Semi-analytical three-dimensional elasticity solutions for generally laminated composite plates

Semi-analytical solutions for bending and free vibration of composite laminated plates have been derived based on three-dimensional elasticity theory using a newly developed hybrid analysis, which perfectly combines the state space approach (SSA) and the technique of differential quadrature (DQ). The thickness direction of laminates is selected as the transfer direction in SSA, and the DQ technique is employed to discretize the in-plane domains. This actualizes the transformation of the original partial differential equations into a state equation consisting of first-order ordinary differential equations. In particular, the use of DQ technique makes ease of the treatment of various boundary conditions, which cannot be considered in the conventional exact SSA. To avoid numerical instabilities in the conventional transfer matrix method, artificial interfaces are introduced to divide each layer into several sub-layers to reduce the transfer distance and the joint coupling matrices are established according to the continuity conditions at actual and artificial interfaces to implement the global analysis. Comprehensive numerical examples are preformed to validate the present hybrid method. Effects of some parameters on mechanical properties of the laminates are discussed.