An Accelerating Convergence Rate Method for Moving Morphable Components

Abstract

In the structural topology optimization approaches, the Moving Morphable Components (MMC) is a new method to obtain the optimized structural topologies by optimizing shapes, sizes, and locations of components. However, the size of the mesh has a strong influence on the rate of which the component builds the initial topological configuration by moving. The influence may slow down the convergence rate. In this paper, a hierarchical mesh subdivision solution method that can accelerate the convergence rate for the MMC is developed. First, the coarse mesh is used as the starting point for the optimization problem, and the construction process of the initial topology structure is increased speed by accelerating the movement of components. Second, the optimized solution obtained by the coarse mesh is equivalently mapped to the same problem with a finer mesh and used to construct a good starting point for the next optimization. Finally, two-dimensional (2D) MBB beam example and three-dimensional (3D) short cantilever beam example are provided so as to validate that with the use of the proposed approach, demonstrating that this method can improve the convergence rate and the stability of the MMC method.