Inclusion of contact in mechanical designs opens a large range of design possibilities, this includes classical designs with contact, such as gears, couplings, switches, clamps etc. However, incorporation of contact in topology optimization is challenging, as classical contact models are not readily applicable when the boundaries are not defined. This paper aims to address the limitations of contact in topology optimization by extending the third medium contact method for topology optimization problems with internal contact. When the objective is to maximize a given contact load for a specified displacement, instabilities may arise as an optimum is approached. In order to alleviate stability problems as well as provide robustness of the optimized designs, a tangent stiffness requirement is introduced to the design objective. To avoid a non-physical exploitation of the third medium in optimized designs, small features are penalized by evaluating the volume constraint on a dilated design. The present work incorporates well-established methods in topology optimization including Helmholtz PDE filtering, threshold projection, Solid Isotropic Material Interpolation with Penalization, and the Method of Moving Asymptotes. Three examples are used to illustrate how the approach exploits internal contact in the topology optimization of structures subjected to large deformations.

翻译：在机械设计中引入接触可实现广泛的设计可能性，包括齿轮、联轴器、开关、夹具等经典接触设计。然而，在拓扑优化中融入接触具有挑战性，因为当边界未定义时，经典接触模型无法直接适用。本文旨在通过扩展第三介质接触方法，解决拓扑优化中内部接触问题的局限性。当目标是在指定位移下最大化给定接触载荷时，随着最优解的趋近可能产生不稳定性。为缓解稳定性问题并增强优化设计的鲁棒性，在目标函数中引入了切线刚度约束。为避免优化设计中非物理地利用第三介质，通过在膨胀设计上评估体积约束来惩罚微小特征。本研究融合了拓扑优化中的成熟方法，包括亥姆霍兹偏微分方程滤波、阈值投影、带罚函数的固体各向同性材料插值法以及移动渐近线法。通过三个算例展示该方法如何利用大变形结构拓扑优化中的内部接触。