Stochastic finite element analysis of plates with the Certain Generalized Stresses Method

• The Certain Generalized Stresses Method for membrane and bending plates is presented.
• The CGSM is a non-intrusive method that requires only one finite element analysis with several load cases.
• The first example is a square membrane plate with a circular hole under tension.
• The second example is a simply supported square bending plate under uniformly distributed load.
• The CGSM is efficient in terms of quality of results and computational time.

The Certain Generalized Stresses Method (CGSM) takes into account variability in static finite element analysis. The CGSM is dedicated to thin-walled structures: bars, beams, plates and shells. The objective of this paper is to present and evaluate a methodology based on the CGSM, for the static finite element analysis of plates with variability. 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 statistical results: mean value, standard deviation and distribution are obtained by Monte Carlo simulations, using a semi-analytical formula. Two examples are treated: a square plate with a circular hole under tension and a simply supported square bending plate under uniformly distributed load. The method provides results of good quality and is very economical from a computational time point of view.