Abstract
This paper deals with the application of a new algorithm of probabilistic limit and shakedown analysis for 2D structures, in which the loading and strength of the material are to be considered as random variables. The procedure involves a deterministic shakedown analysis for each probabilistic iteration, which is based on the primal-dual approach and the edge-based smoothed finite element method (ES-FEM). The limit state function separating the safe and failure regions is defined directly as the difference between the obtained shakedown load factor and the current load factor. A Sequential Quadratic Programming (SQP) is implemented for finding the design point. Sensitivity analyses are performed numerically from a mathematical model and the probability of failure is calculated by the First Order Reliability Method. Because of use of constant smoothing functions in the ES-FEM, only one Gaussian point is required for each smoothing domain ensuring that the total number of variables in the resulting optimization problem is kept to a minimum compared with standard finite element formulation. Numerical examples are presented to show the validity and effectiveness of the present method.
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