Three-dimensional Analysis for Functionally Graded Piezoelectric Semiconductors by the Local Radial Basis Function Collocation Method

This thesis presents three-dimensional analysis of functionally graded piezoelectric semiconductor by the local radial basis function collocation method (LRBFCM). The LRBFCM is a commonly-used meshless numerical method in the field of engineering and sciences. On account of the advantages of addressing the problems with much different length scales in three dimensions and circumventing numerical quadrature, the LRBFCM is investigated and applied in the problems of piezoelectric materials. Piezoelectric materials can be divided by dielectrics and semiconductors. Unlike piezoelectric dielectric materials, the conservation of charge which is composed of electron density and electric current is additionally considered to depict the phenomenon for piezoelectric semiconductors. This will complicate our analyzing the mutual coupling of elastic displacements and electric fields. For the solution of the set of partial differential equations with non-constant coefficients the LRBFCM is proposed in this work. The spatial variations of all physical fields are approximated by the multiquadric radial basis function. For time dependent problems a resulting system of ordinary differential equations is solved by the Houbolt finite difference scheme as a time stepping method. The presented LRBFCM method is verified by using the corresponding results obtained by the finite element method. The effect of various loading scenarios is then considered in the numerical examples to analyze the mutual properties of the mechanical responses, electrical fields, and electrical current field. The influence of material parameter gradation and initial electron density is then investigated. The transient analysis is also analyzed.