Analysis of an interface crack between two dissimilar piezoelectric solids

A meshless method based on the local Petrov–Galerkin approach is proposed, to solve the interface crack problem between two dissimilar piezoelectric solids. Permeable and impermeable electrical boundary conditions are considered on the crack-faces. Quasi-static governing equations for the electrical fields and elastodynamic equations with an inertial term for the 2-D mechanical fields are considered. Nodal points are spread on the analyzed domain, and each node is surrounded by a small circle for simplicity. A Heaviside step function as the test functions is applied in the weak-form on the local subdomain. The local integral equations are derived. The spatial variations of the 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. The system of the ordinary differential equations of the second order resulting from the equations of motion is solved by the Houbolt finite-difference scheme as a time-stepping method.