Regular Position-Oriented Method for Mesh Smoothing
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ISSN 1860-2134
Regular Position-Oriented Method for Mesh Smoothing Yongqing Hai1
Yufei Guo2
Siyuan Cheng3
Yunpeng Hai4
1
( Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China) (2 X Lab, Second Academy of China Aerospace Science and Industry Corporation, Beijing 100854, China) (3 State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China) (4 College of Electromechanical Engineering, Qingdao University of Science and Technology, Qingdao 266061, China)
Received 25 August 2020; revision received 20 October 2020; Accepted 21 October 2020 c The Chinese Society of Theoretical and Applied Mechanics 2020
ABSTRACT Mesh smoothing is an essential technique for the improvement of mesh quality in finite element analysis, due to the fact that mesh quality has a large impact on the convergence of the computational scheme and the accuracy of the numerical results. A novel mesh smoothing method based on regular-position-guided operations is presented in this paper. The method introduced here contains two main stages: The first stage computes the regular position of each vertex based on the shape of the element and conducts regular-position-oriented-based element transformations independently; the second stage determines the finial position of each vertex according to its surrounding elements with an assembly strategy. This method is not limited to planar triangular mesh, but applicable to surface polygonal mesh. Numerical experiments on various mesh models demonstrate the effectiveness and potential of this method.
KEY WORDS Mesh smoothing, Element transformation, Finite element analysis, Mesh quality
1. Introduction For the feasibility and efficiency of computation, mesh is widely used as a fundamental approach of model discretization. Obtaining high-quality meshes is a prerequisite task in many applications. In the field of finite element analysis, amounts of cases reveal that poorly shaped elements can result in ill-conditioning of stiffness matrices and large interpolation error, which can be the cause of precision decline in simulation results [1]. Precisely speaking, these are called the quasi-uniform conditions that the element size is almost the same or the element density changes slowly in a local region, and the element aspect ratio is almost the same or isotropic in a local region. And finite element meshes conforming such conditions will lead to a good convergence behavior. Meanwhile, final performance is also influenced by mesh quality in many other areas such as 3D printing and geological modeling. In order to preserve rendering success and visual fidelity, it is also necessary to eliminate distortions in geometry models. Mesh generation has gained many achievements in decades of years. However, the initially generated meshes are not always satisfactory to various applications. Hence, quality improvement techniques need
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