Topology optimization with closed B-splines and Boolean operations

In this work, free-form curves of closed B-splines (CBS) are introduced as basic design primitives to realize structural topology optimization in the way of shape optimization. Unlike the existing density and level-set methods, the CBS takes full advantage of its parametric form for the design deformability and flexibility with a few number of design variables, and its implicit form for Boolean operations of the structural topology accounting for any overlapping, merging and separation of different CBS no matter how geometric complexities of the CBS and the design domain are. The CBS is implemented within the computing framework of finite cell method (FCM) so that structural analysis and topology optimization can efficiently be carried out using the fixed mesh. Typical examples are tested to demonstrate the effectiveness and generality of the proposed method in dealing with engineering design problems.