3D mixed finite elements for curved, flat piezoelectric structures
For engineers modeling piezoelectric patch actuators and sensors, this method provides efficient and accurate simulation of curved thin structures, but the contribution is incremental as it extends an existing method to new geometries.
The paper extends the TDNNS finite element method to curved, flat piezoelectric structures, demonstrating that hexahedral and prismatic elements of arbitrary polynomial order can model thin, curved geometries efficiently without shear locking, achieving good agreement with ABAQUS for displacements, electric potential, stresses, strains, and electric field using only one element in thickness direction.
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.