Fracture Analyses in Continuously Nonhomogeneous Piezoelectric Solids by the MLPG
J. Sladek; V. Sladek; Ch. Zhang; P. Solek; and L. Starek

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 19, No. 3, pp. 247-262, 2007
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Keywords Meshless local Petrov-Galerkin method (MLPG), Moving least-squares (MLS) interpolation, piezoelectric solids, functionally graded materials, 2-D and 3-D axisymmetric problems
Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-D) and three-dimensional (3-D) axisymmetric piezoelectric solids with continuously varying material properties. Axial symmetry of geometry and boundary conditions reduces the original 3-d boundary value problem into a 2-d problem. Stationary problems are considered in this paper. The axial cross section is discretized into small circular subdomains surrounding nodes randomly spread over the analyzed domain. A unit step function is used as the test functions in the local weak-form. Then, the derived local integral equations (LBIEs) involve only contour-integrals on the surfaces of subdomains. The moving least-squares (MLS) method is adopted for the approximation of the physical quantities in the LBIEs. The accuracy of the present method for computing the stress intensity factors (SIF) and electrical displacement intensity factors (EDIF) are discussed by comparison with available analytical or numerical solutions.
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