An efficient method for nonlinear analysis of layered shells

Finite element formulation based on explicit through-thickness integration scheme assumes importance when applied to multilayered shells, as it is numerically accurate and computationally efficient. Explicit integration becomes possible on assuming the variation of the inverse Jacobian through the thickness. The element stiffness matrices are discussed for (i) large rotation, and (ii) small rotation. Relative efficiencies of the explicit through-thickness integration schemes are compared with that of the conventional formulation involving numerical integration in three directions in each layer and summation over the layers. The small rotation formulation assuming linear variation of the Jacobian inverse across the thickness and based on further approximation regarding certain submatrices is seen to be computationally efficient. The geometric nonlinear behaviours of laminated composite cylindrical panels subjected to external pressure are discussed. The parameters considered are: number of layers, symmetric/antisymmetric, cross-ply/angleply, boundary conditions and central angle. The strength of shallow panels with longitudinal edges hinged and curved edges free is controlled by the limit point load, while for deep panels it is controlled by the bifurcation load. The boundary conditions have significant influence on load carrying capacities. A list of symbols is given at the end of the paper