Robustness Optimization Algorithm for Nonlinear Solid Mechanics Problems

萨兰9908393号。工业问题由于其复杂性，通常对设计参数的变化非常敏感。这在行为的非线性范围内尤其如此。这项研究将以固体力学、系统灵敏度和最优化的基本理论为基础，以准确的定量方式解决这个问题。从与变形分析相同的严格固体力学方程出发，提出了一个更广泛的问题，其中设计参数可以变化。因此，不仅可以计算基本响应，而且可以计算响应对所选系统参数的变化的结果变化(系统鲁棒性)。因此，所提出的数值工具将修改设计变量，以获得最稳健的最终设计。我们考虑了一类重要的工业问题，这些问题可以通过对受任意载荷的变形体进行几何和材料上的非线性分析来描述，包括考虑惯性效应的瞬时载荷。可能的应用包括金属成形、耐撞性和各种冲击问题。

9908393 Saran. Industrial problems, due to their complexity, aretypically very sensitive with respect to variations of designparameters. This is particularly so in a nonlinear range of behavior. This research will address the problem in an accurate quantitative way,based on underlying theories of solid mechanics, systems sensitivity,and optimization. Starting from the same rigorous solid mechanicsequations as in deformation analysis, a broader problem is formulated,where the design parameters can vary. Thus, not only the basicresponse, but also the resulting variation of the response (systemrobustness) to the variations of the selected system parameters, can becalculated. As a result, the proposed numerical tool will modify thedesign variables to obtain the most robust final design. We consider alarge and industrially important class of problems that can be describedby a geometrically and materially nonlinear analysis of deformablebodies subject to any loading including transient loading with inertiaeffects taken into account. Possible applications include metalforming, crashworthiness, and various impact problems.***