Meshless Local Petrov-Galerkin Method for Stress and Crack Analysis in 3-D Axisymmetric FGM Bodies
J. Sladek, V. Sladek, J. Krivacek; Ch. Zhang

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 8, No. 3, pp. 259-270, 2005
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Keywords Meshless method, local weak-form, unit step function, moving least-squares approximation, Laplace-transform, functionally graded materials (FGMs), transient elastodynamics, crack problems
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$(x_1 ,x_3 )$-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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