Linear smoothed polygonal and polyhedral finite elements
Linear smoothed polygonal and polyhedral finite elements
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DOI：
10.1002/nme.5324
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发表时间：
2017-03
影响因子：
2.9
通讯作者：
Amrita Francis;A. Ortiz-Bernardin;S. Bordas;S. Natarajan
中科院分区：
文献类型：
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作者：
Amrita Francis;A. Ortiz-Bernardin;S. Bordas;S. Natarajan
在高阶单元和任意多面体上的应变平滑技术比诸如常规多边形有限元方法等其他技术产生的解精度更低。在这项工作中，我们提出一种线性应变平滑方案，该方案提高了凸多面体上线性和二次近似的精度。主要思路是将多面体细分为单纯子单元，并在每个子单元中使用线性平滑函数来计算应变。然后将这个新的应变用于刚度矩阵的计算。通过求解一些基准问题来讨论所提出方案的收敛特性和精度。数值结果表明，所提出的线性应变平滑方案使得基于多面体的近似能够提供与传统四边形和六面体近似相同的最优收敛速率。精度也得到了提高，并且所有测试的方法都能以机器精度通过分片检验。版权所有©2016约翰威立父子有限公司
The strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes. The main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain. This new strain is then used in the computation of the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving a few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the same optimal convergence rate as traditional quadrilateral and hexahedral approximations. The accuracy is also improved, and all the methods tested pass the patch test to machine precision. Copyright © 2016 John Wiley & Sons, Ltd.