Hybrid Finite Element Models for Piezoelectric Materials

Abstract

In this paper, hybrid variational principles are employed for piezoelectric "nite 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 coe$cients 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 e!ective in improving the element accuracy. 1999 Academic Press 0022-460X/99/380519#29 $30.00/0 522 K. Y. SZE AND Y. S. PAN

A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation

“…Hybrid and mixed approaches are also presented in [30,31,16,17]. Miranda and Ubertini [30] discuss the fully compatible approach in comparison to a hybrid approach.…”

“…The electric field and the strains are derived from the constitutive equations. Sze and Pan [31] consider the most general variational principle which includes six field variables. Form this general principle they degenerate some variational formulations by eliminating some of the independent fields.…”

A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

“…The bimorph is subjected to an electrical field 1 V m again. The tip deflection, normalized on the analytical solution w 0 = 3.45μm, is depicted in Figure 8, dependent on the distortion parameter s. We compare the results with the data given by Sze and Pan [62] and by Sze and Ghali [63] for the mixed hexahedral elements (H8D and H8DS) and (H8DS*), respectively. Here the elements "H8D" and "H8DS" vary in the number of independent variables.…”

“…The bimorph has a tip deflection of w = 3.45μm, which corresponds to the solution of an analytical calculation with a Bernoulli beam, see Tzou [61]. In order to analyze the influence of mesh distortion, the finite element mesh of the bimorph is modified according to Sze und Pan [62]. The initial configuration has four rectangular elements.…”

“…Shell formulations incorporating a quadratic thickness potential can be found in References [16,8,7]. Mixed shell formulations including independent fields for the electric potential, the electric field, the dielectric displacement as well as the mechanical fields of the displacement, the strain, and the stress can be found in [19]. Accounting for nonlinear material behavior, the polarization state has to be analyzed.…”