Development of the boundary element method for 2D piezoelectricity

The analytical and numerical foundations are laid out for the formulation o f the boundary element method (BEM) for plane piezoelectric solids. We exte nd a physical interpretation of Somigliana's identity to piezoelectricity a nd give a direct formulation of the BEM in terms of the continuous distribu tions of point forces/charges and displacement/electric potential discontin uities in the infinite piezoelectric domain. We adopt Stroh's complex varia ble formalism for piezoelectricity to derive the point force/charge and the displacement/electric potential discontinuity, their dipoles and continuou s distributions systematically. The duality relations between the force/cha rge and the displacement/electric potential solutions, embedded in the Stro h formalism, are exploited as the foundations for the analytic and the nume rical approaches to the piezoelectric boundary value problems in two dimens ions. These approaches enable us to solve important problems of piezoelectr icity with arbitrary geometry and composition. (C) 1999 Elsevier Science Lt d. All rights reserved.