A higher-order theory and refined three-node triangular element for functionally graded plates

Based on the higher-order laminated beam theory proposed by Chen Wanji and Wu Zhen [Chen Wanji and Wu Zhen, 2005. A new higher-order shear deformation theory and refined beam element of composite laminates. Acta Mech. Sinica 2, 65–69], a higher-order shear deformation theory for the analysis of functionally graded plates has been presented in this paper, which includes the global and local displacement components. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. For single layer plate, the higher-order theory compared with Reddy theory is more accurate. For the multilayered plates, the theory fully satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The number of unknowns of the higher-order theories is independent of the layer numbers of the functionally graded laminate. Based on this theory, a refined three-node triangular element is presented, which satisfies the interelement C 1 weak-continuity conditions. Numerical results show that present refined triangular element has high computational efficiency and high accuracy.