基于并行计算的金属塑性成形仿真分析中关键技术研究
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摘要
薄板成形是利用模具使板料发生塑性变形而形成零件的制造技术。为了缩短模具的开发周期，很多公司都推出了非常适合于模具设计工程师使用的板料成形数值模拟软件。但是随着板料成形的几何模型日趋复杂，有限元模型的日趋庞大，计算时间也随之大量增加。为了提高计算效率，本文采用并行策略对大规模薄板成形问题进行仿真求解，针对有限元模型的特点，建立了相关初始化分区系统。对于金属体积成形工艺，采用有限元法求解金属塑性体积成形仿真问题时，当工件变形到一定程度，将产生严重的网格畸变，此时，就有必要对有限元模型进行网格重构。然而，网格重构必须依赖于某种控制准则，不同的控制准则将产生不同的计算结果，目前没有统一的准则可用。另外，力学量在新旧网格之间的转换也会带来新的计算误差。因此，重构网格会造成精度下降和质量损失。对于较复杂的三维成形件，快速可靠的网格重划分至今仍是世界一大难题。无网格法可以解决金属体积成形仿真中单元畸变的问题，并且具有较高的计算精度，但由于无网格法中的形函数由离散点通过高次插值构造，因此计算效率较低。为此，本文建立了以RKPM无网格方法为理论基础的金属体积成形并行仿真系统。
综上所述，本文的创新点总结如下：
(1) 根据显式算法和并行计算环境的特点，建立了基于消息传递机制的粗粒度并行构架。显式有限元法和无网格数值计算方法具有良好的计算局部特性，即在不考虑接触过程的情况下，除了节点内力的传递过程，所有的计算均是在单元内部进行的。而IBM pSeries 690是一款先进的高端IBM UNIX服务器。针对数据中心所需的容量、性能和可靠性，pSeries 690上的POWER4+处理器采用了SMP-on-a-chip设计结构，而强大的逻辑分区功能使更多资源的处理过程可以从其它使用不那么频繁的处理过程中借入其他资源。基于以上原因，我们选择了基于消息传递模式的粗粒度并行构架。为了验证显式数值并行算法的优势，分别编制了相应的基于MPI和OPENMP并行测试程序，对雅克比迭代问题分别进行了求解。通过对二者加速比的比较，验证了粗粒度并行构架的可行性和高效性。
(2) 提出了基于多层次分区策略的修正多层次谱二分分区法和修正多层次几何二分分区法及其高效的存储结构。多层次算法分为粗化，分区和还原三个阶段，其中在粗化阶段，本文提出了基于顶点平衡策略(VBS)的混合边权重匹配粗化方法(MEM)；在分区阶段，针对谱二分分区法和几何二分分区法，构造了高效合理的存储结构；在还原阶段，本文采用了Kernighan-Lin局部优化算法，在并对其缺陷进行了修正的基础上提出了平衡KL(BKL)局部优化分区方法。根据以上分区优化理论，本文建立了基于修正多层次谱二分分区法(MMRSB)和修正多层次几何二
Sheet metal forming is an important process with utilizing the plasticity of metal to transform a sheet metal blank into a part with shell configuration by dies. In order to shorten the development cycle, some numerical computational software fitting for sheet forming simulation process were developed. With the complexity of geometry models of blank forming and reduction of the size of iterative step, the blank model needs meshing more fine finite element grids. For improving the computation efficiency, the simulation process will cost much more computational time. In order to solve large scale sheet forming problems, we introduce parallel strategy with simulation process and develop sheet forming explicit dynamics simulation system based on the Mindlin-Reissner theory and the Belytschko-Tsay shell element. We build the initial partition system according to the characters of finite element grids and programmed the interface program connecting the FEM parallel and partition system .Commonly bulk forming problems simulations adopt finite element method. The mesh distortions maybe occur while large deformation problems are solved by FEM. The underlying structure of these methods which originates from their reliance on a mesh is not well fit for the treatment of discontinuities which do not coincide with the original mesh grids. Thus, the most viable strategy for dealing with moving discontinuities in method with moving discontinuities in methods based on meshes is to remesh in each step of the evolution so that mesh grids remain coincident with the discontinuities throughout the evolution of the problem. This can, of course, introduce numerous difficulties such as the need to project between meshes in successive stages of problem, which leads to degradation of accuracy and complexity in the computer program, not to mention the burden associated with a large number of meshes. Currently, the adaptive mesh grids method is limited for tetrahedron element, so the rapid and credibility remesh method is the hard mission in computational mechanics fields. Meshless methods do not require costly mesh generation remeshing. Furthermore, meshless methods implement a functional basis and allow arbitrary placement of points, therefore the solution and its derivatives may be obtained directly where they are needed and with better accuracy than with finite element method where interpolation is required. Limitation of meshless method is the low computational efficiency due to high order interpolation. With the increasing size and complexity of the numerical structural models to solve, the analysis tends to be a very
综上所述，本文的创新点总结如下：
(1) 根据显式算法和并行计算环境的特点，建立了基于消息传递机制的粗粒度并行构架。显式有限元法和无网格数值计算方法具有良好的计算局部特性，即在不考虑接触过程的情况下，除了节点内力的传递过程，所有的计算均是在单元内部进行的。而IBM pSeries 690是一款先进的高端IBM UNIX服务器。针对数据中心所需的容量、性能和可靠性，pSeries 690上的POWER4+处理器采用了SMP-on-a-chip设计结构，而强大的逻辑分区功能使更多资源的处理过程可以从其它使用不那么频繁的处理过程中借入其他资源。基于以上原因，我们选择了基于消息传递模式的粗粒度并行构架。为了验证显式数值并行算法的优势，分别编制了相应的基于MPI和OPENMP并行测试程序，对雅克比迭代问题分别进行了求解。通过对二者加速比的比较，验证了粗粒度并行构架的可行性和高效性。
(2) 提出了基于多层次分区策略的修正多层次谱二分分区法和修正多层次几何二分分区法及其高效的存储结构。多层次算法分为粗化，分区和还原三个阶段，其中在粗化阶段，本文提出了基于顶点平衡策略(VBS)的混合边权重匹配粗化方法(MEM)；在分区阶段，针对谱二分分区法和几何二分分区法，构造了高效合理的存储结构；在还原阶段，本文采用了Kernighan-Lin局部优化算法，在并对其缺陷进行了修正的基础上提出了平衡KL(BKL)局部优化分区方法。根据以上分区优化理论，本文建立了基于修正多层次谱二分分区法(MMRSB)和修正多层次几何二
Sheet metal forming is an important process with utilizing the plasticity of metal to transform a sheet metal blank into a part with shell configuration by dies. In order to shorten the development cycle, some numerical computational software fitting for sheet forming simulation process were developed. With the complexity of geometry models of blank forming and reduction of the size of iterative step, the blank model needs meshing more fine finite element grids. For improving the computation efficiency, the simulation process will cost much more computational time. In order to solve large scale sheet forming problems, we introduce parallel strategy with simulation process and develop sheet forming explicit dynamics simulation system based on the Mindlin-Reissner theory and the Belytschko-Tsay shell element. We build the initial partition system according to the characters of finite element grids and programmed the interface program connecting the FEM parallel and partition system .Commonly bulk forming problems simulations adopt finite element method. The mesh distortions maybe occur while large deformation problems are solved by FEM. The underlying structure of these methods which originates from their reliance on a mesh is not well fit for the treatment of discontinuities which do not coincide with the original mesh grids. Thus, the most viable strategy for dealing with moving discontinuities in method with moving discontinuities in methods based on meshes is to remesh in each step of the evolution so that mesh grids remain coincident with the discontinuities throughout the evolution of the problem. This can, of course, introduce numerous difficulties such as the need to project between meshes in successive stages of problem, which leads to degradation of accuracy and complexity in the computer program, not to mention the burden associated with a large number of meshes. Currently, the adaptive mesh grids method is limited for tetrahedron element, so the rapid and credibility remesh method is the hard mission in computational mechanics fields. Meshless methods do not require costly mesh generation remeshing. Furthermore, meshless methods implement a functional basis and allow arbitrary placement of points, therefore the solution and its derivatives may be obtained directly where they are needed and with better accuracy than with finite element method where interpolation is required. Limitation of meshless method is the low computational efficiency due to high order interpolation. With the increasing size and complexity of the numerical structural models to solve, the analysis tends to be a very
引文
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