A fast uncertainty analysis for material nonlinear problems based on reanalysis and semi-analytic strategy

A novel semi-analytic method for interval-based uncertainty analysis is suggested to calculate the uncertainty measure index in this study. As nonlinear problems commonly cannot be solved analytically, an analytic interval-based uncertainty analysis method for linear problems is deduced, and an explicit expression of the measure index of uncertainty is given. To extend this form to nonlinear analysis, a semi-analytic uncertainty analysis (SAUA) method is suggested by integrating gradient-based optimization methods and Taylor expansion. Initially, a pseudo optimal solution is obtained. Sequentially, a Taylor expansion is used to calculate the performance function based on the pseudo optimal solution. In this way, the uncertainty measure index can be obtained analytically. Considering the bottleneck of surrogate model, an efficient reanalysis assisted material nonlinear analysis (RAMNA) method is integrated. Thus, the efficiency and accuracy of the suggested method are both enhanced. The SAUA method has been applied to large-scale reliability analysis of vehicle components. The results show that the SAUA is effective and efficient, especially for large-scale problems. Furthermore, the SAUA method can also be extended for other mechanical design, and contribute to shortening the design period.