A sensitivity interpolation algorithm for the concurrent optimization of bodies sharing a common design space

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.