MODIFIED H-R MIXED VARIATIONAL PRINCIPLE FOR PIEZOELECTRIC MATERIAL AND EXACT SOLUTION OF PIEZOELECTRIC LAMINATES

The Hellinger-Reissner(H-R) mixed variational principle for three-dimensional purely elastic bodies is introduced into the static analysis of piezoelectric material with mechanical-electric coupling effect.The modified H-R mixed variational principle for piezoelectric material is established and a state-vector equation of piezoelectric material is derived from the principle.Analytical solution is presented for the static behavior of the state-vector equation of laminated piezoelectric plates with simply supported edges.Numerical results obtained by present method are in good agreement with other available solutions.The present theory and solution can also be applied to the static analysis of hybrid laminates made of conversational elastic material and piezoelectric material.The proposed variational principle will facilitate the derivation of corresponding semi-analytical or finite element method for piezoelectric laminated plates.