Finite element analysis of nonlinear shell structures with uncertain material property

The statistical dynamic responses of geometrically nonlinear shell structures with stochastic Youngʹs modulus of elasticity are investigated in this study. In general, large deformation of the shell structures must be considered when shell structures are under excessive loading, and then the governing equations of the shell structures become nonlinear since the stiffness matrix of the system is related to the deflection. In this paper, the stochastic finite element method along with the perturbation technique is used to deal with statistical responses of shell structures with structural randomness; in particular, the Newton–Raphson iteration procedure in conjunction with Newmark scheme is adopted to solve the nonlinearity of the dynamic governing equation of shell structures. Some results obtained by the perturbation technique and those from the Monte Carlo simulation approach show a good agreement. Finally, it should be emphasized that these statistically dynamic responses are very useful for estimating the reliability of structures.