Nonlinear Static Response and Free Vibration Analysis of Doubly Curved Cross-Ply Panels

Abstract

In this paper, the nonlinear static and free vibration analyses of doubly curved cross-ply laminated panels subjected to thermomechanical loading are examined. The shell theory adopted in the present case is an extension of Reissner’s shallow shell simplifications that accounts for parabolic distribution of the transverse shear strains through thickness of the shell and tangential stress-free boundary conditions. A multiterm Galerkin’s method is adopted to solve the governing nonlinear partial differential equations. The static equilibrium paths are traced using the Newton-Raphson method in conjunction with the Riks approach to overcome the limit points. The free vibration frequencies about a static equilibrium state of a deformed panel are reported by solving the linear eigenvalue problem. Analytical results are presented for symmetric [0/90/0] and antisymmetric [0/90] cross-ply laminated doubly curved panels that illustrate the influence of geometric properties, in-plane edge boundary conditions, lateral distributed load and temperature field on the nonlinear behavior and natural frequencies.