A computationally efficient method for the buckling analysis of shells with stochastic imperfections

Abstract

A computationally efficient method is presented for the buckling analysis of shells with random imperfections, based on a linearized buckling approximation of the limit load of the shell. A Stochastic Finite Element Method approach is used for the analysis of the "imperfect" shell structure involving random geometric deviations from its perfect geometry, as well as spatial variability of the modulus of elasticity and thickness of the shell, modeled as random fields. A corresponding eigenproblem for the prediction of the buckling load is solved at each MCS using a Rayleigh quotient-based formulation of the Preconditioned Conjugate Gradient method. It is shown that the use of the proposed method reduces drastically the computational effort involved in each MCS, making the implementation of such stochastic analyses in real-world structures affordable.

The stochastic finite element method: Past, present and future

“…Spectral representation has also been successfully implemented in the framework of Monte Carlo simulation (MCS) for the solution of realistic problems with the stochastic finite element approach e.g. [4,20,99,133,[135][136][137][138]145,146,173].…”

Incomplete factorization preconditioners for the iterative solution of Stochastic Finite Element equations

“…In fact, certain nonlinear and/or dynamic SFE procedures may be formulated in a way allowing the exploitation of the special features encountered in nearby/reanalysis problems (e.g. [8]). Thus, several linear/nonlinear static/dynamic stochastic analysis applications may benefit from implementing the iterative solution methods and corresponding preconditioning techniques considered in this paper for efficiently treating SFE equations.…”

“…Hence, the effective and efficient handling of SFE equations has emerged as a research topic of special interest and importance within the SFE community and a number of related publications have appeared dealing with MC simulation-based and other SFE formulations (e.g. [1][2][3][4][5][6][7][8]). …”

Efficient Iterative Solution Techniques for Finite Element Reanalyses in the Context of Monte Carlo Simulation

“…[1,2,[4][5][6][7][8][9][10][11][12]). In the present work, an established PCG-based solution method is overviewed and a new FPI-based solution method is introduced.…”