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A generalized beta finite element method with coupled smoothing techniques for solid mechanics

机译：结合固体技术的广义β有限元方法

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摘要

This paper presents a generalized smoothing techniques based beta finite element method (βFEM) to improve the performance of standard FEM and the existing smoothed finite element methods (S-FEM) in solid mechanics. As we know, the edge-based (for 2D) or face-based (for 3D) strain smoothing techniques can bring much more accurate solutions than standard FEM, and offer lower bounds for force driven problems. The node-based smoothing technique with "overly-soft" feature, on the other hand has a unique property of producing upper bound solutions. This work proposes a novel generalized S-FEM with the smoothing domains generated based on both edges/faces and nodes. An adjustable parameter β is introduced to control the ratio of the area of edge/face-based and node-based smoothing domains. It is found that nearly exact solutions in strain energy can be obtained by tuning the parameter, making use of the important property that the exact solution is bonded by the solutions of NS-FEM and ES/FS-FEM. Standard patch tests are likewise satisfied. A number of numerical examples (static, dynamic, linear and nonlinear) have shown that the present βFEM method is found to be ultra-accurate, insensitive to mesh quality, temporal stable, capable of modeling complex geometry, immune from volumetric locking, etc.
机译：本文提出了一种基于β有限元方法（βFEM）的广义平滑技术，以提高标准FEM的性能以及现有的实体力学中的平滑有限元方法（S-FEM）。众所周知，基于边缘的（用于2D）或基于表面的（用于3D）应变平滑技术可以提供比标准FEM更精确的解决方案，并为受力驱动的问题提供了更低的界限。另一方面，具有“过软”功能的基于节点的平滑技术具有产生上限解的独特属性。这项工作提出了一种新颖的广义S-FEM，其平滑域基于边/面和节点生成。引入可调节参数β以控制基于边缘/面部和基于节点的平滑域的面积比。发现通过利用NS-FEM和ES / FS-FEM的溶液结合精确溶液的重要性质，可以通过调节参数来获得应变能的几乎精确的溶液。同样满足标准补丁测试。许多数值示例（静态，动态，线性和非线性）表明，目前的βFEM方法非常精确，对网格质量不敏感，时间稳定，能够对复杂的几何图形建模，不受体积锁定的影响等。

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  • 来源
    《Engineering analysis with boundary elements》 |2016年第12期|103-119|共17页
  • 作者

    W. Zeng; G.R. Liu; C. Jiang; T. Nguyen-Thoi; Y. Jiang;

  • 作者单位

    CEAS-Biomedical Engineering (BME), University of Cincinnati, 2901 Woodside, Cincinnati, OH 45221, USA,CEAS-School of Aerospace Systems, University of Cincinnati, 2851 Woodside, Cincinnati, OH 45221, USA;

    CEAS-School of Aerospace Systems, University of Cincinnati, 2851 Woodside, Cincinnati, OH 45221, USA;

    State Key Laboratory of Advanced Technology of Design and Manufacturing for Vehicle Body, Hunan University, 410082, China,CEAS-School of Aerospace Systems, University of Cincinnati, 2851 Woodside, Cincinnati, OH 45221, USA;

    Division of Computational Mathematics and Engineering, Institute for Computational Science (INCOS), Ton Duc Thang University, Ho Chi Minh City, Viet Nam,Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Viet Nam;

    Hefei General Machinery Research Institute, 888 West Changjiang Rd., Hefei 230031 China;

  • 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

    Computational methods; Strain smoothing techniques; Generalized beta finite element method (βFEM); Vibration analysis; Large deformation; Solution bound;

    机译：计算方法;应变平滑技术;广义β有限元法（βFEM）;振动分析;大变形;解界;

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