Flexible Thin Shell Elements under Nonwhite and Nonzero Mean Loads

Abstract

A finite element formulation combined with stochastic linearization and normal mode methods developed earlier for the study of geometrically non‐linear random vibration responses of beam and frame structures subjected to simultaneously spatial and temporal Gaussian stationary nonwhite and nonzero mean random excitations is now extended to treat the plate and shell structures in the same fashion. Examples include dynamic random responses of simply supported square plate, cylindrical panel with all edges supported by rigid diaphragms, clamped spherical cap, and double‐curved square panel under different random loadings. To validate the present formulation and solutions, results are compared with alternative analytical solutions whenever available. The Monte Carlo simulation method is also used to generate solutions to compare with some of the present results when alternative solutions are not available.