Coupled variational principles of piezoelectricity. (English) Zbl 1210.74175

Summary: A family of generalized variational principles of piezoelectricity can be obtained straightforwardly from the field equations and boundary conditions via the semi-inverse method of establishing variational principles proposed by He without using Lagrange multipliers. The present theory provides a quite straightforward tool to search for various variational principles for physical problems. This paper aims at providing a more complete theoretical basis for the finite element applications and other direct variational methods such as Ritz’s, Trefftz’s and Kantorovitch’s methods.


74S30 Other numerical methods in solid mechanics (MSC2010)
74F15 Electromagnetic effects in solid mechanics
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