Extension of the Certain Generalized Stresses Method for the stochastic analysis of homogeneous and laminated shells

Abstract The paper presents an extension of the Certain Generalized Stresses Method (CGSM) for the static finite element analysis of homogeneous and laminated shells with variability. The basic assumption is that the generalized stresses do not depend on input parameters perturbation. The CGSM is a non-intrusive method that requires only one finite element analysis with some load cases to calculate the variability of mechanical quantities of interest. The uncertain input parameters are material and physical properties. Uniform random parameters as well as random fields are considered. The displacements statistical results: mean value, standard deviation and distribution are obtained by Monte Carlo simulations, using a semi-analytical formula. Two examples are treated: the Scordelis–Lo shell roof and an automotive windscreen. The method provides results of good quality and is very economical from a computational time point of view.