ANALYSIS OF T-STRESS FOR CRACKS IN 3D LINEAR PIEZOELECTRIC MEDIA

Abstract

This thesis aims to present an accurate and efficient computational scheme for determining the generalized T-stresses of impermeable cracks in a three-dimensional linear piezoelectric infinite medium. A symmetric Galerkin boundary element method (SGBEM), based principally on a weakly-singular generalized traction boundary integral equation, is developed to determine the relative crack-face generalized displacement. Such computed information is then utilized along with the generalized displacement boundary integral equation to obtain the sum of the crack-face generalized displacement. This obtained essential data is then post-processed to extract the generalized T-stresses at any point along the crack front. Use of completely regularized boundary integral equations in the formulation allows the primary unknowns to be approximated by continuous basis functions and, additionally, eases the numerical integration of all involved singular integrals. To further improve the approximation of the near-tip field and lessen the requirement of using fine meshes, special basis functions are utilized in a region adjacent the crack boundary. Extensive numerical experiments for various scenarios are considered and results for certain cases are compared with reference solutions not only to verify the formulation but also to show the ability of the present technique to solve general crack problems.