Nonlinear stability analysis of rotationally-restrained imperfect doubly-curved composite shallow shells

The semi-analytical solution for nonlinear stability analysis of imperfect doubly-curved laminated composite shallow shells with rotationally-restrained edges and under in-plane loading is presented. The nonlinear governing equations are established using the Galerkin method, and the arc-length and quadratic control method is implemented to capture the snapping phenomenon of the doubly-curved composite shells. The nonlinear load-displacement relationships of four special curvature radii of doubly-curved shell structures are obtained, and they are compared and validated with the numerical finite element solutions. A parametric study is conducted to evaluate the effects of the initial imperfection, edge rotationally-restrained spring stiffness, various load parameters, and curvature radius on the nonlinear stability behavior of doubly-curved shells. Finally, the computational efficiency and capability of the semi-analytical solution are demonstrated in comparison with the finite element analysis. The present semi-analytical solution can be effectively and efficiently used in simplified nonlinear stability analysis of complex doubly-curved composite shallow shells with periodic and restrained boundary conditions.