Nonlinear Stochastic Dynamical Post-buckling Analysis of Uncertain Cylindrical Shells

This paper presents the nonlinear dynamical post-buckling analysis of an uncertain cylindrical shell. The proposed approach is adapted to the dynamical analysis of geometrically nonlinear structures subjected to a stochastic ground-based motion in the presence of both system parameter uncertainties and model uncertainties. The structure is modeled by a large finite element model using 3D elasticity theory. The ground-based motion is represented by a Gaussian centered non-stationary second-order stochastic process. Then, a reducedorder basis is constructed using the POD (Proper Orthogonal Decomposition) analysis of a nonlinear static reference response combined with selected linear eigenmodes of vibrations. The mean reduced-order nonlinear computational model is then explicitly constructed. A positive-definite operator involving the nonlinear stiffness of the structure is defined, allowing the nonparametric probabilistic approach to be used for constructing the uncertain nonlinear reduced-order computational model. The dispersion parameter controlling the level of stiffness uncertainty is a scalar which has been previously identified experimentally in a nonlinear static context. Finally, the instantaneous spectral density power of the dynamical response is analyzed in order to quantify the influence of both geometrical nonlinearities and random uncertainties on the stochastic dynamical response.