Layerwise third-order shear deformation theory with transverse shear stress continuity for piezolaminated plates

Regarding laminated structures, an electromechanically coupled Finite Element (FE) model based on Layerwise Third-Order Shear Deformation (LW-TOSD) theory is proposed for static and dynamic analysis. LW-TOSD ensures the continuity of in-plane displacements and transverse shear stresses. The current LW-TOSD can be applied to arbitrary multi-layer laminated structures with only seven Degrees of Freedom (DOFs) for each element node and eliminates the use of the shear correction factors. Moreover, a shear penalty stiffness matrix is constructed to satisfy artificial constraints to optimize the structural shear strain. A dynamic finite element model is obtained based on LW-TOSD using the Hamilton’s principle. First, the accuracy of the current model is validated by comparing with literature and ABAQUS results. Then, this study carries out numerical investigations of piezolaminated structures for different width-to-thickness ratios, length-to-width ratios, penalty stiffness matrix, boundary conditions, electric fields and dynamics.