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Advanced Finite Element Formulation for Piezoelectric Smart Shell Structures Under Consideration of Geometrical Nonlinearity

[+] Author Affiliations
Katrin Schulz, Sven Klinkel, Werner Wagner

University of Karlsruhe, Karlsruhe, Germany

Paper No. IMECE2008-67335, pp. 323-332; 10 pages
doi:10.1115/IMECE2008-67335
From:
  • ASME 2008 International Mechanical Engineering Congress and Exposition
  • Volume 12: Mechanics of Solids, Structures and Fluids
  • Boston, Massachusetts, USA, October 31–November 6, 2008
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4873-9 | eISBN: 978-0-7918-3840-2
  • Copyright © 2008 by ASME

abstract

A geometrically nonlinear highly accurate finite element formulation to analyze piezoelectric shell problems is presented. The formulation is based on the mixed field variational principle of Hu-Washizu including the independent fields displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. The normal zero stress condition and the normal zero dielectric displacement condition for shells are enforced by the independent resultant stress and resultant dielectric displacement fields. The arbitrary reference surface of the shell is modeled with a four node element. Each node possesses six mechanical degrees of freedom, three displacements and three rotations, and one electrical degree of freedom, which is the difference of the electric potential through the shell thickness. The developed shell element fulfills the patchtests and is able to model arbitrary curved shell structures. Some numerical examples demonstrate the applicability of the present shell element for piezoelectric systems and integrated piezoelectric structures.

Copyright © 2008 by ASME

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