A thinning algorithm based approach to controlling structural complexity in topology optimization

Shape and topology optimization techniques aim to maximize structural performance through material redistribution. Effectively controlling structural complexity during the form-finding process remains a challenging issue. Structural complexity is usually characterized by the number of connected components (e.g., beams and bars), tunnels, and cavities in the structure. Existing structural complexity control approaches often prescribe the number of existing cavities. However, for three-dimensional problems, it is highly desirable to control the number of tunnels during the optimization process. Inspired by the topology-preserving feature of a thinning algorithm, this paper presents a direct approach to controlling the topology of continuum structures under the framework of the bi-directional evolutionary structural optimization (BESO) method. The new approach can explicitly control the number of tunnels and cavities for both two- and three-dimensional problems. In addition to the structural topology, the minimum length scale of structural components can be easily controlled. Numerical results demonstrate that, for a given set of loading and boundary conditions, the proposed methodology may produce multiple high-performance designs with distinct topologies. The techniques developed from this study will be useful for practical applications in architecture and engineering, where the structural complexity usually needs to be controlled to balance the aesthetic, functional, economical, and other considerations.