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| 多尺度六面体单元网格连接方法研究 |
| Research on the connection of multi-scale hexahedral finite element meshes |
| 投稿时间：2020-12-31 修订日期：2021-02-20 |
| DOI： |
| 中文关键词: 等参变换 虚结点 多尺度网格 形函数 有限元 |
| 英文关键词:isoparametric transformation virtual node multiscale mesh shape function finite element |
| 基金项目:国家自然基金;南京工程学院创新项目面上基金 |
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| 中文摘要: |
| 提出多结点六面体单元的结点形函数构建方法，解决了数字化分析时两个多尺度有限元网格在接触界面由于单元结点不匹配而导致的结点属性不能连续传递的问题。首先将全局坐标下的六面体单元及其表面上多结点通过等参逆变换转成局部坐标下的规则六面体单元及其表面上多结点；在规则单元中，以每个结点为基点，分别沿三个正交的局部坐标方向在单元内寻找三个邻近结点，以基点与邻近结点间的距离和其属性变化值之间的关系建立三个一次函数，以这三个函数的乘积形式来构建或修正六面体单元的多结点和原结点的形函数，形函数将结点场值的影响域限制在由基点和邻近结点所确定的六面体可控区域之内，实现了网格结点属性在接触界面的无缝连接，保证了分析区域的场变量变化的连续性、一致性和各向同性。 |
| 英文摘要: |
| A nodal shape function construction method of a multi-node hexahedral element is put forward for the discontinuous transmission of nodal property on the interface of two nonmatching finite element meshes in analyzing multi-scale problems. First, each irregular hexahedral element and its nodes including additional nodes on its face are transferred into regular cubic element and nodes with the numerical inverse isoparametric mapping, then, on cubic element, each node is treated as a base point, its three neighboring nodes can be searched in three orthogonal directions, and three linear functions can be established respectively by the relationship between the distance from the base point to its neighboring nodes and the changing nodal property value, thus the nodal shape function can be built with the product of the three linear functions. The shape function makes the influence domain of a nodal property in a controlled hexahedral area determined by the base point and its three neighboring nodes. It makes the nodal property on the interface of two contact meshes seamless connect, and it ensures the change of the field in the region for analysis be continuous, conforming and isotropic. |
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