三维进化弹塑性并行有限元反分析系统研究
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摘要
随着国家基础建设的不断发展,越来越多大型、超大型岩土工程相继上马,这些工程不仅规模越来越大,而且其复杂程度也越来越高。传统的基于单机的有限元求解不仅面临着超大的自由度,而且还涉及到复杂的非线性本构关系,计算时间长、精度低已经成为人们不得不面对的一个问题。
区域分解算法是在并行机上求解偏微分方程数值解的一种方法。该方法先将偏微分方程求解区域划分为若干个子区域,然后在各个子区域并行求解。随着计算机及网络技术的发展,组建PC机联网的计算机群为人们提供了一个高效率的并行计算平台。本文在此背景下,对如何充分利用现有的计算资源,获得高效的有限元计算效率进行了研究。围绕这一问题,开展了以下几个方面的研究:
1) 结合区域分解算法的特点,引入锚固组合单元来模拟岩土工程中锚杆的加固效果,采用虚拟单元法模拟岩土工程开挖过程,结合大型稀疏矩阵方程组的并行共轭梯度算法,编制了基于Windows操作系统,适用于PC机群的岩土工程并行有限元计算程序。
2) 结合遗传算法和区域分解并行有限元算法,设计了进化并行有限元反分析算法,计算采用主—从并行模式,可根据测点的位移监测信息快速反演岩体的力学参数。
3) 并行程序开发采用面向对象的方式,其中包含了单元、材料、荷载、求解器、遗传算法等有限元类库,通过类库的管理可以方便地对程序进行维护和扩充。
4) 对水布垭电站尾水洞开挖断面锚固效果进行了并行有限元计算,分析了锚杆的加固效果及并行加速比;水布垭电站尾水洞阶段施工开挖工程计算规模大(百万单元)、开挖步多(20步),通过对其进行三维并行弹塑性分析,实现了在PC机群上完成海量计算的目的;最后对水布垭地下厂房岩层参数进行了并行反演计算。
With the base-construction developing in our country, more and more large-scale, super large-scale geotechnical engineering are constructing. These engineering not only have huge dimension but also have very complicated geological condition, traditional serial FEM program running on single PC becomes a "bottleneck" to meet the demands of such engineering. Faced the super-large degree of freedoms and intricate nonlinear constitutive relation, time-consuming, low-precision become a disadvantage of it.The domain decomposition is a numerically approximating solution to partial differential equations on parallel computers. It is to divide the domain over which the problem is defined into subdomains, and solve the subproblems in parallel. Mode. Within the past few years, workstation clusters have gained an increasing importance as platforms for parallel high-performance simulation problems. On this background, this dissertation makes a scientific research on how to get the maximum efficient computational result by taking full advantage of the restricted hardware. Surrounding this goal, we have completed the following work.1) Study the trait of domain decomposition method, introduce bolted element to simulate the anchor's support effect, use the null element method to simulate the excavation process, adopt the parallel precondition conjugate gradient for large-scale sparse matrix equations; develop a high efficient geotechnical parallel FEM program based on the PC cluster.2) Combined with genetic algorithm, utilized the quickly analysis trait of parallel FEM, design the 3D Evolution elasto-plastic parallel FEM back analysis algorithm using master-slave parallel mode, achieve the aim to quickly back-analysis rock's parameter.3) Using the C++ object-oriented techniques develop a parallel FEM program, codes include a set of element library, material library, load library, and solver library, design a class map for further research and developing.4) First make a parallel FEM analysis for Shuibuya tail-tunnels on COW, analysis the reinforcement effect of bolts and the parallel efficiency of program. Second complete the 3D parallel elastic-plastic FEM analysis for
区域分解算法是在并行机上求解偏微分方程数值解的一种方法。该方法先将偏微分方程求解区域划分为若干个子区域,然后在各个子区域并行求解。随着计算机及网络技术的发展,组建PC机联网的计算机群为人们提供了一个高效率的并行计算平台。本文在此背景下,对如何充分利用现有的计算资源,获得高效的有限元计算效率进行了研究。围绕这一问题,开展了以下几个方面的研究:
1) 结合区域分解算法的特点,引入锚固组合单元来模拟岩土工程中锚杆的加固效果,采用虚拟单元法模拟岩土工程开挖过程,结合大型稀疏矩阵方程组的并行共轭梯度算法,编制了基于Windows操作系统,适用于PC机群的岩土工程并行有限元计算程序。
2) 结合遗传算法和区域分解并行有限元算法,设计了进化并行有限元反分析算法,计算采用主—从并行模式,可根据测点的位移监测信息快速反演岩体的力学参数。
3) 并行程序开发采用面向对象的方式,其中包含了单元、材料、荷载、求解器、遗传算法等有限元类库,通过类库的管理可以方便地对程序进行维护和扩充。
4) 对水布垭电站尾水洞开挖断面锚固效果进行了并行有限元计算,分析了锚杆的加固效果及并行加速比;水布垭电站尾水洞阶段施工开挖工程计算规模大(百万单元)、开挖步多(20步),通过对其进行三维并行弹塑性分析,实现了在PC机群上完成海量计算的目的;最后对水布垭地下厂房岩层参数进行了并行反演计算。
With the base-construction developing in our country, more and more large-scale, super large-scale geotechnical engineering are constructing. These engineering not only have huge dimension but also have very complicated geological condition, traditional serial FEM program running on single PC becomes a "bottleneck" to meet the demands of such engineering. Faced the super-large degree of freedoms and intricate nonlinear constitutive relation, time-consuming, low-precision become a disadvantage of it.The domain decomposition is a numerically approximating solution to partial differential equations on parallel computers. It is to divide the domain over which the problem is defined into subdomains, and solve the subproblems in parallel. Mode. Within the past few years, workstation clusters have gained an increasing importance as platforms for parallel high-performance simulation problems. On this background, this dissertation makes a scientific research on how to get the maximum efficient computational result by taking full advantage of the restricted hardware. Surrounding this goal, we have completed the following work.1) Study the trait of domain decomposition method, introduce bolted element to simulate the anchor's support effect, use the null element method to simulate the excavation process, adopt the parallel precondition conjugate gradient for large-scale sparse matrix equations; develop a high efficient geotechnical parallel FEM program based on the PC cluster.2) Combined with genetic algorithm, utilized the quickly analysis trait of parallel FEM, design the 3D Evolution elasto-plastic parallel FEM back analysis algorithm using master-slave parallel mode, achieve the aim to quickly back-analysis rock's parameter.3) Using the C++ object-oriented techniques develop a parallel FEM program, codes include a set of element library, material library, load library, and solver library, design a class map for further research and developing.4) First make a parallel FEM analysis for Shuibuya tail-tunnels on COW, analysis the reinforcement effect of bolts and the parallel efficiency of program. Second complete the 3D parallel elastic-plastic FEM analysis for
引文
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