Shape sensitivity analysis of piezoelectric structures by the adjoint variable method

Abstract

Shape sensitivity expressions are derived for linear piezoelectric structures with coupled mechanical and elastic fields. By adopting the quasielectrostatic approximation for these inherently anisotropic materials, the adjoint variable method of optimization and the material derivative formulation of shape variations are used in a systematic procedure to evaluate the total variation of a general performance criterion with respect to shape variations. The material (total) derivative of the adopted integral functional is found in terms of primary and adjoint quantities, as well as the deformation velocity field. Since the structure is assumed to undergo dynamic response, domain integrations evaluated at the initial time are also needed in this formulation.