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

• Published in: Computational mechanics Vol. 43; no. 5; pp. 687 - 700
• Main Authors: Papadopoulos, Vissarion, Charmpis, Dimos C., Papadrakakis, Manolis
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.04.2009; Springer Nature B.V
• Subjects: Buckling; Classical and Continuum Physics; Computational efficiency; Computational Science and Engineering; Conjugate gradient method; Defects; Engineering; Fields (mathematics); Finite element method; Limit load; Modulus of elasticity; Original Paper; Quotients; Shells; Stochastic processes; Theoretical and Applied Mechanics; Random imperfections; Stochastic finite element; Preconditioned Conjugate Gradient method; Buckling analysis of shells; Random eigenvalues
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-008-0338-3

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.