大型结构三维地震反应分析并行计算方法研究

发布时间：2018-06-06 14:57

本文选题：结构动力分析 + 非线性　；参考：《中国地震局工程力学研究所》2012年博士论文

【摘要】：随着科学技术的快速进步和经济条件的迅速改善，世界各地对大型结构的需求越来越多。对这些大型结构进行地震反应分析时，存在两个科学技术上的挑战：（1）结构有限元模型的单元数和自由度数巨大；（2）该类结构受高阶振型影响较大，需要建立高阶的求解方程。并行计算技术的出现，为顺利的求解该类型结构，确保计算精度，提供了很好的方法和手段。本研究利用并行计算技术，研究了大型结构的地震反应分析方法。研究内容主要包括以下几个方面： 1．深入研究了区域剖分方法的国内外研究现状，对部分方法编制了C/C++程序并进行区域剖分效果的对比，分析了各个方法的优缺点及适用范围。 2．对各种区域分解算法进行了深入的研究，分析总结了各种常用算法的优缺点。 3．专门对子结构分析方法进行了研究，编制了相应的C/C++程序，并利用ANSYS作前处理器，得到相应的结构刚度矩阵和荷载矩阵后，对二个单元和四个单元的简单悬臂梁进行了试验性并行计算算法的研究，此方法的详细研究为后续方法的研究奠定了基础。 4．详细研究了BDD（Balancing Domain Decomposition）方法，BDD方法是一种子结构方法，其主要是把结构分成若干个子区域，每个子区域分成区域与区域间的边界节点和剩余的内部节点，每个子区域首先进行自由度静力凝聚，形成界面节点自由度方程。然后应用BDD预处理子的预处理共轭梯度法求解各个界面方程，在求解过程中要交换界面之间的信息，最终得到各个节点的位移和应力情况。 5．基于区域分解算法对结构的静力和动力问题进行了并行计算方法研究，在进行大型结构的动力并行计算分析时，利用Newmark-β法对时间离散化积分。对于动力分析，基于ADVENTURE编制了并行计算程序，实例证明，编译的程序可以用于大型结构的动力并行计算分析。 6．基于区域分解算法对静力非线性和动力非线性有限元进行了并行计算方法的研究，在非线性方程求解中，在每个荷增量步内采用了牛顿-拉夫逊迭代法，，在牛顿-拉夫逊的每个迭代步内使用了共轭梯度法进行相应的迭代计算，对于动力非线性分析，也基于ADVENTURE编制了并行计算程序，实例证明，编译的程序可以用来求解大型结构的动力非线性反应。 7．应用上述方法对意大利的万神庙进行了三维地震反应分析，该结构总共划分为1,329,027个四结点的四面体单元，结果表明，当采用96个计算节点时，只需要短短的十一分钟左右的计算时间。
[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.
【学位授予单位】：中国地震局工程力学研究所
【学位级别】：博士
【学位授予年份】：2012
【分类号】：TP338.6;TU311.3

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