Hybrid finite element models for piezoelectric materials

In this paper, hybrid variational principles are employed for piezoelectric finite element formulation. Starting from eight-node hexahedral elements with displacement and electric potential as the nodal d.o.f.s, hybrid models with assumed stress and electric displacement are devised. The assumed stress and electric displacement are chosen to be contravariant with the minimal 18 and seven modes respectively. The pertinent coefficients can be condensed at the element level and do not enter the system equation. A number of benchmark tests are exercised. The predicted results indicate that the assumed stress and electric displacements are effective in improving the element accuracy. (C) 1999 Academic Press.