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A simple finite element formulation for a composite plate with laminated piezoelectric layers is presented. Classical laminate theory with electromechanical induced actuation and variational principles are used to formulate the equations of motion for a Mindlin plate element based upon uniformly reduced numerical integration and hourglass stabilization. The equations of motion are discretized with four-node, 24 degree of freedom quadrilateral shell elements with one electrical degree of freedom per piezoelectric layer. Performance of the finite element formulation developed here has been tested and compared to the experimental and analytical results documented in literature.

SUMMARYA brief review of the structural optimization literature and a description of the present status of optimization methods are presented. The scope of the review is limited and does not profess to cover the entire literature.Results of the optimization of two structures (by the optimality criteria approach) are presented. There are some conclusions and recommendations for future developments in structural optimization.

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