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

Abstract

This paper is concerned with a geometrically nonlinear solid shell element to analyze piezoelectric structures. The finite element formulation is based on a variational principle of the Hu-Washizu type and includes six independent fields: displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. The element has 8 nodes with 4 nodal degrees of freedoms, 3 displacements and the electric potential. A bilinear distribution through the thickness of the independent electric field is assumed to fulfill the electric charge conservation law in bending dominated situations exactly. The presented finite shell element is able to model arbitrary curved shell structures and incorporates a 3D-material law. A geometrically nonlinear theory allows large deformations and includes stability problems. Linear and nonlinear numerical examples demonstrate the ability of the proposed model to analyze piezoelectric devices.

Hybrid asymptotic–direct approach to finite deformations of electromechanically coupled piezoelectric shells

“…8. The same problem has been studied by Klinkel et al [52], using a solid shell finite element formulation. The sphere has an inner radius of 0.1 m and consists of a steel kernel sandwiched between two PZT-4 ceramic layers with the thickness values (0.25; 0.5; 0.25) × 10 −3 m; perfect bonding of the layers is assumed.…”

“…This results in an ill-conditioned boundary value problem, such that particular care had to be taken in order to obtain numerically accurate results when solving it using the shooting method. For the sake of comparing the results to the literature, we used the material parameters from [52] when computing the structural properties of the through-the-thickness element of the shell according to the procedure presented in Appendix A.…”

Numerical Modeling of Flow-Driven Piezoelectric Energy Harvesting Devices

“…Mixed and hybrid finite element formulations are presented in [13,14,15,16]. These formulations contain additional unknown fields besides mechanical displacements and electrical potential which reduces locking phenomena and makes the elements less susceptible to mesh distortion.…”

“…Further mixed formulations with three and four unknown fields are derived from the six field formulation. A six field formulation is used by [15,16] with additional enhancements for strain and electric field which further reduce locking.…”

Frictional contact of an anisotropic piezoelectric plate

“…The material parameters are taken from the Tables VIII and XI in [19]. Both layers are assumed to be of the same thickness h = 0.01 leading to a plate of thickness 0.02.…”