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Methods for field quantity updating during plastic forming of metals using numerical manifold methods

DOI：

 作者 单位 邮编 黎梓雯 广东工业大学 510006 章争荣* 广东工业大学 510006

数值流形方法采用数学覆盖和物理覆盖两套分开且独立的覆盖网格进行数值计算，采用数值流形方法模拟塑性成形过程时，自由界面在固定数学网格上会产生运动变化，因此需要基于数学覆盖网格去更新物理网格以及进行物理覆盖的信息转换。本文针对轴对称问题采用四节点流形单元，提出了基于映射插值方法，计算当前时刻更新后的物理网格节点在上一时刻的坐标，使用上一时刻的覆盖函数及覆盖权函数求得更新后的物理覆盖网格节点的场量信息，并对计算结果进行迭代修正以降低误差。以二维轴对称变形中镦粗变形的场量更新为例展开数值计算，误差分析结果表明，以节点映射插值计算得到的节点信息作为初始值，在修正过程中迭代次数较少，更新速度快，说明使用该方法进行新旧物理覆盖网格的场量更新效果理想。

The numerical manifold method uses two sets of separate and independent coverage grids: mathematical cover and physical cover. When the numerical manifold method is used to simulate the plastic forming process, the physical domain will deform on the fixed mathematical mesh, so it is necessary to update the physical mesh based on the mathematical covering mesh and carry out the physical covering information transformation. In this paper, an interpolation mapping method is proposed to calculate the coordinates of the physical grid nodes updated at the current time at the previous time, and the field information of the physical mesh nodes updated at the previous time is obtained by using the cover function and weight function of cover at the previous time, and the calculation error can be reduced by revised iteration. The result of error analysis shows that the node information obtained by the node interpolation mapping is used as the initial value, and the number of iterations is less and the updating speed is faster, which indicates that the field quantity updating effect of the new and old physical covering grids is ideal. Key words: plastic forming; numerical manifold method; field update.
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