Automated extraction method of STM for 3D topology optimization based on moving morphable components

The Strut-and-Tie Method is considered a helpful tool for the analysis and design of reinforced concrete structures and has been incorporated into different structural design codes. However, the low efficiency of the construction of the three-dimensional (3D) Strut-and-Tie model (STM) has been a key problem limiting the widespread use of the STM. To realize the efficient construction of STM, an automated extraction method based on the moving morphable components (MMC) is established. The presented method is divided into four parts: 3D topology optimization, curve skeleton extraction, spatial frame extraction, and shape optimization. To improve the computational efficiency, the 3D topology optimization and curve skeleton extraction are based on the MMC method and the Laplacian method based on the mean curvature flow (MCF), respectively. A spatial frame consistent with the topological form of the optimization result is formed by point identification and connection. In shape optimization, the truss-like index that can reflect the proportion of shear forces in the internal forces of the bars is introduced. The results of numerical examples show that the method efficiently constructs the STM with reasonable stress and regular geometry. A smooth and medial curve skeleton is extracted from the optimized structure by the Laplacian extraction method. Shape optimization constrained by the truss-like index enhances the regularity of STM and realizes the change of optimized structures from frames to trusses.