A mesh-grading material point method and its parallelization for problems with localized extreme deformation
A mesh-grading material point method and its parallelization for problems with localized extreme deformation
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DOI：
10.1016/j.cma.2015.02.020
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发表时间：
2015-06
影响因子：
7.2
通讯作者：
Yanping Lian;P. Yang;Xiong Zhang;Fang Zhang;Yuangao Liu;P. Huang
中科院分区：
文献类型：
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作者：
Yanping Lian;P. Yang;Xiong Zhang;Fang Zhang;Yuangao Liu;P. Huang
物质点法作为一种无网格方法，在每一时间步采用欧拉背景网格作为有限元网格，其精度和效率主要取决于背景网格单元尺寸的设置。然而，传统的MPM通常使用具有均匀单元的规则背景网格，从计算效率的角度来看，这不适合于局部极端变形问题，实际上，局部细化背景网格是优选的。因此，网格分级材料点法（MGMPM），提出了这样的问题提供MPM的局部细化模拟的能力。与网格分级相关联的边缘位移连续性被嵌入到节点形状函数中。此外，在前人工作的基础上，将桁架单元引入到MGMPM中，模拟钢筋混凝土中的钢筋碰撞问题。此外，所提出的方法是并行化使用OpenMP（开放式多处理），以利用PC机的多核和超线程技术的大规模工程问题，其中使用循环级并行和代码块并行。通过对应力波传播、Taylor杆碰撞和侵彻问题的数值算例分析，表明该方法的计算效率比传统的MPM方法高得多，且内存要求低。
As a kind of meshless method, material point method (MPM) applies an Eulerian background grid served as a finite element mesh in each time step, and therefore its accuracy and efficiency are mainly dependent on the cell size setting of background grid. However, the conventional MPM commonly uses a regular background grid with uniform cells, which is not apposite for localized extreme deformation problems from the view point of computation efficiency, where, in fact, a local refined background grid is preferable. Hence, a mesh-grading material point method (MGMPM) is proposed here for such problems to supply MPM with the ability for local refinement simulation. The edge displacement continuity associated with mesh grading is embedded in the nodal shape functions. Besides, the truss element is incorporated into MGMPM to model the steel reinforcement bars in reinforced concrete impacting problems, based on our previous work. Furthermore, the proposed method is parallelized using OpenMP (Open Multi-Processing) to take advantage of PC power with multi-core and hyper threading technologies for large scale engineering problems, where both loop-level parallelism and code-block parallelism are used. Several numerical examples including stress wave propagation, Taylor bar impact, and penetration problems, are studied, which show that the efficiency of MGMPM is much higher than that of conventional MPM, and with lower memory requirement.