8 April 2008 A geometrically nonlinear mixed finite element formulation for the simulation of piezoelectric shell structures
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Abstract
The paper is concerned with a geometrically nonlinear finite element formulation to analyze piezoelectric shell structures. The classical shell assumptions are extended to the electromechanical coupled problem. The consideration of geometrical nonlinearity includes the analysis of stability problems and other nonlinear effects. The formulation is based on the mixed field functional of Hu-Washizu. The independent fields are displacements, electric potential, strains, electric field, stresses and dielectric displacements. The mixed formulation allows an interpolation of the strains and the electric field through the shell thickness, which is an essential advantage when using nonlinear 3D material laws. With respect to the numerical approximation an arbitrary reference surface of the shell is modeled with a four node element. Each node possesses six mechanical and one electrical degree of freedom. Some simulations demonstrate the applicability of the present piezoelectric shell element.
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Katrin Schulz, Katrin Schulz, Sven Klinkel, Sven Klinkel, } "A geometrically nonlinear mixed finite element formulation for the simulation of piezoelectric shell structures", Proc. SPIE 6932, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2008, 69320G (8 April 2008); doi: 10.1117/12.774655; https://doi.org/10.1117/12.774655
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