عنوان مقاله [English]
Contact problems are one of widely used and important branches in solid mechanics. This paper aims at extending the bi-directional evolutionary structural optimization (BESO) algorithm for optimal contact shape design in structures under the multiple load cases. In this study, the gap elements between the corresponding nodes on both surfaces are used not only to model contact states but also to modify the contact profile by changing the spacing to lengthen or shorten the gap between the corresponding nodes. Using gap elements, the analysis of contact problems by finite element method is simplified and the Enormous volume of non-linear calculations is reduced. Evolutionary structural optimization (ESO) method for obtaining the optimal shape of the contact surface, through a simple process with a gradual increase over the length of inefficient gap elements, the shape of the structure will converge to an optimal design. But in this paper by using the bi-directional evolutionary optimization method, there is the Possibility of increasing and decreasing of length gap elements simultaneously and so the speed of convergence has increased. In this paper, weighted average method and stress criterion are used for evaluation of the performance of gap element in optimization algorithm and finally a uniform distribution of stress along the contact surface is obtained.