Separate control meshes for displacements and rotations for a shear locking free isogeometric Reissner‐Mindlin plate
Separate control meshes for displacements and rotations for a shear locking free isogeometric Reissner‐Mindlin plate
复制标题
用于无剪切锁定等几何 ReissnerâMindlin 板的位移和旋转的单独控制网格
DOI：
10.1002/pamm.201710129
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Klinkel S.
中科院分区：
文献类型：
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作者：
Kikis G.;Klinkel S.
在使用等几何Reissner‐Mindlin方法分析板壳弯曲问题时，可能会出现横向剪切锁定效应，特别是对于薄结构。克服锁定效应的一种可能性是增加NURBS基函数的多项式阶数。然而，在某些例子中，这种方法显示出一些缺陷，如振荡。对于低次多项式，只有少数几个有效的概念来消除锁定效应。一种是增强型假设应变（EAS）方法，该方法用于有限元公式，对变形单元的几何形状敏感。Beirão da Veiga等人[1]介绍了Reissner‐Mindlin板公式的新方法，其中使用不同的控制网格近似网格的位移和旋转。建筑物的物理空间始终保持不变。因此，该方法是根据等参范式。然而，用于位移和旋转的近似的形状函数可以具有不同的多项式次数和控制点的数量。通过这种方式，满足了纯弯曲的相容性要求，并避免了剪切锁定。该方法用于等几何Reissner‐Mindlin板公式，该公式基于退化壳公式[2]。选择基本的例子，并将结果与未改变的等几何Reissner-Mindlin板和使用MITC单元的有限元方法进行比较。结果表明，该方法具有与MITC单元相似的精度和效率，并且也适用于斜交单元。（© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA，魏因海姆）
In the analysis of plate and shell bending problems using an isogeometric Reissner‐Mindlin approach, transversal shear locking effects may occur especially for thin structures. One possibility to overcome locking effects is to increase the polynomial order of the NURBS basis functions. However, there are certain examples where this method shows some deficiencies, like oscillations. For low polynomial degrees, there exist only a few effective concepts for the elimination of locking effects. One is the enhanced assumed strain (EAS) method which is used in finite element formulations and which is sensitive to distorted element geometries. Beirão da Veiga et al. [1] introduced a new approach for a Reissner‐Mindlin plate formulation where the displacements and rotations of the mesh are approximated using different control meshes. The physical space of the structure always remains the same. Hence, the method is in accordance to the isoparametric paradigm. However, the shape functions for the approximation of the displacements and the rotations may have different polynomial degrees and number of control points. In this way, the compatibility requirement for pure bending is fulfilled and shear locking is avoided. The method is tested for an isogeometric Reissner‐Mindlin plate formulation, which is based on a degenerated shell formulation [2]. Basic examples are chosen and the results are compared to the unaltered isogeometric Reissner‐Mindlin plate and the finite element Method using MITC elements. The results show that the method has similar accuracy and efficiency as the MITC element and is also applicable for skew element geometries. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)