A Four-Noded Triangular (Tr4) Element for Solid Mechanics Problems with Curved Boundaries

Author:

Yue Jun Hong1ORCID,Liu Guirong23,Niu Ruiping4,Li Ming1

Affiliation:

1. Taiyuan University of Technology, Taiyuan, P. R. China

2. Consultant, Taiyuan University of Technology, Taiyuan, P. R. China

3. School of Aerospace Systems, University of Cincinnati, Cincinnati, USA

4. College of Mathematics, Taiyuan University of Technology, Taiyuan, P. R. China

Abstract

Linear triangular elements with three nodes (Tr3) were the earliest, simplest and most widely used in finite element (FE) developed for solving mechanics and other physics problems. The most important advantages of the Tr3 elements are the simplicity, ease in generation, and excellent adaptation to any complicated geometry with straight boundaries. However, it cannot model well the geometries with curved boundaries, which is known as one of the major drawbacks. In this paper, a four-noded triangular (Tr4) element with one curved edge is first used to model the curved boundaries. Two types of shape functions of Tr4 elements have been presented, which can be applied to finite element method (FEM) models based on the isoparametric formulation. FE meshes can be created with mixed linear Tr3 and the proposed Tr4 (Tr3-4) elements, with Tr3 elements for interior and Tr4 elements for the curved boundaries. Compared to the pure FEM-Tr3, the FEM-Tr3-4 can significantly improve the accuracy of the solutions on the curved boundaries because of accurate approximation of the curved boundaries. Several solid mechanics problems are conducted, which validate the effectiveness of FEM models using mixed Tr3-4 meshes.

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Lt

Subject

Computational Mathematics,Computer Science (miscellaneous)

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. An Element Decomposition Method for Three-Dimensional Solid Mechanics;International Journal of Computational Methods;2023-04-28

2. Fast Computations for the Lagrangian-averaged Vorticity Deviation Based on the Eulerian Formulations;International Journal of Computational Methods;2019-12-09

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