A three‐dimensional C1 finite element for gradient elasticity
A three‐dimensional C1 finite element for gradient elasticity
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DOI：
10.1002/nme.2449
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发表时间：
2009-03
影响因子：
2.9
通讯作者：
Stefanos‐Aldo Papanicolopulos;A. Zervos;I. Vardoulakis
中科院分区：
文献类型：
--
作者：
Stefanos‐Aldo Papanicolopulos;A. Zervos;I. Vardoulakis
在梯度弹性中，应变梯度项出现在虚功的表达式中，导致仅在位移场的有限元离散中需要C1连续插值。由于C1有限元的稀缺性及其可感知的计算成本，通常避免采用这种插值，而采用插值其他量以及位移的替代方法。在这种情况下，缺乏三维C1元素是特别令人关注的。在本文中，我们提出了一个新的C1六面体单元，据我们所知，这是有史以来第一个三维C1单元。结果表明，它可以通过单元素和补丁测试，并给出良好的收敛速度在基准边值问题的梯度弹性。进一步表明，C1元素不一定比替代方法在计算上更昂贵，并且有人认为它们在提供高质量解决方案方面可能更有效。版权所有© 2008约翰威利父子有限公司。
In gradient elasticity strain gradient terms appear in the expression of virtual work, leading to the need for C1 continuous interpolation in finite element discretizations of the displacement field only. Employing such interpolation is generally avoided in favour of the alternative methods that interpolate other quantities as well as displacement, due to the scarcity of C1 finite elements and their perceived computational cost. In this context, the lack of three‐dimensional C1 elements is of particular concern. In this paper we present a new C1 hexahedral element which, to the best of our knowledge, is the first three‐dimensional C1 element ever constructed. It is shown to pass the single element and patch tests, and to give excellent rates of convergence in benchmark boundary value problems of gradient elasticity. It is further shown that C1 elements are not necessarily more computationally expensive than alternative approaches, and it is argued that they may be more efficient in providing good‐quality solutions. Copyright © 2008 John Wiley & Sons, Ltd.