Material stiffness optimization for contact stress distribution in frictional elastic contact problems with multiple load cases

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.