摘 要
形狀優(yōu)化設(shè)計(jì)作為結(jié)構(gòu)優(yōu)化設(shè)計(jì)的一個(gè)重要分支，可以通過改變區(qū)域的幾何形狀來達(dá)到某種約束條件下的最優(yōu)，并要求某些物理量在邊界上滿足某種要求，以改善結(jié)構(gòu)的特性。在以往的形狀優(yōu)化設(shè)計(jì)過程中，很多是把節(jié)點(diǎn)坐標(biāo)和節(jié)點(diǎn)坐標(biāo)組合作為設(shè)計(jì)變量，這些描述結(jié)構(gòu)形狀的方法設(shè)計(jì)變量多，不易收斂，且在優(yōu)化迭代過程中易發(fā)生網(wǎng)格畸變的一些問題。如何建立一個(gè)能夠保證結(jié)構(gòu)分析網(wǎng)格不發(fā)生畸變，通過較少的設(shè)計(jì)變量就可以方便而有效地控制和描述復(fù)雜形狀變化的方法，是一個(gè)受到普遍關(guān)注的關(guān)鍵課題。
針對目前形狀優(yōu)化設(shè)計(jì)的難點(diǎn)問題，本文提出一種基于基本形狀向量法的復(fù)雜結(jié)構(gòu)形狀優(yōu)化設(shè)計(jì)方法。建立了一套基本形狀向量法的優(yōu)化設(shè)計(jì)理論模型，對基本形狀向量法的關(guān)鍵問題進(jìn)行了研究，編制了基本形狀向量法的分析和優(yōu)化程序，最后利用編制的分析和優(yōu)化程序?qū)拘螤钕蛄糠ㄟM(jìn)行了實(shí)例驗(yàn)證并取得了良好的優(yōu)化效果。
本文主要完成了以下幾個(gè)方面的研究：
（1）深入研究了結(jié)構(gòu)形狀優(yōu)化的基本理論，對結(jié)構(gòu)形狀優(yōu)化的邊界描述方法、設(shè)計(jì)變量和目標(biāo)函數(shù)的選擇、約束條件的確定進(jìn)行了分析。將基本形狀向量的概念引入結(jié)構(gòu)形狀優(yōu)化設(shè)計(jì)中，研究基本形狀優(yōu)化算法，建立了基于基本向量法結(jié)構(gòu)形狀優(yōu)化設(shè)計(jì)的優(yōu)化模型。
（2）對基本形狀向量法諸如基本形狀獨(dú)立性的檢查，基本形狀變化時(shí)其內(nèi)部形狀的從屬變動(dòng)問題等關(guān)鍵問題進(jìn)行了研究，并通過算例對其進(jìn)行驗(yàn)證，得出了基本形狀向量法在解決具有工藝約束和結(jié)構(gòu)約束的形狀設(shè)計(jì)的優(yōu)越性。
（3）對基本形狀向量生成方法進(jìn)行了研究，研究了網(wǎng)格劃分軟件模塊開發(fā)難點(diǎn)，提出了關(guān)聯(lián)線（面）法、節(jié)點(diǎn)均勻化法、映射變化法等幾種基本形狀向量的生成方法。
（4）深入研究基本形狀向量法的分析程序算法和優(yōu)化算法，并基于基本形狀向量法利用C語言進(jìn)行了分析程序和優(yōu)化程序的編制。
（5）利用編制的分析程序和優(yōu)化程序，結(jié)合MATLAB、Hyperworks軟件對汽輪機(jī)葉根齒形和汽車發(fā)動(dòng)機(jī)支架進(jìn)行了形狀優(yōu)化設(shè)計(jì)。從設(shè)計(jì)結(jié)果來看，對具有結(jié)構(gòu)約束的結(jié)構(gòu)，利用基本形狀向量法在改善結(jié)構(gòu)應(yīng)力、降低結(jié)構(gòu)重量的形狀優(yōu)化設(shè)計(jì)中可以達(dá)到較好的優(yōu)化效果。
關(guān)鍵詞 形狀優(yōu)化；基本形狀向量；有限元分析；優(yōu)化設(shè)計(jì)






Abstract
As an important branch of structure optimization design, shape optimization can get the optimum under certain condition by changing geometry shape of some region, and make some physics parameters satisfy certain demand on the border, in order to improve some characteristic of structure. In the past, the combination of node coordinates is often used as design variables during the shape optimization of the structures. These description of the shape methods have many design variables and always difficult to converge. Furthermore, it always have the mesh distortion problems during the shape iterations. How to build a method to ensure the mesh distortion does not occur and through fewer design variables can be easily and effectively control and describe the complex shape of the change in approach is a key issue of universal concern.
Refer to the difficult problem of the shape optimization, this paper presented a shape optimization method based on the basic shape vectors. Established a set of theoretical model based on the basic shape vectors method. Studied on the issue of the basic shape vectors method. Programmed on the analysis and the shape optimization of the shape method. At last, conducted examples certification based on the shape optimization method and achieved good effect of optimization.
In this paper, complete the following aspects:
(1) The fundamental theory of shape optimization was studied deeply. The describe method of border, the selecting of design variables and objective function, and how to determine constraint condition were analyzed. Basic shape vector design was introduced into shape optimization, the basic shape algorithms were studied and the theoretical model was established.
(2) The key issue of the basic shape vector method was studied deeply, such as the independent inspection of the basic vectors, the inner subordinate changes during the shape vectors changes. Draw the basic shape vector method in solving has the craft constraints and the shape of the structure restriction the superiority of the design.
(3) The basic shape vector generation method was studied, and puts forward the related line (surface) method and the mapping method, and attempt to use program to realize basic shape vector generation.
(4) The analysis program algorithm and optimized algorithm based on the basic shape vectors was deeply studied, and formulate the analysis and the optimization procedure using C language .
(5) Based on these studies, using the analysis of programs and optimization program, combined with MATLAB、Hyperworks software to conduct the shape optimization design of steam turbine hub tooth shape and automobile engine stent. From the design result, with the structure of the structural constraint, using the basic shape vector method in improving the structure stress reduce weight of the structure of the shape optimization design can achieve better optimization effect.

Key words : Shape Optimization; Basic Shape Vectors; Finite-Element Analysis;
Optimization design












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