發(fā)布時間：2018-11-18 14:50

【摘要】：作為一種新型的結(jié)構(gòu)拓?fù)鋬?yōu)化方法，，移動粒子法成功地消除了優(yōu)化過程中出現(xiàn)的一些數(shù)值不穩(wěn)定現(xiàn)象。但是與其他類型的拓?fù)鋬?yōu)化方法相同，移動粒子法也存在著計算耗時長、優(yōu)化求解效率低等問題，這也制約了其在工程實際中的應(yīng)用。本文主要從本質(zhì)邊界條件的處理方式與移動步長大小的確定方法兩方面研究了拓?fù)鋬?yōu)化效率的影響因素，在此基礎(chǔ)上提出運用位移約束方程法施加本質(zhì)邊界條件并利用自適應(yīng)移動步長插點法進(jìn)行拓?fù)鋬?yōu)化，主要研究內(nèi)容如下： 1.分析了無網(wǎng)格Galerkin法結(jié)構(gòu)分析時本質(zhì)邊界條件的處理方法對計算效率的影響；提出運用位移約束方程法施加本質(zhì)邊界條件，闡述了位移約束方程法的基本理論。利用Visual Fortran編程分析了相關(guān)算例，結(jié)果表明位移約束方程法在保證計算結(jié)果精度的前提下可以提高計算效率并能夠節(jié)省存儲量。 2.對比了拉格朗日乘子法與位移約束方程法在拓?fù)鋬?yōu)化時的效率，進(jìn)一步證實了位移約束方程法在提高拓?fù)鋬?yōu)化效率方面的優(yōu)勢；分析了移動粒子法節(jié)點最小密度值出現(xiàn)退化的原因，提出了自適應(yīng)移動步長插點法。通過Visual Fortran編寫程序?qū)ο嚓P(guān)算例進(jìn)行了分析討論，驗證了該方法在提高拓?fù)鋬?yōu)化求解效率方面的優(yōu)勢。 3.針對可移動節(jié)點密度判定值這一重要參數(shù)對拓?fù)鋬?yōu)化結(jié)果及優(yōu)化效率的影響進(jìn)行了分析討論；得到了可移動節(jié)點密度判定值的大小與迭代次數(shù)及最終拓?fù)溥吔邕B續(xù)性的相互關(guān)系，為改進(jìn)優(yōu)化算法的提出提供了一個突破口。 4.分析了自適應(yīng)移動步長插點法在計算節(jié)點最小密度值小于0.1時迭代次數(shù)多、耗時長的原因；結(jié)合可移動節(jié)點密度判定值對優(yōu)化迭代過程的影響，提出了一種改進(jìn)的優(yōu)化算法。利用Visual Fortran編程將其實現(xiàn)，算例分析結(jié)果表明，改進(jìn)的優(yōu)化算法縮短了節(jié)點最小密度值小于0.1的迭代次數(shù)與計算時間，提高了拓?fù)鋬?yōu)化效率。 本文運用位移約束方程法處理本質(zhì)邊界條件，并利用自適應(yīng)移動步長插點法進(jìn)行拓?fù)鋬?yōu)化，成功地消除了在迭代過程中出現(xiàn)的節(jié)點最小密度值及其梯度值退化現(xiàn)象。在前面分析基礎(chǔ)上提出的改進(jìn)優(yōu)化算法，縮短了節(jié)點最小密度值小于0.1時的計算時間，在保證計算結(jié)果質(zhì)量的同時，進(jìn)一步提高了拓?fù)鋬?yōu)化效率。
[Abstract]:As a new topology optimization method, moving particle method successfully eliminates some numerical instability in the optimization process. However, as with other topology optimization methods, the moving particle method also has the problems of long calculation time and low efficiency, which restricts its application in engineering practice. In this paper, the factors affecting the efficiency of topology optimization are studied from two aspects: the treatment of essential boundary conditions and the determination of moving step size. On this basis, the essential boundary condition is applied by the displacement constraint equation method and the topology optimization is carried out by the adaptive moving step interpolation method. The main research contents are as follows: 1. This paper analyzes the influence of the treatment method of essential boundary conditions on the computational efficiency in the structural analysis of meshless Galerkin method, and puts forward the application of the displacement constraint equation method to the essential boundary conditions, and expounds the basic theory of the displacement constraint equation method. The results show that the displacement constraint equation method can improve the calculation efficiency and save the storage capacity on the premise of ensuring the accuracy of the calculation results. 2. The efficiency of Lagrange multiplier method and displacement constraint equation method in topology optimization is compared, and the superiority of displacement constraint equation method in improving topology optimization efficiency is further confirmed. In this paper, the causes of the degradation of the minimum density of moving particle method nodes are analyzed, and the adaptive moving step insertion method is proposed. Some examples are analyzed and discussed by Visual Fortran, and the advantages of this method in improving the efficiency of topology optimization are verified. 3. The influence of the decision value of mobile node density on the topology optimization results and optimization efficiency is analyzed and discussed. The relationship between the decision value of mobile node density and the number of iterations and the continuity of the final topological boundary is obtained, which provides a breakthrough for the improvement of the optimization algorithm. 4. The reasons for the number of iterations and the time consuming of adaptive step insertion method in calculating the minimum density of nodes less than 0.1 are analyzed. Combined with the influence of mobile node density decision value on the optimization iterative process, an improved optimization algorithm is proposed. The result of example analysis shows that the improved optimization algorithm shortens the number of iterations and computation time when the minimum density of nodes is less than 0.1, and improves the efficiency of topology optimization. In this paper, the essential boundary conditions are dealt with by using the displacement constraint equation method, and the topological optimization is carried out by using the adaptive moving step insertion method, which successfully eliminates the degradation of the minimum density and gradient values of nodes in the iterative process. The improved optimization algorithm based on the previous analysis shortens the computing time when the minimum density of the node is less than 0.1 and improves the efficiency of topology optimization while ensuring the quality of the results.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：TH122

【參考文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前4條

1 陳敏;基于EFG法的連續(xù)體結(jié)構(gòu)模態(tài)拓?fù)鋬?yōu)化研究[D];湘潭大學(xué);2010年

2 曾興國;基于移動粒子法的連續(xù)體結(jié)構(gòu)拓?fù)鋬?yōu)化研究[D];湘潭大學(xué);2011年

3 伍賢洪;基于自適應(yīng)的EFG法連續(xù)體結(jié)構(gòu)拓?fù)鋬?yōu)化研究[D];湘潭大學(xué);2011年

4 張建平;基于RKPM的結(jié)構(gòu)動力分析及形狀優(yōu)化研究[D];湘潭大學(xué);2007年

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