3D mixed finite elements for curved, flat piezoelectric structures

Autor: Martin Meindlhumer, Astrid Pechstein
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: International Journal of Smart and Nano Materials, Vol 10, Iss 4, Pp 249-267 (2019)
Druh dokumentu: article
ISSN: 1947-5411
1947-542X
19475411
DOI: 10.1080/19475411.2018.1556186
Popis: 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 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.
Databáze: Directory of Open Access Journals
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