A Fully Automatic Computational Framework for Beam Structure Design from Continuum Structural Topology Optimization

This paper proposes a new fully automatic computational framework from continuum structural topology optimization to beam structure design. Firstly, the continuum structural topology optimization is performed to find the optimal material distribution. The centers of the elements (i.e., vertices) in the final topology are considered as the original model of the skeleton extraction. Secondly, the Floyd-Warshall algorithm is used to calculate the geodesic distances between vertices. By combining the geodesic distance-based mapping function and a coarse-to-fine partition scheme, the original model is partitioned into regular components. The skeleton can be extracted by using edges to link the barycenter of the components and decomposed into branches by identified joint vertices. Each branch is normalized into a straight line. After mesh generation, a beam finite element model is established. Compared to other methods in the literature, the beam structures reconstructed by the proposed method have a desirable centeredness and keep the homotopy properties of the original models. Finally, the cross-sectional areas of members in the beam structure are considered as the design variables, and the sizing optimization is performed. Four numerical examples, both 2D and 3D, are employed to demonstrate the validity of the automatic computational framework. The proposed method extracts a parameterized beam finite element model from the topology optimization result that bridges the gap between the topology optimization of continuum structures and the subsequent optimization or design that enables a fully automatic design of beam-like structures.