Topology Optimization Method Based On Moving Morphable Components (MMC) Framework

Topology optimization, which aims at distributing available material in a prescribed design domain in an optimal way, as an important part of creative design methods, has undergo tremendous development in a wide range of industrial fields. As the economy is developing sustainably and healthily, people's demand for optimization of industrial products is growing. Traditional topology optimization methods dedicated to theoretical approaches, however, are limited by their implicit geometry characteristics. In the process of the conversion from optimization results to actual products, the result is not satisfactory. In order to overcome the deficiency of traditional topology optimization methods, the researches discussed in the present paper are as follows.Firstly, the basic contents of the moving morphable components (MMC) are given through the introduction of MMC. Mathematically, the general definition of components is given strictly with the movement and deformation mechanisms of components describing in details. Furthermore, topology changing description is also introduced in this section.Secondly, a new topology optimization approach based on moving morphable components is proposed. The proposed method improves several weaknesses of the previous approach in the sense that it can not only allow for components with variable thickness but also enhance the numerical solution efficiency substantially. This is achieved by constructing the topological description functions of components appropriately, and utilizing the ersatz material model through projecting the topological description functions of the components. In the present dissertation, problem formulation and shape sensitivity analysis are given under this MMC framework. Furthermore, some numerical examples are also illustrated to demonstrate the effectiveness of the proposed approach.Lastly, a new method for solving three-dimensional topology optimization problem, which usually involves a large number of design variables, is proposed. The novel aspect of the proposed method is that a set of structural components is introduced to describe the topology of a three-dimensional structure and the optimal structural topology is found by optimizing the layout of the components explicitly. Compared to the existing methods, the description of structural topology is totally independent on the finite element/finite difference resolution in the proposed solution framework and therefore the number of design variables can be reduced substantially. In the present dissertation, problem formulation and shape sensitivity analysis are also given under this MMC framework. And some benchmark examples are presented to demonstrate the effectiveness of the proposed approach.In the present dissertation, both theoretical derivation and numerical examples are considered. It proposes new topology optimization approach based on MMC framework. The optimal structural topology can be found by optimizing the layout of the components with the explicit geometry information. Large numbers of numerical examples demonstrate the effectiveness of the proposed approach.