Trefftz solutions for piezoelectricity by Lekhnitskiiʹs formalism and boundary-collocation method

In this paper, a solution procedure for plane piezoelectricity is developed by Trefftz boundarycollocation method. Starting with the general plane piezoelectricity solution derived by Lekhnitskii’s formalism, the basic sets of Trefftz functions which satisfy the homogeneous governing equations are derived. Moreover, special sets of Trefftz functions are derived for impermeable elliptical voids, impermeable sharp cracks and permeable sharp cracks with arbitrary orientations with respect to the material poling direction. The functions in the special sets satisfy not only the homogeneous governing equations but also the boundary conditions at the peripheries of the pertinent defects. By adopting Trefftz functions as the trial functions, multi-domain Trefftz boundary-collocation method is formulated. Numerical examples are presented to illustrate the efficacy of the formulation