Concurrent topological optimization of two bodies sharing design space: problem formulation and numerical solution

Topology optimization is a widely used technique for deriving efficient structural layouts for components in many engineering fields. The optimization process deals with the definition of the optimal material distribution of single components subjected to specified loads and boundary conditions, in case made of different materials or with embedded regions corresponding to other components or actuators. In this paper, a novel topology optimization problem is proposed. The case of the concurrent topological optimization of two different components sharing a part of the design spaces is considered. The design problem represents a design situation in which more than one component has to be fitted in an enclosed space and each component has its own load carrying function. In the paper, the problem is solved by a numerical technique able to allocate the common part of the design space to each component. Inside the allocated space, the actual material distribution of the component is optimized by a standard topological optimization algorithm. Numerical examples are provided to show the potentialities of the method. A (simplified) practical design problem is also considered.