Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel using nonlinear FEM

In the present paper, nonlinear free vibration behaviour of single/doubly curved shell panel is addressed within the post-buckled state. Thermal post-buckling of shell panel is accounted for a uniform temperature field. A general mathematical model is developed for the curved panel by introducing the geometric nonlinearity in Green–Lagrange sense based on higher order shear deformation theory. The system governing differential equations are derived using Hamiltonʹs principle. The derived differential equations are converted to set of algebraic equations with the help nonlinear finite element and solved numerically employing a direct iterative method. Effect of various parameters such as lamination schemes, amplitude ratios, aspect ratios, support conditions, thickness ratios, curvature ratios and the material properties on the nonlinear free vibration frequencies are analysed in detail and discussed. The obtained results are validated with those available in literature. The difference between the results necessitates the present nonlinear model for more actual prediction of nonlinear behaviour of the laminated panel type structures having severe nonlinearity when it exposed to temperature field.