Abstract
In the present paper, the meshless local Petrov‐Galerkin (MLPG) method is applied to cracked piezoelectric solids under a stationary or transient dynamic load and unspecified electrical conditions on the crack surfaces. On the outer surface of the cracked solid the electrical boundary conditions are over‐specified. The coupled governing partial differential equations are satisfied in a weak‐form on small fictitious sub‐domains. Nodal points are introduced and spread on the analyzed domain and each node is surrounded by a small circle for simplicity, but without loss of generality. The spatial variations of the displacements and the electric potential are approximated by the Moving Least‐Squares (MLS) scheme. After performing the spatial integrations, a system of linear algebraic equations for unknown nodal values is obtained. Singular value decomposition (SVD) is applied to solve the ill‐conditioned linear system of algebraic equations obtained from the local integral equations (LIEs) after the MLS approximation.
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