Coupled variational principles of piezoelectricity

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.