A hierarchic family of isogeometric shell finite elements
A hierarchic family of isogeometric shell finite elements
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DOI：
10.1016/j.cma.2012.10.018
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发表时间：
2013-02-01
影响因子：
7.2
通讯作者：
Bischoff, M.
中科院分区：
文献类型：
--
作者：
Echter, R.;Oesterle, B.;Bischoff, M.
提出了一种基于NURBS形函数的等几何壳单元的层次结构。与经典的壳有限元公式相比，至少C-1的单元间连续性使得在一个NURBS面片内能够唯一且连续地表示表面法线。这不仅有利于Kirchhoff-Love型壳模型的制定，其中标准Galerkin弱形式的变分指数为2，但它也提供了剪切变形（Reissner-Mindlin型）壳和高阶壳模型的显着优势。对于一个5-参数壳配方与Reissner-Mindlin运动学的分层差矢量，占剪切变形叠加到旋转Kirchhoff-Love型导演的变形配置。在壳体运动学中，这种弯曲变形和剪切变形的分离导致了一种不受横向剪切闭锁影响的单元公式，而不需要采用进一步的补救措施，如减少积分、假定自然应变或混合有限元公式。层次结构的第三个成员是一个7参数模型，包括厚度变化，并允许应用未经修改的三维本构关系。曲率厚度锁定的现象，伴随着这种运动学延伸沿着，再次通过分层差矢量概念自动避免，而无需任何进一步的处理。膜锁定和面内剪切锁定通过两种不同的方法来消除：首先通过离散应变间隙（DSG）方法消除，其次使用基于Hellinger-Reissner变分原理的混合-混合方法去除寄生膜应变。三种不同的壳配方的层次运动学结构允许这些元素在一个网格内的直接组合，因此是模型自适应方法的理想基础。(C)2012爱思唯尔有限公司版权所有。
A hierarchic family of isogeometric shell finite elements based on NURBS shape functions is presented. In contrast to classical shell finite element formulations, inter-element continuity of at least C-1 enables a unique and continuous representation of the surface normal within one NURBS patch. This does not only facilitate formulation of Kirchhoff-Love type shell models, for which the standard Galerkin weak form has a variational index of 2, but it also offers significant advantages for shear deformable (Reissner-Mindlin type) shells and higher order shell models. For a 5-parameter shell formulation with Reissner-Mindlin kinematics a hierarchic difference vector which accounts for shear deformations is superimposed onto the rotated Kirchhoff-Love type director of the deformed configuration. This split into bending and shear deformations in the shell kinematics results in an element formulation which is free from transverse shear locking without the need to apply further remedies like reduced integration, assumed natural strains or mixed finite element formulations. The third member of the hierarchy is a 7-parameter model including thickness change and allowing for application of unmodified three-dimensional constitutive laws. The phenomenon of curvature thickness locking, coming along with this kinematic extension, again is automatically avoided by the hierarchic difference vector concept without any further treatment. Membrane locking and in-plane shear locking are removed by two different approaches: firstly elimination via the Discrete Strain Gap (DSG) method and secondly removal of parasitic membrane strains using a hybrid-mixed method based on the Hellinger-Reissner variational principle. The hierarchic kinematic structure of the three different shell formulations allows a straightforward combination of these elements within one mesh and is thus the ideal basis for a model adaptive approach. (C) 2012 Elsevier B.V. All rights reserved.