Weak form quadrature element analysis on nonlinear bifurcation and post-buckling of cylindrical composite laminates

This paper presents a weak form quadrature element formulation in the analysis of nonlinear bifurcation and post-buckling of cylindrical composite laminates subjected to transverse loads. A total Lagrangian updating scheme is used in combination with arc-length method and the branch switching method is adopted to identify the whole post-buckling procedure of the laminates. The formulation of the shell model is based on the basic concept of Ahmad. The coincidence of discrete nodes and integration points in quadrature element endows it with compactness and conciseness in the nonlinear buckling analysis of cylindrical laminates. Shear and membrane locking problems are avoided in the quadrature element formulation for its high-order approximation property. Several numerical examples are firstly presented to verify the effectiveness and accuracy of the present formulation. Parametric studies of the effects including rise, thickness, boundary conditions and lamination scheme of the cylindrical composite laminates on the bifurcation and post-buckling behaviors are performed.