Crack Analysis in Piezoelectric Solids with Energetically Consistent Boundary Conditions by the MLPG
J. Sladek; V. Sladek; Ch. Zhang; M. Wünsche

doi:10.3970/cmes.2010.068.185
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 68, No. 2, pp. 185-220, 2010
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Keywords Meshless local Petrov-Galerkin method (MLPG), Moving least-squares (MLS) interpolation, piezoelectric solids, functionally graded materials, intensity factors, dynamic loading
Abstract A meshless method based on the local Petrov-Galerkin approach is proposed to solve initial-boundary value crack problems of piezoelectric solids with nonlinear electrical boundary conditions on crack faces. Homogeneous and continuously varying material properties of the piezoelectric solid are considered. Stationary governing equations for electrical fields and the elastodynamic equations with an inertial term for mechanical 2-D fields are considered. Nodal points are spread on the analyzed domain, and each node is surrounded by a small circle for simplicity. The spatial variation of displacements and electric potential are approximated by the Moving Least-Squares (MLS) scheme. After performing the spatial integrations, one obtains a system of ordinary differential equations for certain nodal unknowns. That system is solved numerically by the Houbolt finite-difference scheme as a time-stepping method. An iterative solution algorithm is developed to consider the energetically consistent crack-face boundary conditions. The accuracy of the present method for computing the stress intensity factors (SIF) and electrical displacement intensity factor (EDIF) are discussed by comparison with available analytical or numerical solutions.
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