Research on the Connection of Multi-scale Quadrilateral Finite Element Meshes

doi:10.3901/JME.2019.09.100

Abstract

Abstract: A nodal shape function construction method of a multi-node quadrilateral element is put forward in this paper for the discontinuous transmission of nodal property on the interface of two nonmatching finite element meshes in analyzing multi-scale problems. First, each irregular quadrilateral element and its nodes including additional nodes are transferred into regular quadrilateral element and nodes by interpolating with numerical inverse isoparametric mapping, then, each node on the regular quadrilateral element is treated as a base point, its neighboring nodes can be searched in two orthogonal directions, and two product factors of this nodal shape function are established by the distance from the base point to its neighboring nodes and the changing value of their nodal properties, thus all the nodal shape functions can be built. Each of the shape function makes the influence range of a nodal property in a controlled quadrilateral area determined by the base point and its neighboring nodes. It makes the property of the nodes 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.

Key words: finite element, heterogeneous meshes, isoparametric transformation, shape function, virtual node

CLC Number:

TP391

FANG Xiwu, LIN Xiaohua, LIU Zhenyu. Research on the Connection of Multi-scale Quadrilateral Finite Element Meshes[J]. Journal of Mechanical Engineering, 2019, 55(9): 100-106.

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