Variable Density Interpolation for Dynamic Topology Optimization

ABSTRACT Topology optimization problems are usually nonconvex, and different optimization paths often lead to different local optima. This phenomenon is particularly pronounced in dynamic situations, where it typically causes grayscale. The occurrence of grayscale is greatly dependent on material parameters such as stiffness and density. In particular, under finite deformation conditions, the effect of inertia becomes more significant, and the nonconvexity becomes more pronounced, making it difficult to achieve a clear topology with conventional interpolation functions. To address this issue, the present study proposes two novel interpolation functions for density in dynamic topology optimization considering finite deformation. The proposed interpolation functions can adjust their shape during optimization, effectively reducing the grayscale by driving the design variable towards a binary state (0 or 1). Firstly, we investigate the conditions under which grayscale is likely to occur by performing many optimization calculations using various material parameters and load frequencies, and then use the findings obtained to develop new interpolation functions. The proposed methods leverage a gradient‐based method, and the accuracy of sensitivity is verified. Finally, the effectiveness of the proposed methods is demonstrated through several numerical examples, highlighting their ability to achieve clear topologies while maintaining robustness in challenging dynamic scenarios.