Three-Dimensional Asymptotic Analysis of Multiple-Electroded Piezoelectric Laminates

Theproblemofpiezoelectriclaminateswithspecie edsurfacetractionsandsurfaceandinternalelectricpotentials is studied. By writing the governing equations in the state-space formulation, employing an asymptotic expansion technique, and expressing electric displacement jumps across internal electrodes in terms of basic unknowns, the three-dimensional problem is reduced to a hierarchy of two-dimensional equations with the same homogeneous operators for each order. Different nonhomogeneous terms are only related to the preceding-order solution and can be readily determined by recurrence relations. Moreover, for pure elasticity, the present e eld equations of the leading order represent the classical thin elastic plate model. The proposed formulation is illustrated by considering arectangular piezoelectric plate madeof an orthotropic material, and with its edges simplysupported and grounded. The convergence of the solution is discussed and the repeated averaging technique for partial sums is used to accelerate the convergenceof the series solution. Computed results arefound toagree well with available analytical results, and new results for electromechanically coupled problems are presented.