Analysis of piezoelectric materials and anisotropic materials subjected to arbitrary loads at the boundary (Similar formulation in elliptical plate problem and elliptical cavity problem)

Abstract

This paper presents general solutions for piezoelectric materials and anisotropic materials subjected to arbitrary loads at the boundary. General solutions are provided by using complex functions based on Lekhnitskii formalism. In the analysis, similarities of fundamental equation between piezoelectric materials and anisotropic materials are shown. By defining new similarity-based complex functions, expressions of mechanical and electrical quantities are derived by analogous form. It is shown that expression forms of electric displacement in piezoelectric materials are corresponding to those of out-of-plane share stress in anisotropic materials. And stress distribution, electric displacement distribution and coupling effect are shown by graphical representation from several analysis results.