An efficient framework for the elasto-plastic reliability assessment of uncertain wind excited systems

• A model is developed for analyzing the post-yield behavior of wind-excited systems.
• The approach is centered on analyzing uncertain and stochastic dynamic systems.
• The model combines dynamic shakedown analysis with advanced Monte Carlo simulation.
• A case study with 60 plastic hinges and 10,249 uncertain parameters was considered.
• One hour was needed to find a solution to the case study on a typical laptop.

In this paper a method to efficiently evaluate the reliability of elastic-perfectly plastic structures is proposed. The method is based on combining dynamic shakedown theory with Subset Simulation. In particular, focus is on describing the shakedown behavior of uncertain elasto-plastic systems driven by stochastic wind loads. The ability of the structure to shakedown is assumed as a limit state separating plastic collapse from a safe, if not elastic, state of the structure. The limit state is therefore evaluated in terms of a probabilistic load multiplier estimated through solving a series of linear programming problems posed in terms of the responses of the underlying linear elastic model and self-stress distribution. The efficiency of the proposed procedure is guaranteed by the simplicity of the mathematical programming problem, the underlying structural model solved at each iteration, and the efficiency of Subset Simulation. The rigor of the approach is assured by the dynamic shakedown theory. The applicability of the framework is illustrated on a steel frame example.