Abstract
ABSTRACTThe 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 actuator 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.
Highlights
The direct and reverse piezoelectric effects allow to transform mechanical energy into electrical energy and vice versa
When it comes to design and control of piezoelectric structures, simulation results are of high interest
The finite element discretization leads to a system with a huge number of eigenvalues of which typically only a few of the smallest are of interest
Summary
The direct and reverse piezoelectric effects allow to transform mechanical energy into electrical energy and vice versa. Allik and Huges [1] and later Lerch [2] carried out first simulations using volume elements based on the principle of virtual work. These elements are an extension of standard small-strain mechanical elements by degrees of freedom for the electric potential. Pechstein and Schoberl [13] introduced an arbitrary order mixed FE-method for linear elasticity based on a Hellinger-Reissner formulation, which uses tangential displacements and normal normal stresses as degrees of freedom (TDNNSmethod). This method was shown to be locking-free [14], and later extended to piezoelectric materials [15].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
