A hybrid Bézier based multi-step method and differential quadrature for 3D transient response of variable stiffness composite plates

Three-dimensional (3D) transient analysis of a variable stiffness composite laminated (VSCL) plate with curvilinear fibers is presented. The fiber orientation angle changes linearly with respect to the horizontal coordinate in each layer. Various combinations of arbitrary boundary conditions at edges of the plate are assumed. Layerwise-differential quadrature method (LW-DQM) as an efficient and accurate numerical tool is employed to discretize the obtained governing equations for each layer in the spatial domain. Using the DQM enables one to accurately and efficiently discretize the partial differential equations and also implement the boundary and compatibility conditions in their strong forms. Then, solution of the resulting system of differential equations in the time domain, a novel multi-step method based on the Bézier curves is applied. Much lower computational time of the new multi-step with respect to the Newmark time integration scheme together with numerical stability of the method is presented. Apart from convergence and accuracy of the method, effects of variation in the fiber path, different geometrical parameters and boundary conditions on the transient response of the VSCL plates under dynamic loading are investigated.