本文選題：結構動力分析 + 非線性�。� 參考：《中國地震局工程力學研究所》2012年博士論文

【摘要】：隨著科學技術的快速進步和經(jīng)濟條件的迅速改善，世界各地對大型結構的需求越來越多。對這些大型結構進行地震反應分析時，存在兩個科學技術上的挑戰(zhàn)：（1）結構有限元模型的單元數(shù)和自由度數(shù)巨大；（2）該類結構受高階振型影響較大，需要建立高階的求解方程。并行計算技術的出現(xiàn)，為順利的求解該類型結構，確保計算精度，提供了很好的方法和手段。本研究利用并行計算技術，研究了大型結構的地震反應分析方法。研究內(nèi)容主要包括以下幾個方面： 1．深入研究了區(qū)域剖分方法的國內(nèi)外研究現(xiàn)狀，對部分方法編制了C/C++程序并進行區(qū)域剖分效果的對比，分析了各個方法的優(yōu)缺點及適用范圍。 2．對各種區(qū)域分解算法進行了深入的研究，分析總結了各種常用算法的優(yōu)缺點。 3．專門對子結構分析方法進行了研究，編制了相應的C/C++程序，并利用ANSYS作前處理器，得到相應的結構剛度矩陣和荷載矩陣后，對二個單元和四個單元的簡單懸臂梁進行了試驗性并行計算算法的研究，此方法的詳細研究為后續(xù)方法的研究奠定了基礎。 4．詳細研究了BDD（Balancing Domain Decomposition）方法，BDD方法是一種子結構方法，其主要是把結構分成若干個子區(qū)域，每個子區(qū)域分成區(qū)域與區(qū)域間的邊界節(jié)點和剩余的內(nèi)部節(jié)點，每個子區(qū)域首先進行自由度靜力凝聚，形成界面節(jié)點自由度方程。然后應用BDD預處理子的預處理共軛梯度法求解各個界面方程，在求解過程中要交換界面之間的信息，最終得到各個節(jié)點的位移和應力情況。 5．基于區(qū)域分解算法對結構的靜力和動力問題進行了并行計算方法研究，在進行大型結構的動力并行計算分析時，利用Newmark-β法對時間離散化積分。對于動力分析，基于ADVENTURE編制了并行計算程序，實例證明，編譯的程序可以用于大型結構的動力并行計算分析。 6．基于區(qū)域分解算法對靜力非線性和動力非線性有限元進行了并行計算方法的研究，在非線性方程求解中，在每個荷增量步內(nèi)采用了牛頓-拉夫遜迭代法，，在牛頓-拉夫遜的每個迭代步內(nèi)使用了共軛梯度法進行相應的迭代計算，對于動力非線性分析，也基于ADVENTURE編制了并行計算程序，實例證明，編譯的程序可以用來求解大型結構的動力非線性反應。 7．應用上述方法對意大利的萬神廟進行了三維地震反應分析，該結構總共劃分為1,329,027個四結點的四面體單元，結果表明，當采用96個計算節(jié)點時，只需要短短的十一分鐘左右的計算時間。
[Abstract]:With the rapid progress of science and technology and the rapid improvement of economic conditions, there is more and more demand for large structures all over the world. In the seismic response analysis of these large structures, there are two scientific and technical challenges: 1) the finite element number and the free degree of the finite element model of these large structures are very large. The emergence of parallel computing technology provides a good method and means to solve this type of structure smoothly and ensure the calculation accuracy. In this paper, parallel computing technique is used to study the seismic response analysis of large structures. The research mainly includes the following aspects: 1. In this paper, the current research situation of the regional division method is deeply studied, and the C / C program of some methods is compiled and compared with the results of the regional partition method. The advantages and disadvantages of each method and its application range are analyzed. 2. Various domain decomposition algorithms are studied, and their advantages and disadvantages are analyzed and summarized. 3. The substructure analysis method is studied, and the corresponding C / C program is compiled, and the corresponding stiffness matrix and load matrix are obtained by using ANSYS as the preprocessor. The experimental parallel computing algorithm for simple cantilever beams with two elements and four elements is studied in this paper. The detailed study of this method lays a foundation for the further study of the method. 4. In this paper, the BDD(Balancing Domain Decompositionmethod is studied in detail. It is a substructure method, which divides the structure into several sub-regions, each subregion is divided into boundary nodes and residual internal nodes. In each sub-region, the degree of freedom (DOF) is firstly condensed to form the interface node degree of freedom (DOF) equation. Then the preprocessing conjugate gradient method of BDD preprocessor is used to solve each interface equation. The information between interfaces is exchanged and the displacement and stress of each node are obtained. 5. Based on domain decomposition algorithm, the parallel computation method for static and dynamic problems of structures is studied. Newmark- 尾 method is used to discretize time integration in dynamic parallel computation and analysis of large structures. For dynamic analysis, a parallel computing program based on ADVENTURE is developed. The example shows that the compiled program can be used for dynamic parallel computation and analysis of large structures. 6. Based on the domain decomposition algorithm, the static nonlinear finite element method and the dynamic nonlinear finite element method are studied. In solving the nonlinear equations, Newton-Raphson iteration method is used in each incremental step. In each iteration step of Newton-Raphson, the conjugate gradient method is used to carry out the corresponding iterative calculation. For dynamic nonlinear analysis, a parallel calculation program based on ADVENTURE is also developed, which is proved by an example. The compiled program can be used to solve the dynamic nonlinear response of large structures. 7. Three-dimensional seismic response analysis of Panshenmiao in Italy is carried out by using the above method. The structure is divided into 1329027 tetrahedral elements with four nodes. The results show that 96 nodes are used. It only takes about eleven minutes to calculate.
【學位授予單位】：中國地震局工程力學研究所
【學位級別】：博士
【學位授予年份】：2012
【分類號】：TP338.6;TU311.3

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