3D mixed finite elements for curved, flat piezoelectric structures

TL;DR

This paper extends the TDNNS finite element method to curved, shell-like piezoelectric structures, enabling efficient modeling of thin, curved geometries with high accuracy and independent geometry and polynomial orders.

Contribution

The paper introduces high-order curved hexahedral and prismatic elements for the TDNNS method, suitable for complex shell-like piezoelectric geometries.

Findings

Good agreement with ABAQUS results for displacements and electric potential.

Effective modeling of curved geometries with high aspect ratio elements.

Accurate stress, strain, and electric field predictions with minimal elements.

Abstract

The Tangential-Displacement Normal-Normal-Stress (TDNNS) method is a finite element method that was originally introduced for elastic solids and later extended to piezoelectric materials. It uses tangential components of the displacement and normal components of the normal stress vector as degrees of freedom for elasticity. For the electric field, the electric potential is used. The TDNNS method has been shown to provide elements which do not suffer from shear locking. Therefore thin structures (e.g. piezoelectric patch actuators) can be modeled efficiently. Hexahedral and prismatic elements of arbitrary polynomial order are provided in the current contribution. We show that these elements can be used to discretize curved, shell-like geometries by curved elements of high aspect ratio. The order of geometry approximation can be chosen independently from the polynomial order of the shape functions. We present two examples of curved geometries, a circular patch actor and a radially polarized piezoelectric semi-cylinder. Simulation results of the TDNNS method are compared to results gained in ABAQUS. We obtain good results for displacements and electric potential as well as for stresses, strains and electric field when using only one element in thickness direction.