Reliability Analysis of Inelastic Shell Structures Under Variable Loads

Abstract

This paper concerns the application of a new algorithm of probabilistic limit and shakedown analysis for shell structures, in which the loading and strength of the material as well as the thickness of the shell are to be considered as random variables. The procedure involves a deterministic limit and shakedown analysis for each probabilistic iteration, which is based on the kinematical approach and the use of the re-parameterized exact Ilyushin yield surface proposed by Burgoyne and Brennan. The limit state function separating the safe and failure regions is defined directly as the difference between the obtained limit load factor and the current load factor. Different kinds of distribution of basic variables are taken into consideration and performed with First- and Second-Order Reliability Methods (form/sorm) for calculation of the failure probability of the structure. A non-linear optimization was implemented, which is based on the Sequential Quadratic Programming for finding the design point. Non-linear sensitivity analyses are also performed for computing the Jacobian and the Hessian of the limit state function. This direct approach reduces considerably the necessary knowledge of uncertain technological input data, computing costs and the numerical error. Numerical examples are presented to show the validity and effectiveness of the present method.