EXPLICIT SOLUTIONS FOR AN ANISOTROPIC PIEZOELECTRIC HALF-SPACE SUBJECT TO LINEARLY-VARYING SURFACE LOADINGS ALONG x₃-DIRECTION

Abstract

Explicit results for a piezoelectric half-space x 2 ≥ 0 subject to linearly-varying surface loadings along x 3 axis are derived. The extended Stroh formalism is employed to provide three-dimensional solutions with the generalized displacement vector u expressed as a function of (z, x 2 , x 3 ). A general polynomial solution for u with order of m in x 3 is suggested and it provides a particularly efficient solution for half-space problem with loadings on the surface. A simple uniform surface loading is considered first to clarify the derivations. Then explicit solution in case of a linearly-varying surface loading along x 3 -direction is obtained. In addition, the Green's function for a piezoelectric half-space with a linearly-varying surface line loading along x 3 -axis is constructed.