A theoretical analysis of piezoelectric/composite laminate with larger-amplitude deflection effect, Part II: Hermite differential quadrature method and application

Incorporating the effects of larger-amplitude deflection and electro-elastical properties of piezoelectric lamina, the Hamilton’s variation principle was used to deduce the fundamental formulations of smart anisotropic composite plate in Part I in terms of Reddy’s simple higher-order theory. In order to solve the five highly coupled nonlinear partial differential equations with complicated overlapping boundary conditions, a novel numerical method-Hermite differential quadrature (HDQ) method was developed to implement the differential equations with complicated overlapping boundary conditions. Based on the presently developed HDQ method, any orders derivatives of the unknown functions or any boundary conditions can be point-collocation-based discretized by a set of point-values along x- and y-direction. Then, a system of complete algebraic nonlinear equations can be constructed to calculate out the final point-values of the mid-plane displacements by using the governing equations and relative boundary conditions with HDQ method. Finally, some detailed numerical examples for the anisotropic piezoelectric/composite laminate with the distributed poling directions of piezoelectric layer and fiber orientations of composite layers were studied to validate the developed theoretical analysis model and HDQ numerical method.