Solving anti-plane problems of piezoelectric materials by the Trefftz finite element approach

Applications of the Trefftz finite element method to anti-plane electroelastic problems are presented in this paper. A dual variational functional is constructed and used to derive Trefftz finite element formulation. Special trial functions which satisfy boundary conditions are also used to develop a special purpose element with local defects. The performance of the proposed element model is assessed by an example and comparison is made with results obtained by other approaches. The Trefftz finite element approach is demonstrated to be ideally suited for the analysis of the anti-plane problem.