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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Finite element analysis on implicitly defined domains: An accurate representation based on arbitrary parametric surfaces
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Finite element analysis on implicitly defined domains: An accurate representation based on arbitrary parametric surfaces

机译：隐式定义域上的有限元分析：基于任意参数曲面的精确表示

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摘要

In this paper, we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis. The novel contributions of this paper are threefold: (1) describe and validate a method to represent arbitrary parametric surfaces implicitly; (2) represent arbitrary solids implicitly, including sharp features using level sets and boolean operations; (3) impose arbitrary Dirichlet and Neumann boundary conditions on the resulting implicitly defined boundaries. The methods proposed do not require local refinement of the finite element mesh in regions of high curvature, ensure the independence of the domain's volume on the mesh, do not rely on boundary regulariza-tion, and are well suited to methods based on fixed grids such as the extended finite element method (XFEM). Numerical examples are presented to demonstrate the robustness and effectiveness of the proposed approach and show that it is possible to achieve optimal convergence rates using a fully implicit representation of object boundaries. This approach is one step in the desired direction of tying numerical simulations to computer aided design (CAD), similarly to the isogeometric analysis paradigm.
机译：在本文中，我们提出了一些新颖的结果和思想，用于有限元分析中几何表面的鲁棒且准确的隐式表示。本文的创新之处包括三个方面：（1）描述和验证一种隐式表示任意参数曲面的方法； （2）隐式表示任意实体，包括使用级别集和布尔运算的尖锐特征； （3）在结果隐式定义的边界上施加任意Dirichlet和Neumann边界条件。所提出的方法不需要在高曲率的区域中对有限元网格进行局部细化，确保域体积在网格上的独立性，不依赖于边界规则化，并且非常适合基于固定网格的方法，例如作为扩展有限元方法（XFEM）。数值算例表明了所提方法的鲁棒性和有效性，并表明使用对象边界的完全隐式表示可以实现最佳收敛速度。这种方法是将数值模拟与计算机辅助设计（CAD）捆绑在一起的理想方向上的第一步，类似于等几何分析范例。

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  • 作者

    Mohammed Moumnassi; Salim Belouettar; Eric Bechet; Stephane PA Bordas; Didier Quoirin; Michel Potier-Ferry;

  • 作者单位

    Centre de Recherche Public Henri Tudor, 29, Avenue JohnF. Kennedy, L-1855 Luxembourg, CD. Of Luxembourg, Luxembourg,Laboratoire d'ttude des Microstructures et de M6canique des Matiriaux, LEM3, CNRS, Universite Paul Verlaine - Metz, lie du Saulcy, 57045 Metz, France;

    Centre de Recherche Public Henri Tudor, 29, Avenue JohnF. Kennedy, L-1855 Luxembourg, CD. Of Luxembourg, Luxembourg;

    LTAS - Department of Aerospace and Mechanical Engineering, Universite de Lie~ge, Chemin des Chevreuils 1, 4000 Liige, Belgium;

    Cardiff School of Engineering, Institute of Modelling & Simulation in Mechanics & Materials, Cardiff University, Queen's Buildings, The Parade, Cardiff CF24 3AA, Wales, UK;

    Goodyear Innovation Center, L-7750 Cotmar-Berg, Luxembourg;

    Laboratoire d'ttude des Microstructures et de M6canique des Matiriaux, LEM3, CNRS, Universite Paul Verlaine - Metz, lie du Saulcy, 57045 Metz, France;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    implicit boundary representation; level set method; curved boundary and sharp edges; extended finite element method; cad-analysis; dirichlet;

    机译：隐式边界表示法;水平集方法;弯曲边界和锐边;扩展有限元法;CAD分析;Dirichlet;

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