A Neumann expansion-based sequential simulation method for structural interval finite element analysis

The interval finite element method, which cooperates finite elements with interval analysis, aims to determine the structural upper and lower response bounds under interval inputs. The sequential simulation method provides an efficient strategy for evaluating the structural response bounds, which performs sampling of interval variables and structural response simulations sequence by sequence. However, the structural response analyses in each simulation sequence are accurately solved, even though most of them are not contributing components to the final response bound. It is realized that structural response computations for the earlier sequences are mainly used to identify the contributing samples, focusing on assessing the relative magnitude of their values rather than obtaining their exact values. Therefore, the Neumann expansion is introduced in this paper to approximate the structural response and to identify potential contributing samples. In each simulation sequence, accurate numerical solutions of the structural response are performed only for the potential contributing samples. In addition, this study proposes an adaptive sampling strategy that accelerates the convergence by continuously adjusting the sampling neighborhood of the contributing sample. Several numerical examples are investigated to illustrate the efficiency and accuracy of the proposed Neumann expansion-based sequential simulation method.