Analysis of Piezoelectric Semiconducting Solids by Meshless Method

In this paper, a meshless local Petrov-Galerkin (MLPG) method is proposed to calculate mechanical and electrical responses of three-dimensional piezoelectric semiconductors under static load. The analyzed solid is discretized by a set of generally distributed nodal points distributed over 3D geometry. Local integral equations (LIEs) are derived from the weak form of governing equations over small local subdomains. The subdomains have a spherical shape with a nodal point located in its centre. A unit step function is used as the test functions in the local weak-form. The moving least-squares (MLS) method is adopted for the approximation of the physical quantities in the LIEs. The proposed MLPG method is verified by using the corresponding results obtained with the finite element method. Numerical examples are presented and discussed for various boundary conditions and loading scenarios to show the performance of the developed MLPG method for analysis piezoelectric semiconducting solids.