本文選題：無(wú)網(wǎng)格Galerkin法 + 自適應(yīng)��； 參考：《三峽大學(xué)》2013年碩士論文

【摘要】：隨著結(jié)構(gòu)拓?fù)鋬?yōu)化方法和無(wú)網(wǎng)格法的不斷成熟，將無(wú)網(wǎng)格方法應(yīng)用于結(jié)構(gòu)拓?fù)鋬?yōu)化中是一個(gè)研究熱點(diǎn)。不斷深入研究發(fā)現(xiàn)，在無(wú)網(wǎng)格法拓?fù)鋬?yōu)化離散和求解的過(guò)程中依然會(huì)存在諸多的問(wèn)題，如離散點(diǎn)云現(xiàn)象、棋盤(pán)格式、計(jì)算不穩(wěn)定、計(jì)算效率低等問(wèn)題。本文針對(duì)無(wú)網(wǎng)格法求解效率低的問(wèn)題，提出基于無(wú)網(wǎng)格伽遼金法的自適應(yīng)方法，并將該方法引入二維結(jié)構(gòu)的拓?fù)鋬?yōu)化中，主要研究?jī)?nèi)容如下： 1）基于節(jié)點(diǎn)應(yīng)變能梯度的自適應(yīng)無(wú)網(wǎng)格伽遼金法。以節(jié)點(diǎn)應(yīng)變能梯度的大小作為節(jié)點(diǎn)加密準(zhǔn)則選出需要加密的節(jié)點(diǎn)，然后按照一定的節(jié)點(diǎn)加密方法完成對(duì)需要加密節(jié)點(diǎn)的局部細(xì)化，再次根據(jù)新的節(jié)點(diǎn)分布情況進(jìn)行下一輪的無(wú)網(wǎng)格求解，如此循環(huán)計(jì)算，有效的提高計(jì)算的精度。通過(guò)多個(gè)典型的算例驗(yàn)證了該自適應(yīng)無(wú)網(wǎng)格伽遼金法的有效性。 2）基于上述研究成果，提出以節(jié)點(diǎn)相對(duì)密度值作為設(shè)計(jì)變量的自適應(yīng)無(wú)網(wǎng)格伽遼金拓?fù)鋬?yōu)化方法。對(duì)于使用無(wú)網(wǎng)格方法求解結(jié)構(gòu)拓?fù)鋬?yōu)化時(shí)計(jì)算效率低，結(jié)果存在離散點(diǎn)云及求解困難等問(wèn)題，在結(jié)構(gòu)拓?fù)鋬?yōu)化無(wú)網(wǎng)格離散的過(guò)程中，以節(jié)點(diǎn)相對(duì)密度作為設(shè)計(jì)變量，以優(yōu)化后的節(jié)點(diǎn)相對(duì)密度值作為拓?fù)鋬?yōu)化的節(jié)點(diǎn)加密準(zhǔn)則，，選出需要加密的節(jié)點(diǎn)，然后采用自適應(yīng)節(jié)點(diǎn)加密方法完成對(duì)該節(jié)點(diǎn)的加密，再次根據(jù)新的節(jié)點(diǎn)分布進(jìn)行下一輪無(wú)網(wǎng)格拓?fù)鋬?yōu)化計(jì)算，直到能得到清晰的拓?fù)浣Y(jié)果為止。算例結(jié)果表明，采用本文提出的自適應(yīng)EFG拓?fù)鋬?yōu)化方法可以減少結(jié)構(gòu)分析和優(yōu)化的設(shè)計(jì)變量數(shù)目，提高優(yōu)化效率。 3）將前述研究成果拓展到柔性機(jī)構(gòu)拓?fù)鋬?yōu)化設(shè)計(jì)領(lǐng)域，進(jìn)行柔性機(jī)構(gòu)自適應(yīng)無(wú)網(wǎng)格拓?fù)鋬?yōu)化設(shè)計(jì)。柔性機(jī)構(gòu)是利用自身柔性構(gòu)件的彈性變形來(lái)實(shí)現(xiàn)設(shè)計(jì)功能的一類(lèi)機(jī)械，具有自身運(yùn)動(dòng)大變形的特征，因此使用本文前述提出的自適應(yīng)EFG法進(jìn)行柔性機(jī)構(gòu)拓?fù)鋬?yōu)化，能滿足其幾何非線性及求解效率的要求，該方法發(fā)揮了無(wú)網(wǎng)格無(wú)需依賴網(wǎng)格和重構(gòu)網(wǎng)格的優(yōu)點(diǎn)，又有效的提高了無(wú)網(wǎng)格拓?fù)鋬?yōu)化的求解效率，拓展了本文研究方法的應(yīng)用領(lǐng)域。 本文利用無(wú)網(wǎng)格法易于對(duì)節(jié)點(diǎn)進(jìn)行加密的特點(diǎn)，提出適用于無(wú)網(wǎng)格伽遼金法力學(xué)分析和基于節(jié)點(diǎn)密度的自適應(yīng)結(jié)構(gòu)拓?fù)鋬?yōu)化方法。深入研究了自適應(yīng)節(jié)點(diǎn)加密準(zhǔn)則、節(jié)點(diǎn)加密方法和新增節(jié)點(diǎn)設(shè)計(jì)變量更新方法，通過(guò)對(duì)多個(gè)典型算例的編程計(jì)算，驗(yàn)證了該自適應(yīng)EFG法的正確性和優(yōu)越性，提高了求解精度和拓?fù)鋬?yōu)化的優(yōu)化效率，并有效的應(yīng)用于柔性機(jī)構(gòu)拓?fù)鋬?yōu)化中。
[Abstract]:With the development of structural topology optimization method and meshless method, it is a hot topic to apply meshless method to structural topology optimization. It is found that there are still many problems in the discretization and solution of meshless topology optimization, such as discrete point cloud phenomenon, chessboard format, unstable computation, low efficiency and so on. In this paper, an adaptive method based on meshless Galerkin method is proposed to solve the problem of low efficiency, and the method is introduced into the topology optimization of two-dimensional structure. The main research contents are as follows: 1) Adaptive meshless Galerkin method based on nodal strain energy gradient. The size of the strain energy gradient of the node is used as the encryption criterion to select the nodes that need to be encrypted, and then the local refinement of the nodes needed to be encrypted is completed according to a certain node encryption method. Based on the new node distribution, the next round of meshless solution is carried out, so the calculation accuracy can be improved effectively. The effectiveness of the adaptive meshless Galerkin method is verified by several typical examples. 2) based on the above research results, an adaptive meshless Galerkin topology optimization method with the relative density of nodes as the design variable is proposed. For the problems of low computational efficiency, discrete point cloud and difficulty in solving structural topology optimization using meshless method, the relative density of nodes is taken as the design variable in the process of structural topology optimization without meshless discretization. Using the optimized relative density value of the node as the topology optimized node encryption criteria, select the node to be encrypted, and then use adaptive node encryption method to complete the encryption of the node. The next round of meshless topology optimization is carried out again according to the new node distribution until clear topological results can be obtained. The numerical results show that the proposed adaptive EFG topology optimization method can reduce the number of design variables for structural analysis and optimization and improve the optimization efficiency. 3) the research results are extended to the field of topology optimization design of flexible mechanism, and adaptive meshless topology optimization design of flexible mechanism is carried out. The flexible mechanism is a kind of machinery which realizes the design function by using the elastic deformation of its own flexible members. It has the characteristics of large deformation of its own motion. Therefore, the adaptive EFG method proposed in this paper is used to optimize the topology of the flexible mechanism. This method can satisfy the requirements of geometric nonlinearity and solving efficiency. This method takes advantage of meshless and meshless without relying on meshes and reconstructing meshes, and improves the efficiency of solving meshless topology optimization effectively, which expands the application field of this method. In this paper, the meshless method is used to encrypt nodes easily, and a new adaptive topology optimization method based on node density is proposed for the meshless Galerkin method. The adaptive node encryption criterion, node encryption method and new node design variable updating method are deeply studied. The correctness and superiority of the adaptive EFG method are verified by programming calculation of several typical examples. It improves the accuracy and efficiency of topology optimization, and is applied to the topology optimization of flexible mechanism effectively.
【學(xué)位授予單位】：三峽大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類(lèi)號(hào)】：TH122

【參考文獻(xiàn)】

相關(guān)期刊論文 前7條

1 徐勝利;程耿東;;基于自適應(yīng)網(wǎng)格的結(jié)構(gòu)拓?fù)鋬?yōu)化[J];大連理工大學(xué)學(xué)報(bào);2009年04期

2 杜義賢;陳立平;羅震;;基于無(wú)網(wǎng)格Galerkin方法的整體式柔性機(jī)構(gòu)的多準(zhǔn)則拓?fù)鋬?yōu)化設(shè)計(jì)[J];固體力學(xué)學(xué)報(bào);2007年01期

3 榮見(jiàn)華,姜節(jié)勝,徐飛鴻,徐斌;一種基于應(yīng)力的雙方向結(jié)構(gòu)拓?fù)鋬?yōu)化算法[J];計(jì)算力學(xué)學(xué)報(bào);2004年03期

4 倪國(guó)喜;王瑞利;林忠;;無(wú)網(wǎng)格方法中粒子分布與自適應(yīng)研究[J];計(jì)算物理;2006年04期

5 張征;劉更;劉天祥;;自適應(yīng)無(wú)網(wǎng)格伽遼金方法的研究[J];機(jī)械科學(xué)與技術(shù);2008年08期

6 龔曙光;劉翔;謝桂蘭;張建平;;多載荷工況下無(wú)網(wǎng)格Galerkin法的拓?fù)鋬?yōu)化[J];機(jī)械工程學(xué)報(bào);2009年12期

7 伍賢洪;龔曙光;曾興國(guó);鐘勇文;;積分背景網(wǎng)格對(duì)自適應(yīng)EFG法拓?fù)鋬?yōu)化的影響研究[J];計(jì)算力學(xué)學(xué)報(bào);2012年05期

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