دانلود رایگان مقاله آنالیز عدم قطعیت سریع برای مسائل غیر خطی مواد

Abstract

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

6. Conclusions

This work suggests an efficient interval uncertainty analysis method for material nonlinear problems. Compared with other interval uncertainty analysis methods, the distinctive characteristics of this method can be summarized as: (1) The formulations of an analytic uncertainty analysis for linear problems are proposed. The numerical example shows that the analytic method can calculate the uncertainty measure index efficiently. (2) To extend the analytic interval method to nonlinear problems, a novel SAUA method is developed. The SAUA method is a combination of gradient-based optimization method and Taylor expansion. At the beginning of optimization, gradient-based optimization method is used to obtain a pseudo solution with a relax convergence criterion. Then the Taylor expansion is used when the optimization converges to a small region. In this way the optimization problem can be solved analytically. The numerical examples show that the SAUA method can reach a trade-off between efficiency and accuracy. A highly accurate solution can be achieved efficiently via the SAUA method. (3) An efficient RAMNA method is proposed. Compared with surrogate-based optimization and real evaluation, the accuracy and efficiency of suggested strategy can be promised simultaneously. In conclusion, the proposed SAUA method is effective and effi- cient, which can contribute to shortening the period of structure design.