In this paper the problem of the concurrent topological optimization of two different bodies sharing a region of the design space is dealt with. This design problem focuses on the simultaneous optimization of two bodies (components) where not only the material distribution of each body has to be optimized but also the design space has to be divided among the two bodies. This novel optimization formulation represents a design problem in which more than one component have to be located inside a limited allowable room. Each component has its own function and load carrying requirements. In the paper a novel development solution algorithm is presented. With respect to previously published papers, the new algorithm comprises an interpolation of the density fields which allows a complete independence of the meshes of the two bodies. As the bodies can be meshed with any arbitrary mesh, this new algorithm can be applied to any real geometry. The developed algorithm is used to design a complex three dimensional system, namely a multi-component arm for a tube bending machine.

本文讨论了共享设计空间区域的两个不同实体同时进行拓扑优化的问题。该设计问题集中在两个主体（组件）的同时优化上，不仅必须优化每个主体的材质分布，而且还必须在两个主体之间划分设计空间。这种新颖的优化公式代表了一个设计问题，其中一个以上的组件必须位于一个有限的允许空间内。每个组件都有自己的功能和承载要求。本文提出了一种新颖的开发解决方案算法。关于先前发表的论文，新算法包括密度场的插值，该插值允许两个物体的网格的完全独立。由于可以将实体与任何任意网格划分网格，因此该新算法可以应用于任何实际几何形状。所开发的算法用于设计复杂的三维系统，即用于弯管机的多组件臂。