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Variational Integrators for Piezoelectricity

[+] Author Affiliations
P. Nasiri, Gary F. Dargush

University at Buffalo, State University of New York, Buffalo, NY

Paper No. IMECE2013-65356, pp. V009T10A071; 8 pages
doi:10.1115/IMECE2013-65356
From:
  • ASME 2013 International Mechanical Engineering Congress and Exposition
  • Volume 9: Mechanics of Solids, Structures and Fluids
  • San Diego, California, USA, November 15–21, 2013
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5638-3
  • Copyright © 2013 by ASME

abstract

Variational integrators have been used to study the transient response of a number of dynamical problems, while displaying superior conservation characteristics. The purpose of this paper is to develop variational integrators for linear piezoelectric problems. A two-field piezoelectric functional is first discretized in space and time and the coupled discrete Euler-Lagrange equations for displacement and electrical potential are then derived. Afterwards, to validate this new formulation, the numerical results for two initial/boundary value problems involving a piezoelectric plate are compared to the corresponding analytical solutions and finite element results obtained from a commercial software package. The excellent correlation of these solutions indicates the capability of variational integrators in modeling transient piezoelectric behavior. Finally, the superior energy conservation behavior of the developed method is demonstrated.

Copyright © 2013 by ASME

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