摘 要

本文的主要研究内容是基于变密度法的拓扑优化设计方法，研究其基本原理，用MATLAB编程实现，并将其应用于汽车摆臂结构设计实例上。首先简要介绍了本文的研究背景以及拓扑优化的研究现状，然后介绍了基于SIMP模型的变密度法基本理论，之后用MATLAB实现上述理论并应用于简单的案例，再使用OptiStruct对汽车摆臂进行轻量化设计，重建优化结果的三维模型并进行性能检验，最后同样使用OptiStruct对某型摆臂进行拓扑优化然后重建优化结果的三维模型并检验其可靠性。

首先，本文对基于SIMP插值模型的变密度法数学模型进行了重建和推导。简要归纳了变密度法的基本思想和理论，重新建立了SIMP数学模型，提出了常用于拓扑优化计算中的优化准则法，采用了敏度过滤法来抑制优化结果中棋盘格现象以及网格依赖现象的产生，并总结出基于优化准则法的拓扑优化计算的基本求解步骤。

其次，本文通过MATLAB编程实现上述基于变密度法的拓扑优化基本求解流程，并应用于简单的案例。在将理论应用到实际案例之前，先对优化结果影响较大的重要相关参数的取值进行讨论，得到每个重要相关参数的最佳取值范围。使用MATLAB编程对两个简单又有一定代表性的案例进行拓扑优化，并通过一个简单案例将拓扑优化过程中常用的两种求解方法进行对比，讨论优劣性及适用范围。

接着，本文使用OptiStruct对汽车摆臂进行拓扑优化设计。介绍了OptiStruct等相关软件以及结构优化设计的基本流程，描述了汽车摆臂结构的任务要求，使用HyperMesh模块在原三维模型的基础上构建汽车摆臂结构的有限元模型，然后使用OptiStruct求解，对求解过程以及优化结果进行分析，并使用Inventor对优化结果重建并进行性能检验。

最后，本文使用OptiStruct对某型摆臂结构进行拓扑优化设计。与汽车摆臂的设计要求不同的是，某型摆臂的结构以及工况更为复杂，且需要采用脱模方向约束。同样简要描述了某型摆臂的任务要求，利用HyperMesh模块对某型摆臂结构的三维模型构建有限元模型，进行相关设置后使用OptiStruct模块计算，根据各个性能指标的迭代曲线和优化结果简要评价计算过程的好坏，根据优化结果重建三维模型，并进行了应力分析，探讨了优化结果的性能。

关键词：拓扑优化 变密度法 SIMP模型 优化准则法 结构优化设计 汽车摆臂

Abstract

The main research content of this paper is topology optimization design method in view of the variable density method, researches its basic principle, uses MATLAB programming to realize it, and applies it to the automobile sway arm structure design example. Firstly, the research background and the current situation of topology optimization are introduced. Then, based on SIMP model, the basic theory of variable density method is introduced. Then MATLAB is used to realize the above theory and apply it to a series of simple cases. Next, OptiStruct is used to carry on the lightweight design to the automobile sway arm and Inventor is used to carry on the performance test to the optimization result reconstruction. Finally, OptiStruct is also used to carry on the work about topology optimization to a certain sway arm and then Inventor is used to carry on the reconstruction to the optimization result to test its reliability.

Firstly, the mathematical model of variable density method based on SIMP interpolation model is reconstructed and deduced. In this chapter, the basic idea and theory of the variable density method are briefly summarized. The SIMP interpolation mathematical model is rederived and established. And the OC algorithm commonly applied in topology optimization is put forward. The sensitivity filtering method is used for the numerical instability phenomenon which is easy to appear in the solution process. And the basic solution steps of topology optimization calculation based on OC algorithm are summarized.

Secondly, this paper uses MATLAB programming to realize the basic solution process of topology optimization in view of the variable density method, and applies it to a series of simple cases. Before applying the theory to the actual case, this paper first discuss the value of the important parameters which have great influence on the optimization results, and get the best value range of each important parameter. Then use MATLAB programming to go on optimal topology design of two simple and representative cases. A simple case is used to compare the two methods in the process of solution, and analyses their merits, demerits and the scope of application.

Then, this paper adopts the OptiStruct to carry on the topology optimization design to the car sway arm. This chapter introduces the related software such as OptiStruct and the basic process of structural optimization design. The design requirements of the automobile sway arm is described. Use HyperMesh to establish the automobile sway arm finite element model on the basis of the original three-dimensional model, then use OptiStruct to solve. After that, discuss the solution procedure and the optimization results. Inventor is adopted to rebuild and test the optimization results.

Finally, this paper uses OptiStruct to optimize the topology of a certain type of control sway arm structure. Different from the design requirements of automobile sway arm, the structure and working conditions of a control sway arm are more complex, and the release direction constraint is needed. In the same way, briefly describe the task requirements of the swing arm, HyperMesh module is adopted to build a finite element model of the swing arm structure. After relevant settings, OptiStruct module is used to calculate. According to the iteration curve of each performance index and the optimization results, the calculation process is briefly evaluated. Rebuild the three-dimensional model according to the optimization results, carry out the stress analysis, and discuss the performance of the optimization results.

key words: topological optimization, Variable density method, SIMP model, Optimization criterion method, Structural optimization design, Automobile sway arm

目 录

第1章 绪论 1

1.1 汽车摆臂研究背景及意义 1

1.2 拓扑优化概况 1

1.3 拓扑优化国内外研究现状 2

1.4 主要研究内容 3

第2章 基于变密度法的拓扑优化设计技术研究 6

2.1 引言 6

2.2 变密度法理论基础及基本原理 6

2.3 SIMP密度-刚度插值模型 7

2.4 优化准则法基本原理 8

2.5 敏度过滤法 9

2.6 拓扑优化的基本求解流程 11

2.7 本章小结 11

第3章 基于优化准则法的拓扑优化MATLAB实现 13

3.1 引言 13

3.2 重要参数的选取 13

3.3 MATLAB拓扑优化应用实例 16

3.4 OC算法与MMA算法的比较 20

3.5 本章小结 22

第4章 基于OptiStruct的汽车摆臂结构拓扑优化设计 23

4.1 引言 23

4.2 OptiStrust结构优化设计基本流程介绍 23

4.3 问题描述 23

4.4 汽车摆臂有限元模型的建立 24

4.5 拓扑优化设置与求解 28

4.6 优化结果分析 30

4.7 优化结果重建及性能检验 32

4.8 本章小结 34

第5章 基于OptiStruct的某型摆臂结构拓扑优化设计 35

5.1 引言 35

5.2 问题描述 35

5.3 某型摆臂有限元模型的建立 36

5.4 拓扑优化设置与求解 39