Strain smoothing in FEM and XFEM
Strain smoothing in FEM and XFEM
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DOI：
10.1016/j.compstruc.2008.07.006
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发表时间：
2010-12
影响因子：
4.7
通讯作者：
S. Bordas;T. Rabczuk;N. Hung;Vinh Phu Nguyen;S. Natarajan;Tino Bog;Dongliang Quan;Nguyen Vinh Hiep-Nguyen-Vi
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文献类型：
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作者：
S. Bordas;T. Rabczuk;N. Hung;Vinh Phu Nguyen;S. Natarajan;Tino Bog;Dongliang Quan;Nguyen Vinh Hiep-Nguyen-Vi
本文介绍了应变平滑在有限元中的应用所取得的最新成果，并对不连续性和奇异性问题提出了适当的扩展。数值结果表明，对于二维和三维连续体，锁定可以避免。新的板和壳配方，避免剪切和膜锁定也简要回顾。然后将该原理推广到单位分割富集法，以简化扩展有限元法中间断近似的数值积分。文中给出了线弹性连续体裂纹和裂纹板问题的算例。在后一种情况下，所提出的配方抑制锁定和收益率元件的行为非常好，即使在薄板的限制。两个重要的特点，提出的一组元素是他们的不敏感性网格变形和较低的计算成本比标准的有限元相同的精度。这些元素很容易在现有的代码中实现，因为它们只需要修改离散梯度算子B。
We present in this paper recent achievements realised on the application of strain smoothing in finite elements and propose suitable extensions to problems with discontinuities and singularities. The numerical results indicate that for 2D and 3D continuum, locking can be avoided. New plate and shell formulations that avoid both shear and membrane locking are also briefly reviewed. The principle is then extended to partition of unity enrichment to simplify numerical integration of discontinuous approximations in the extended finite element method. Examples are presented to test the new elements for problems involving cracks in linear elastic continua and cracked plates. In the latter case, the proposed formulation suppresses locking and yields elements which behave very well, even in the thin plate limit. Two important features of the set of elements presented are their insensitivity to mesh distortion and a lower computational cost than standard finite elements for the same accuracy. These elements are easily implemented in existing codes since they only require the modification of the discretized gradient operator, B.