A state space formalism for piezothermoelasticity

Abstract

A state space formalism for electrothermoelastic analysis of a linear piezoelectric body is developed. A novel feature of the formalism is that by proper grouping of the field variables and using matrix notations the three-dimensional equations of piezothermoelasticity are concisely formulated into a state equation and an output equation, which bear a striking resemblance to their elastic counterparts. The formalism is remarkably simple, with which one deals with only three vector quantities with the 13 independent electromechanical variables as their components and six submatrices that represent all the material constants for a piezoelectric material of the most general kind. In this work emphasis is placed on the state space formulation and solution to the generalized plane problem. Exact solutions for a piezoelectric half-space under a line of electromechanical loading and an infinite piezoelectric plate with an elliptical notch subjected to inplane loads are determined with relative ease. In many cases, piezoelectric solutions can be obtained directly from the corresponding elastic solutions by a simple replacement of the corresponding matrices on the basis of the formalism.