Three-Dimensional Asymptotic Scheme for Piezothermoelastic Laminates

A three-dimensional asymptotic scheme that combines the transfer matrix method and the asymptotic expansion technique is used to analyze thermo-electro-mechanical deformations of a piezothermoelastic laminate with surface tractions, electric potentials, and temperatures specified on its top and bottom surfaces. The scheme results in a hierarchy of two-dimensional equations with the same homogeneous operator for each order. For an elastic problem, the homogeneous operator reduces to that for classical thin-plate equations. Results computed for a simply supported rectangular plate with edges grounded are found to be in excellent agreement with the exact solution of the problem.