This paper concerns the heuristic-based material stiffness optimization of frictional linear elastic contact problems for having control over the contact stress distribution, aiming to extend the material stiffness optimization to multiple loading conditions, in which each of the loadings acts solely on the structures. A decrease level of the variance of the contact stress is introduced and a weighted sum of the decrease levels under all load cases is constructed as the objective function. The individual criterion for contact problems with multiple contact regions is addressed. The worst case design is adopted for multiple load cases, and an extreme reference stress, which is the highest stress level of the subdomain under all load cases, is defined to control the Young’s modulus modification process in a finite element framework. Through three numerical examples, it is demonstrated how an even distribution of the contact stress can be obtained for contact problems subjected to multiple load cases with single or multiple contact regions. Some new features of the material stiffness optimization with multiple loading conditions are also illustrated.

本文涉及用于控制接触应力分布的摩擦线性弹性接触问题的基于启发式的材料刚度优化，旨在将材料刚度优化扩展到多个载荷条件，其中每个载荷仅作用于结构。引入了接触应力方差的减小水平，并且将所有负载情况下的减小水平的加权总和构造为目标函数。解决了具有多个接触区域的接触问题的个别准则。在多个载荷情况下采用最坏情况设计，并定义了一个极限参考应力（在所有载荷情况下，子域的最高应力水平）来控制有限元框架中的杨氏模量修改过程。通过三个数值示例，说明了如何针对具有单个或多个接触区域的多个载荷工况下的接触问题，获得均匀的接触应力分布。还说明了在多个加载条件下材料刚度优化的一些新功能。