Treatment of multiple input uncertainties using the scaled boundary finite element method

This paper presents a non-intrusive scaled boundary finite element method to consider multiple input uncertainties, viz., material and geometry. The types of geometric uncertainties considered include the shape and size of inclusions. The inclusions are implicitly defined, and a robust framework is presented to treat the interfaces, which does not require explicit generation of a conforming mesh or special enrichment techniques. A polynomial chaos expansion is used to represent the input and the output uncertainties. The efficiency and the accuracy of the proposed framework are elucidated in detail with a few problems by comparing the results with the conventional Monte Carlo method. A sensitivity analysis based on Sobol’ indices using the developed framework is presented to identify the critical input parameter that has a higher influence on the output response.