Variational principles for the equations of porous piezoelectric ceramics

Abstract

The governing equations of a porous piezoelectric continuum are presented in variational form, though they were well established in differential form. Hamilton's principle is applied to the motions of a regular region of the continuum, and a three-field variational principle is obtained with some constraint conditions. By removing the constraint conditions that are usually undesirable in computation through an involutory transformation, a unified variational principle is presented for the region with a fixed internal surface of discontinuity. The unified principle leads, as its Euler-Lagrange equations, to all the governing equations of the region, including the jump conditions but excluding the initial conditions. Certain special cases and reciprocal variational principles are recorded, and they are shown to recover some of the earlier ones.