Mathematical analysis of a quasistatic frictionless antiplane contact problem for piezoelectric materials

Abstract

In this thesis ,we consider a mathematical model describing the antiplane shear deformation of a piezoelectric cylinder in frictionless contact with a conductive foundation. The material is assumed to be electro-elastic, and homogeneous properties, and the process is modeled as quasistatic. This work is divided into three chapters. First, we present preliminary results from functional analysis and partial differential equations, which lay the mathematical foundation for the subsequent analysis. Next, the second chapter focuses on the mathematical modeling of the antiplane shear deformation problem, electro-elastic homogeneity under quasistatic assumptions. Finally, the third chapter establishes derive a variational formulation of the models which ares given by a system coupling two variational equations for the displacement and the electric potential fields . By using the Banach space,Lax-Milgram theorem, we prove the existence and uniqueness of a weak solution to the problem