A dual-layer dimension-wise fuzzy finite element method for structural analysis with epistemic uncertainties

Epistemic uncertainty propagation is gaining momentum but remains a great challenge in the numerical analysis of a mechanical system. A dual-layer dimension-wise analysis procedure for the fuzzy finite element method is proposed. The core algorithm layer is to identify the minimal and maximal (min/max) points of each slice of the response surface at the zero-cut. The data processing layer aims to filtrate the min/max points of each response slice at each nonzero-cut. Subsequently, the min/max input vectors at any alpha-cut are dimension-wisely assembled. And the response interval at alpha-cut is calculated by deterministic finite element analysis at the min/max input vectors. Finally, the fuzzy description of the system response is recomposed. Two examples are investigated to verify both the accuracy and efficiency of the proposed method.