Generalized polynomial chaos expansion by reanalysis using static condensation based on substructuring

Abstract

This paper presents a new computational method for forward uncertainty quantification (UQ) analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs. The method consists of a generalized polynomial chaos expansion (GPCE) for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set. In the reanalysis, we employ substructuring for a structure to isolate its local regions that vary due to random inputs. This allows for avoiding repeated computations of invariant substructures while generating the input-output data set. Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy. Consequently, the GPCE with the static reanalysis method can achieve significant computational saving, thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs. The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses (FEAs). We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional (all-dependent) random inputs.