【作者】 兰日清；

【导师】 王自法；

【作者基本信息】 中国地震局工程力学研究所 ， 防灾减灾工程及防护工程， 2012， 博士

【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。更多还原

【Abstract】 With the development of science and technology and the rapid expansionof economies, a large number of large-scale structures are built around theworld. There are two technical challenges in the earthquake response analysisof these large-scale structures:(1) the number of elements of the finite elementmodels of these structures and the number of degrees of freedom are so huge;(2) these structures are affected by higher order mode and a large number ofequations are needed to better analyze the structural response. In order to solvethe problems of these structures accurately, parallel computing tools can beused. In this dissertation, seismic response analysis of large-scale structure isstudied based on the application of parallel computing techniques. The researchmainly includes the following aspects:1. Current research of all kinds of domain decomposition methods arestudied, and C/C++programs of some methods are compiled. The merits anddemerits of each method are summarized, and the applicable scope of eachmethod is also studied.2. A variety of domain decomposition algorithms are analyzed, and thenthe advantages and disadvantages of the commonly used algorithms aresummarized.3. Sub-structure analysis method is studied carefully, and correspondingC/C++program is compiled where ANSYS is used for the preprocessor to getthe structural stiffness matrix and load matrix. Then static analysis of thesimple cantilever beam which is divided into two substructures is solved usingsubstructural parallel computing algorithms. Detailed study of this methodprovides the basis for subsequent study.4. BDD (Balancing Domain Decomposition) method is studied detailedly.BDD method is a substructure method, and the structure is split into severalnon-overlapping sub-structures. The node of each sub-structure is divided intointerface boundary nodes and the remaining internal nodes. Firstly, Staticcondensation of the degree of freedom in each sub-structure is carried out, and then equations of degree of freedom of the interface nodes are formulated.Secondly preconditioning conjugate gradient method are applied using BDDpreconditioner to solve the equations. Information between interface nodesmust be exchanged in the solving process. Finally displacement and stress ofeach node can be acquired.5. Based on domain decomposition algorithm, parallel computing methodsof static and dynamic analysis of large-scale structure are researched. Thisdomain decomposition has been implemented within a finite element code forlinear implicit transient dynamic analysis, and time integration is performedusing Newmark-β constant average acceleration method. The example showsthat the compiled program can be used for parallel computing analysis oflarge-scale structure.6. Based on domain decomposition algorithm, parallel computing methodsof static and dynamic nonlinear analysis of large-scale structure are alsoresearched. In the nonlinear equations, Newton-Raphson iteration method isused within each load increment or each time step, and conjugate gradientmethod is used for the corresponding iterative calculation in each iteration stepof the Newton–Raphson. Based on ADVENTURE the corresponding dynamicnonlinear parallel computing program is also compiled, and the example showsthat it can be used for large-scale dynamic nonlinear analysis of large-structure.7. Parallel computing analysis of Pantheon in Itali is implemented usingthe above methods on massive parallel processors. The finite element model ofthis structure is divided into about1,329,027four-node tetrahedral elements.The results show that about eleven minutes are needed when96processors areused.更多还原