New approach of FEM for laminated composite plates and shells

The Mindlin's theory is extended and a new approach of FEM has been established. It considers a laminated plate or shell made of a thin film and N layers of anisotropic plates or shells bonded in order. The in-plane displacements, deflection W of the film and the shear strains in k-th ply are chosen as the independent variables. With this model, some difficulties encountered in the study of composite laminated plates and shells are overcome. 1) Based on an analysis of order of magnitude for each term of stiffness matrix, the asymptotic equations and Gauss-Seidel iterative equations for thick are introduced for thin and thick laminated plated and shells, respectively. In these equations, the in-plane and bending unknown variables and the transverse shear strains of each layer will be uncoupled so that the maximum degrees of freedom are equal to that of one layer Kirchhoff plate. Thus the computing efficiency is improved considerably. 2) The ``shear locking'' in thin plates and shells can be avoided. 3) The distribution of transverse shear stress through the thickness are more accurate than that by previous theories and the shear factor will not be necessary. Furthermore, numerical examples of laminated plates, axisymmetric laminated composite shell structures under arbitrary loads and delamination buckling of laminated plates is given. Solution accuracy and computational efficiency are demonstrated. This model is easy to be generalized for solving other problems, such as vibration and boundary-layer effects.