【摘要】：漸進(jìn)結(jié)構(gòu)優(yōu)化算法(Evolutionary structural optimization,ESO)是基于有限元方法的結(jié)構(gòu)拓?fù)鋬?yōu)化算法研究熱點(diǎn)之一。ESO采用不斷刪除設(shè)計(jì)域中的低效單元使結(jié)構(gòu)逐漸趨于最優(yōu)的樸素思想,方法易于實(shí)現(xiàn)。自創(chuàng)立以來(lái),ESO在算法的理論研究和工程應(yīng)用方面獲得了廣泛的成果。ESO屬于啟發(fā)式算法,Rozvany以Tie-beam算例來(lái)質(zhì)疑ESO方法的算法有效性。就此,目前已有研究者提出多種Tie-beam的解答算法,并以此改進(jìn)ESO算法的不足。其中基于虛擬材料的試探檢測(cè)算法通過(guò)檢測(cè)傳力路徑完整性,較好地解決了ESO方法在Tie-beam問(wèn)題中的缺陷。本文的研究進(jìn)一步表明,檢測(cè)算法對(duì)ESO優(yōu)化進(jìn)程中絕大多數(shù)的迭代步的檢測(cè)是沒(méi)有必要的。因此,本文將原虛擬材料的試探檢測(cè)過(guò)程拆分為兩個(gè)步驟:通過(guò)預(yù)判定選出優(yōu)化進(jìn)程中結(jié)構(gòu)剛度或強(qiáng)度發(fā)生異常變化的迭代步,然后只對(duì)這些可能出現(xiàn)結(jié)構(gòu)連接性破壞的異常迭代進(jìn)行試探檢測(cè),從而大幅提高了檢測(cè)算法的效率。原虛擬材料的試探檢測(cè)算法是就平面問(wèn)題的求解而設(shè)計(jì)的。本文將算法擴(kuò)展到板殼問(wèn)題,推導(dǎo)了相應(yīng)的檢測(cè)判斷準(zhǔn)則,設(shè)計(jì)了算法流程。算例表明,本文擴(kuò)展的基于虛擬材料的ESO檢測(cè)算法可成功彌補(bǔ)原ESO方法在求解某些薄壁結(jié)構(gòu)時(shí)失效的不足。本文將擴(kuò)展的虛擬材料檢測(cè)算法應(yīng)用于某型號(hào)垃圾集裝箱箱體薄壁結(jié)構(gòu)加強(qiáng)筋的布置問(wèn)題,成功獲得可用于生產(chǎn)實(shí)際的箱體薄壁結(jié)構(gòu)最優(yōu)拓?fù)�。本文提出的ESO改進(jìn)算法成功防止了原ESO方法在薄壁結(jié)構(gòu)的拓?fù)鋬?yōu)化中可能發(fā)生的失效,而且不影響ESO方法本身的尋優(yōu)能力,對(duì)ESO算法研究有一定理論意義,同時(shí)具有工程實(shí)用價(jià)值。
[Abstract]:Progressive structural optimization algorithm (Evolutionary structural optimization,ESO) is one of the research hotspots of structural topology optimization algorithm based on finite element method (FEM). ESO adopts the simple idea of deleting inefficient elements in the design domain to make the structure become more and more optimal, and the method is easy to implement. Since its creation, ESO has obtained extensive achievements in the theoretical research and engineering application of the algorithm. ESO is a heuristic algorithm, and Rozvany uses the Tie-beam example to question the validity of the ESO algorithm. At present, researchers have put forward a variety of Tie-beam solution algorithms, and improve the shortcomings of the ESO algorithm. The testing algorithm based on virtual material solves the defect of ESO method in Tie-beam problem by detecting the integrity of the transmission path. The research in this paper further shows that the detection algorithm is not necessary for the detection of most iterative steps in the ESO optimization process. Therefore, in this paper, the testing process of the original virtual material is divided into two steps: the iterative step of abnormal structural stiffness or strength change in the optimization process is selected by pre-determination. Then only these anomalous iterations which may occur structural connectivity breakage are probed and detected, thus greatly improving the efficiency of the detection algorithm. The testing algorithm of the original virtual material is designed to solve the plane problem. In this paper, the algorithm is extended to the plate and shell problem, the corresponding detection criteria are deduced, and the algorithm flow is designed. An example shows that the extended ESO detection algorithm based on virtual materials can successfully compensate for the failure of the original ESO method in solving some thin-walled structures. In this paper, the extended virtual material detection algorithm is applied to the arrangement of stiffeners in a certain type of waste container thin-walled structure, and the optimal topology of the thin-walled structure can be obtained successfully. The improved ESO algorithm proposed in this paper successfully prevents the failure of the original ESO method in the topology optimization of thin-walled structures, and does not affect the optimization ability of the ESO method itself, which is of theoretical significance to the study of the ESO algorithm. At the same time, it has engineering practical value.
【學(xué)位授予單位】：重慶大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：TB30

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