本文選題：漸進(jìn)結(jié)構(gòu)優(yōu)化　切入點(diǎn)：Von　出處：《重慶大學(xué)》2012年碩士論文

【摘要】：機(jī)械產(chǎn)品的設(shè)計(jì)將經(jīng)歷一個(gè)從總體框架設(shè)計(jì)到細(xì)節(jié)結(jié)構(gòu)優(yōu)化設(shè)計(jì)的過程，結(jié)構(gòu)優(yōu)化設(shè)計(jì)始于拓?fù)鋬?yōu)化，一個(gè)優(yōu)良的拓?fù)淠軌驗(yàn)楹罄m(xù)進(jìn)行的形狀和尺寸優(yōu)化指明正確的方向。近二十年來，漸進(jìn)結(jié)構(gòu)優(yōu)化方法（ESO）在結(jié)構(gòu)拓?fù)鋬?yōu)化領(lǐng)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(guān)注。 雖然漸進(jìn)結(jié)構(gòu)優(yōu)化算法在理論研究和工程應(yīng)用方面都取得眾多研究成果，但是該算法被認(rèn)為是一種啟發(fā)式算法，缺乏嚴(yán)格的數(shù)學(xué)理論基礎(chǔ)。基于Von Mises應(yīng)力準(zhǔn)則的ESO的目標(biāo)函數(shù)與優(yōu)化準(zhǔn)則之間模糊的關(guān)系至今未能用合理的顯函數(shù)來表示；設(shè)計(jì)變量的離散特性被視為破壞了目標(biāo)函數(shù)和約束函數(shù)的連續(xù)性和可微性；刪除率和進(jìn)化率等優(yōu)化參數(shù)依靠經(jīng)驗(yàn)取值的做法讓算法的可靠性和通用性飽受質(zhì)疑；算例結(jié)果與Michell桁架結(jié)構(gòu)作粗略對比的驗(yàn)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(dǎo)出基于VonMises應(yīng)力的滿應(yīng)力準(zhǔn)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(jié)構(gòu)的最優(yōu)拓?fù)浜托螤睿瑸轵?yàn)證結(jié)果是否為最優(yōu)解提供了數(shù)學(xué)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(jié)構(gòu)和連續(xù)體結(jié)構(gòu)的拓?fù)鋬?yōu)化過程；以基于Von Mises應(yīng)力準(zhǔn)則的ESO算法的四條基本假設(shè)作為分析對象，從滿應(yīng)力與最小體積、VonMises應(yīng)力與材料效率、漸進(jìn)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(jìn)行了研究；本文研究從實(shí)例驗(yàn)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(jié)構(gòu)拓?fù)鋬?yōu)化設(shè)計(jì)往往在得出比較粗略的結(jié)構(gòu)后就終止，只關(guān)注最主要的承載結(jié)構(gòu)，而忽視了在承載結(jié)構(gòu)間的孔洞區(qū)域內(nèi)合理布置更細(xì)節(jié)的拓?fù)浣Y(jié)構(gòu)的重要性。BESO對單元的恢復(fù)往往只能夠沿著存活單元邊界進(jìn)行，很難在孔洞區(qū)域架起新的支承結(jié)構(gòu)。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(jìn)行改進(jìn)，該算法可在孔洞區(qū)域進(jìn)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(gè)經(jīng)典的簡支梁算例驗(yàn)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(xué)位授予單位】：重慶大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：TH122

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