Nonlinear finite element analysis of thermal post-buckling vibration of laminated composite shell panel embedded with SMA fibre

Numerical investigation of nonlinear free vibration of thermally post-buckled laminated composite spherical shell panel embedded with shape memory alloy (SMA) fibre is presented. The mathematical model is proposed for the first time by taking the geometric nonlinearity in Green–Lagrange sense and the panel kinematics based on higher order shear deformation theory. In addition to the above the material nonlinearity in SMA fibres due to the temperature field is also considered in the present analysis. The system governing differential equation of the shell panel is obtained using Hamiltonʼs principle. A direct iterative method in conjunction with nonlinear finite element is used to discretise and solve the system of equations. Effects of various parameters such as curvature ratios, thickness ratios, amplitude ratios, aspect ratios, support conditions, lamination schemes, SMA prestrains and SMA volume fractions on the nonlinear free vibration behaviour on post-buckled laminated panels are examined in detail and discussed. The results obtained are compared with those available in the literature.