Topology optimization design of continuous body structures with single-phase materials

Abstract The effective utilization of materials and the optimization of structural performance have become important research topics. In this context, the technique of topological optimization emerges as a potent approach to refine the geometrical configuration and structural layout under specified limitations, with the goal of attaining superior functionality. The present study predominantly centers on the utilization of topological optimization, which is enhanced by the modification of feasible regions in the realm of single-phase materials. Firstly, a topology optimization model for single-phase materials is established, aiming to minimize compliance under the constraint of structural volume. A sub-model of this model is proposed based on the feasible region adjustment scheme. Subsequently, leveraging the moving asymptote method for approximating the expansion of the objective function, we derive an approximation of the second-order derivative of the objective function. This derivative is then subjected to a convexity treatment to ensure the robustness of the optimization process. By integrating the primary derivative of the objective function, a quadratic Taylor series approximation for the objective function is formulated. The issue is addressed by employing a smooth dual-solution approach. Ultimately, a series of validation cases are showcased to demonstrate the effectiveness of the method. This method not only effectively improves material utilization and structural performance but also provides a new optimization approach for engineering design.