本文選題：漸進結構優(yōu)化　切入點：Von　出處：《重慶大學》2012年碩士論文

【摘要】：機械產(chǎn)品的設計將經(jīng)歷一個從總體框架設計到細節(jié)結構優(yōu)化設計的過程，結構優(yōu)化設計始于拓撲優(yōu)化，一個優(yōu)良的拓撲能夠為后續(xù)進行的形狀和尺寸優(yōu)化指明正確的方向。近二十年來，漸進結構優(yōu)化方法（ESO）在結構拓撲優(yōu)化領域中扮演著重要的角色，該理論方法的發(fā)展和完善引起了眾多研究者的關注。 雖然漸進結構優(yōu)化算法在理論研究和工程應用方面都取得眾多研究成果，但是該算法被認為是一種啟發(fā)式算法，缺乏嚴格的數(shù)學理論基礎�；赩on Mises應力準則的ESO的目標函數(shù)與優(yōu)化準則之間模糊的關系至今未能用合理的顯函數(shù)來表示；設計變量的離散特性被視為破壞了目標函數(shù)和約束函數(shù)的連續(xù)性和可微性；刪除率和進化率等優(yōu)化參數(shù)依靠經(jīng)驗取值的做法讓算法的可靠性和通用性飽受質(zhì)疑；算例結果與Michell桁架結構作粗略對比的驗證手段比較缺乏說服力。 本文就ESO方法有效性問題，，以解析法推導出基于VonMises應力的滿應力準則下的長懸臂式、短懸臂式以及槽型約束邊界式等幾種靜定結構的最優(yōu)拓撲和形狀，為驗證結果是否為最優(yōu)解提供了數(shù)學依據(jù)；基于ESO算法的思想，分析了幾種不同邊界條件的桁架結構和連續(xù)體結構的拓撲優(yōu)化過程；以基于Von Mises應力準則的ESO算法的四條基本假設作為分析對象，從滿應力與最小體積、VonMises應力與材料效率、漸進方法的必要性及其效率、離散變量與連續(xù)變量的優(yōu)化解法等方面對ESO方法的有效性進行了研究；本文研究從實例驗證方面并在一定程度上從理論方面證明了ESO方法具有很好的尋優(yōu)能力。 結構拓撲優(yōu)化設計往往在得出比較粗略的結構后就終止，只關注最主要的承載結構，而忽視了在承載結構間的孔洞區(qū)域內(nèi)合理布置更細節(jié)的拓撲結構的重要性。BESO對單元的恢復往往只能夠沿著存活單元邊界進行，很難在孔洞區(qū)域架起新的支承結構。本文基于ESO方法和變密度法提出了二次刪除策略以對現(xiàn)有ESO方法進行改進，該算法可在孔洞區(qū)域進行二次或者多次優(yōu)化，具有更好的全局尋優(yōu)能力，并通過一個經(jīng)典的簡支梁算例驗證了該方法的可行性。
[Abstract]:The design of mechanical products will go through a process from the overall frame design to the detailed structure optimization design. The structural optimization design begins with the topology optimization. A good topology can point out the correct direction for the subsequent shape and size optimization.In the past two decades, the evolutionary structural optimization method (ESO) has played an important role in the field of structural topology optimization. The development and improvement of this theoretical method has attracted many researchers' attention.Although the asymptotic structural optimization algorithm has made many achievements in both theoretical research and engineering application, it is considered to be a heuristic algorithm and lacks a strict mathematical theoretical basis.The fuzzy relation between the objective function and the optimization criterion of ESO based on Von Mises stress criterion has not been represented by reasonable explicit function, and the discrete characteristic of design variables is regarded as destroying the continuity and differentiability of objective function and constraint function.The reliability and generality of the algorithm are questioned by the method of empirical selection of the optimization parameters such as deletion rate and evolution rate, and the comparison between the results of the numerical examples and that of Michell truss structures is not convincing.In this paper, the optimal topologies and shapes of several statically indeterminate structures, such as long cantilever, short cantilever and groove-constrained boundary type, are derived by analytical method for the validity of ESO method under the full stress criterion of VonMises stress.Based on the idea of ESO algorithm, the topological optimization process of truss structure and continuum structure with different boundary conditions is analyzed.Taking four basic assumptions of ESO algorithm based on Von Mises stress criterion as analysis object, the necessity and efficiency of progressive method are analyzed from full stress and minimum volume Von Mises stress and material efficiency.In this paper, the validity of ESO method is studied in terms of the optimization method of discrete variables and continuous variables. In this paper, the effectiveness of ESO method is proved to be very good in the aspect of example verification and, to a certain extent, the theoretical aspect.Structural topology optimization design often ends after the relatively rough structure, and only focuses on the most important bearing structure.The importance of reasonable arrangement of more detailed topological structures in the voids between load-bearing structures is neglected. The restoration of the elements by BESO can only be carried out along the boundary of the surviving units, and it is difficult to set up new supporting structures in the voids.Based on the ESO method and the variable density method, this paper proposes a quadratic deletion strategy to improve the existing ESO method. The algorithm can be optimized twice or multiple times in the hole region, and has better global optimization ability.The feasibility of the method is verified by a classical simply supported beam example.
【學位授予單位】：重慶大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：TH122

【參考文獻】

相關期刊論文 前10條

1 莊守兵,吳長春,馮淼林,袁振;基于均勻化方法的多孔材料細觀力學特性數(shù)值研究[J];材料科學與工程;2001年04期

2 程耿東;關于桁架結構拓撲優(yōu)化中的奇異最優(yōu)解[J];大連理工大學學報;2000年04期

3 程耿東，張東旭;受應力約束的平面彈性體的拓撲優(yōu)化[J];大連理工大學學報;1995年01期

4 榮見華,姜節(jié)勝,顏東煌,趙愛瓊;基于人工材料的結構拓撲漸進優(yōu)化設計[J];工程力學;2004年05期

5 王光遠,王志忠;超靜定桁架滿應力解的存在條件[J];固體力學學報;1981年04期

6 榮見華,唐國金,楊振興,傅建林;一種三維結構拓撲優(yōu)化設計方法[J];固體力學學報;2005年03期

7 王健,程耿東;應力約束下薄板結構的拓撲優(yōu)化[J];固體力學學報;1997年04期

8 段寶巖,陳建軍;基于極大熵思想的桿系結構拓撲優(yōu)化設計研究[J];固體力學學報;1997年04期

9 蔡文學,程耿東;桁架結構拓撲優(yōu)化設計的模擬退火算法[J];華南理工大學學報(自然科學版);1998年09期

10 許素強，夏人偉;桁架結構拓撲優(yōu)化與遺傳算法[J];計算結構力學及其應用;1994年04期

相關博士學位論文 前1條

1 劉毅;雙向固定網(wǎng)格漸進結構優(yōu)化方法及其工程應用[D];清華大學;2005年

相關碩士學位論文 前3條

1 何林偉;結構拓撲優(yōu)化啟發(fā)式算法的研究[D];上海交通大學;2011年

2 陳敏志;基于自適應有限元的結構拓撲優(yōu)化法[D];河海大學;2006年

3 孫圣權;基于ESO的液壓機下橫梁結構拓撲優(yōu)化及雙向進化結構優(yōu)化方法研究[D];重慶大學;2008年

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