Geometrically nonlinear bending analysis of variable stiffness composite laminated shell panels with a higher-order theory

A finite element (FE) formulation is developed by extending the third-order shear deformation theory, including the zig-zag effects using the Murakami zig-zag function, for the linear and nonlinear static analyses of variable stiffness composite laminated (VSCL) shell panels. In this work, a nine-noded isoparametric element with thirteen degrees of freedom is employed to model the VSCL shell panels. Geometrical nonlinearity according to von Karman nonlinear strain-displacement relations is considered for the evaluation of the deflections and stresses. The assumed displacement field considers up to third-order terms for in-plane displacements and second-order terms for the transverse displacement through-the-thickness. The accuracy of the formulation is established by comparing the obtained results with the three-dimensional elasticity and two-dimensional numerical/analytical results available in the literature for static analysis of constant stiffness composite laminates (CSCL) and VSCL. New results are presented for the nonlinear deflection and stresses of VSCL shell panels considering the effect of the fibre path angles, defined by the curvilinear fibre orientation for the VSCL spherical, cylindrical and hyperboloid shells. Further, the effect of curvature ratios, number of layers, lamination configurations and boundary conditions on the nonlinear static behaviour of VSCL shells is presented.