Partition-of-Unity Enhanced Polynomial Chaos for Structural Stability Analysis

Abstract eng:
For many engineering structures, particularly thin-walled structures, buckling is the critical failure mechanism. In practice, imperfections that lead to a deterioration of a structure's buckling resistance are often of random nature. Stochastic computational methods have been applied to many problems of engineering interest to take into account randomness, butmost of themwere deemed unfit for the analysis of buckling problems. This is due to the multi-modality of the response, that leads to a discon- tinuity in the transformation from the imperfections to the equilibrium path. As a consequence, expensive sampling-based techniques are predominantly used for the analysis of stochastic buckling problems. In this contribution we demonstrate that the polynomial chaos (PC) or spectral stochastic method can be made suitable for the analysis of random critical buckling loads. After the introduction of the problem we discuss how the partition-of-unity concept, especially devised to model discontinuities, can be used to enrich the tradi- tional PC expansion, leading to the enhanced polynomial chaos (EPC) method. We demonstrate the suitability of the method by means of a numerical example.

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