Three-dimensional asymptotic analysis of multiple-electroded piezoelectriclaminates

The problem of piezoelectric laminates with specified surface tractions and surface and internal electric potentials is studied. By writing the govern ing equations in the state-space formulation, employing an asymptotic expan sion technique, and expressing electric displacement jumps across internal electrodes in terms of basic unknowns, the three-dimensional problem is red uced to a hierarchy of two-dimensional equations with the same homogeneous operators for each order. Different nonhomogeneous terms are only related t o the preceding-order solution and can be readily determined by recurrence relations. Moreover, for pure elasticity, the present field equations of th e leading order represent the classical thin elastic plate model. The propo sed formulation is illustrated by considering a rectangular piezoelectric p late made of an orthotropic material, and with its edges simply supported a nd grounded. The convergence of the solution is discussed and the repeated averaging technique for partial sums is used to accelerate the convergence of the series solution. Computed results are found to agree well with avail able analytical results, and new results for electromechanically coupled pr oblems are presented.