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.

An Eigenfrequency-Constrained Topology Optimization Method with Design Variable Reduction

“…Jia et al [29] combined ESO with LSM, which can reduce the number of iteration steps by automatically generating holes in the low-strain energy region near the node. Lian et al [30] added a hierarchical mesh refinement algorithm into the moving morphable component (MMC) algorithm to improve convergence speed. Joo and Jang [31] proposed a deep neural network topology optimization algorithm, which can improve the convergence speed by obtaining the history of intermediate designs.…”

Multi-material topology optimization considering natural frequency constraint

“…In additional to the conventional TO methods, Guo et al proposed the moving morphable components (MMC) method, which considered the geometry (e.g. thickness, length, angle and position) of the candidate components for TO (Guo et al, 2014, Zhang et al, 2016Lian et al, 2020). The density-based method utilizing the SIMP interpolation scheme has become the predominant TO approach in both literature and industrial applications because of its performance and computational efficiency (Deaton and Grandhi, 2014).…”