發(fā)布時間：2018-05-09 02:44

  本文選題：耦合算法 + 元胞自動機��； 參考：《中國機械工程》2017年17期

【摘要】：結(jié)合有限元和無網(wǎng)格算法的優(yōu)勢,提出了一種元胞自動機算法用以求解二維彈性力學(xué)問題。該算法將二維模型離散成一系列節(jié)點,這些節(jié)點被分成有限元群和無網(wǎng)格群。有限元區(qū)域被定義在問題的邊界附近,其中的任一節(jié)點和其周圍相鄰點的力學(xué)關(guān)系通過有限元單元建立;無網(wǎng)格區(qū)域定義在遠離原理問題邊界處,其中的節(jié)點之間的關(guān)系借用有限元中的位移插值概念建立。無論處于有限元區(qū)域還是無網(wǎng)格區(qū)域,任何一個節(jié)點都被置于元胞自動機的框架下進行處理,即節(jié)點的位移通過元胞自動機進行求解。與有限元方法相比,所提出的元胞自動機算法無需采用高斯消去法等傳統(tǒng)系統(tǒng)求解器,而是通過元胞自動機的自動演化解決問題。依據(jù)該算法,有限元和無網(wǎng)格方法可以實現(xiàn)無縫連接。數(shù)值算例驗證了該算法的新穎性和正確性。
[Abstract]:Combining the advantages of finite element method and meshless algorithm, a cellular automaton algorithm is proposed to solve two-dimensional elastic problems. The algorithm discretizes the two-dimensional model into a series of nodes, which are divided into finite element group and meshless group. The finite element region is defined near the boundary of the problem, in which the mechanical relations between any node and adjacent points are established by finite element element, and the meshless region is defined far from the boundary of the principle problem. The relationship between nodes is established by the concept of displacement interpolation in finite element method. No matter in the finite element region or in the meshless region, any node is dealt with under the framework of cellular automata, that is, the displacement of nodes is solved by cellular automata. Compared with the finite element method, the proposed cellular automata algorithm does not need to use traditional system solvers such as Gao Si elimination method, but solves the problem by the automatic evolution of cellular automata. According to this algorithm, the finite element method and the meshless method can realize the seamless connection. Numerical examples verify the novelty and correctness of the algorithm.
【作者單位】： 西南科技大學(xué)制造科學(xué)與工程學(xué)院;
【基金】：國家自然科學(xué)基金資助項目(11472232) 四川省教育廳教改項目(14JGCX07) 制造過程測試技術(shù)省部共建實驗室基金資助項目(13zxzk05)
【分類號】：O343

【相似文獻】

相關(guān)碩士學(xué)位論文 前2條

1 馬洪嶺;基于元胞自動機算法的有限元方法及實現(xiàn)[D];山東科技大學(xué);2007年

2 周珍珍;基于混合元胞自動機方法的結(jié)構(gòu)拓撲優(yōu)化研究[D];華中科技大學(xué);2009年

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本文編號：1864242