross section in the considered (x₁ ,x₃)-plane. The final form of the local integral equations has a pure contour-integral character only in elastostatic problems. In elastodynamics an additional domain-integral is involved due to inertia terms. The moving least-squares (MLS) method is used for the approximation of physical quantities in LBIEs.

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