Large nonstationary random responses of shell structures with geometrical and material nonlinearities
A novel approach for the prediction of large nonlinear nonstationary random responses of shell structures discretized by the finite element method is presented. It combines: (a) the hybrid-strain-based finite element formulation with emphasis on deformations of finite strains, finite rotations and correct prediction of rigid-body modes; and (b) the stochastic central difference method with time co-ordinate transformation, adaptive time schemes, and the averaged deterministic central difference scheme. The novel approach was applied to a cantilever plate and a spherical cap. The former exhibited stiffness hardening while the latter softening in the large nonlinear range. Computed results for the linear case of the cantilever plate were included for comparison to those previously available in the literature. These results are in excellent agreement. It is concluded that for the first time, a general, accurate and efficient approach, that can deal with systems whose nonlinearities are updated at every time step which is frequently encountered in the updated Lagrangian finite element formulation, is available for the prediction of very large geometrically and materially nonlinear responses of discretized shell structures under strong nonstationary random excitations.
nonstationary random response shell structures finite element large nonlinear deformations