Variational Principles for Piezoelectric, Thermopiezoelectric, and Hygrothermopiezoelectric Continua Revisited

Abstract

In this paper some variational principles are revisited for the fundamental equations of a regular region of piezoelectric, thermopiezoelectric, and hygrothermopiezoelectric (but non-stochastic, non-local, and non-relativistic) materials in the elastic range. Certain oversights, and especially, those involving the so-called Hu-Washizu variational principle of piezoelectricity that was first formulated in a paper (“Variational Principles in Piezoelectricity,” Lettere Al Nuovo Cimentò, vol. 7, 449–454, 1973) are clarified within the “ISI-Web of Science” publications in the open literature. Similar variational principles of piezoelectricity are cited.

Keywords:

• variational principles
• elasticity
• piezoelectricity
• thermopiezoelectricity
• hygrothermopiezoelectricity

ACKNOWLEDGMENTS

The authors are grateful to Professor J. N. Reddy, Editor-in-Chief of the Journal, for his suggestion of the paper as a comment, and they acknowledge the financial support of TUBA. The second author (Dökmeci) is sincerely indebted to the late Professor B. M. Fraeijs De Veubeke and, in particular, to his late Professor Raymond D. Mindlin for their encouragement, late Professor Liviu Librescu (Virginia Polytechnic Institute and State Univ., Blacksburg, VA.) for his kind interest in [133], as the only one who mentioned it in one of his papers, and Professor Oral Buyukozturk (M.I. T., Cambridge) for the funding and kind invitation to a three-day workshop on Engineering Materials on 9–11 June, 2004, Cambridge.