Topology Optimization Of Structure And Compliant Mechanisms

Optimization is the procedure of obtaining the best results under given conditions. As is known to all that the field of the application of structural topology optimization is steadily growing, for the efficient use of materials is of great importance, and the choice of the basic topology of structures and mechanical components is more important than that of sizing or shape optimization. It extends the ability of engineer to master the force-transmitting or thermo-transmitting path in the early design stage, and shorten the design cycle. At the same time, for its highly non-convex, nonlinear, topology optimization is considered as one of the most challenging research fields in structure optimization, especially in multi-physical field. Compared with size and shape optimization, topology optimization can make engineer get more economic advantages, it attracted considerable attention from mathematicians and engineers all over the world. For topology optimization, great improvement is achieved both in theory development and engineering application. During the past two decades, theory of topology optimization has been developed for structural and mechanical systems, including micro-structure (including homogenization and SIMP method etc.) and macro-structure (Bubble, topological derivative etc.) methods. The newly developed Level Set Method falls in the category of Evolutionary methods. Additionally, many optimization techniques have been developed and applied, such as Mathematical Programming. Genetic Algorithm, and Evolutionary Optimization.For divers problems encountered in industry, different objective functions may be defined, such as weight, eignfrenquency. Generally speaking, the goal of the structural topology design problem is to determine the optimal distribution of material within a given design domain that minimizes a given objective, see the minimization of cost function or the maximization of desired deformation, and satisfies a series of constraint functions. For different physical problems, the mathematical formulation of topology optimization is one of the most important problems. In another hand, the solution varies with the essences of the formulation. Thus, the development of solving methods of topology optimization is of great importance in both theory and application.This paper is devoted to the mathematical formulation of topology optimization as well as the numerical realization through the application of the state-of-the-art optimization techniques. The content of this paper spans theory development and practice in engineering problems and falls limitedly into the spirit of Topology Optimization, including the topology optimization of rigid structure, heat dissipationstructure and compliant mechanism. At the same time, analyzed the characteristics ol Level Set Method for topology optimization (LSM). this paper gives the Modi tied LSM algorithm. Main points elucidated in detail in this dissertation arc organized as follows:The Minimum Averaged Compliance Density Based Topology OptimizationMethod (Chapter 3). The objective of general topology optimization is to obtain theoptimal structure through the redistribution of material in design domain, but thegeometry has great influence on optimal topology. The main research of this chapterfocuses on the concurrent design of topology and geometry of structure, and aminimum averaged compliance density (ACD) based method for topologyoptimization of structures is proposed. Unlike the general topology optimizationmethod. ACD is taken as the objective function, and the topology and the dimensionsof design domain are optimized simultaneously. It is difficult to get ideal topology forthin-and-long structure for conventional topology optimization algorithm. Thischapter proposes a thinking of assemblage from topology of basic structure. I sing thenew algorithm, optimize simultaneously the material distribution and dimensions ofdesign domain, and the topology of basic structure with the minimum ACD can begotten easily. Thus the topology optimization of long-and-thin structure can be sohedthrough assembling oi~ the basic topology. Additionally, the influence of differentcombination of loadings (see different combination of the values of bending momentand shear force) on topology is analyzed through an example. Results show that theproposed method generates clear, simple topology.Improved Level Set Method of Topology Optimization (Chapter 4). This chapter gives an improved Level Set Method for topology optimization. Considering the shortcomings of LSM (Level Set Methods) that the resultant topology depends highly on that of initialization, the initial topology of complex structures, in which proper number and position of holes included in. cannot be determined in advance. Nature-Inspired computation of topology optimization shows a wonderful ideal solution to solving the problem. Combined the merits of both evolutionary optimization algorithm and LSM. the newly proposed criteria in this paper consists in inserting new holes at candidate region with low deformation energy during proper iteration. The proposed algorithm improves considerably the ability of LSM to find the optimal topology. In addition to achieving more accurate topology, the proposed algorithm is also more efficient. Numerical examples are presented to show the effectiveness and the high efficiency of the improved algorithm.Topology Optimization of Heat Dissipation Structure (Chapter 5). This chapter elucidates the problem of topology optimization of structural heat dissipation. The formulation of topology optimization of thermo structure is presented, of which pseudo density as design variable, heat dissipation objective function, and material volume limit constraint. The purpose of the structural thermo topology problem is to...