Isogeometric Reissner‐Mindlin shell analysis ‐ employing different control meshes for displacements and rotations
Isogeometric Reissner‐Mindlin shell analysis ‐ employing different control meshes for displacements and rotations
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DOI：
10.1002/pamm.201610093
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发表时间：
2016-10
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影响因子：
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通讯作者：
G. Kikis;W. Dornisch;Sven Klinkel-
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文献类型：
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作者：
G. Kikis;W. Dornisch;Sven Klinkel-
本文的主要目的是开发和实施一种方法，用于减少等几何Reissner‐Mindlin壳公式中所谓的锁定效应。在[1]中，引入了基于连续介质力学的具有指向矢精确插值的等几何Reissner‐Mindlin壳公式。数值算例表明，该方法提高了计算精度和效率.然而，对于低多项式次数，只有很少的有效概念用于防止锁定效应。在Beirão da Veiga [2]的工作中，Reissner‐Mindlin板公式通过使用合适的解空间来防止剪切锁定。在这里，该方法被扩展到Reissner‐Mindlin壳公式。不同的控制网格用于位移和旋转。此外，在相关旋转方向上的基函数比为位移选择的基函数小一度。这导致控制网格具有不同数量和位置的控制点。这样做的目的是为了避免由于剪切应变和曲率的耦合而导致的剪切锁定，因为这样就满足了纯弯曲的相容性要求。针对不同的算例，研究了该方法的精度和效率.此外，将结果与解析解进行了比较。（© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA，魏因海姆）
The main purpose of this paper is the development and implementation of a method for the reduction of the so‐called locking effect in the isogeometric Reissner‐Mindlin shell formulation. In [1] an isogeometric Reissner‐Mindlin shell formulation with an exact interpolation of the director vector based on continuum mechanics was introduced. The numerical examples showed that the accuracy and efficiency increased. However, there are only few effective concepts for the prevention of locking effects for low polynomial degrees. In the work of Beirão da Veiga [2], shear locking is prevented for a Reissner‐Mindlin plate formulation by using suitable solution spaces. Here, the method is extended to the Reissner‐Mindlin shell formulation. Different control meshes are used for displacements and rotations. Furthermore, the basis functions in the direction of the relevant rotation are one degree less than the ones which are chosen for the displacements. That leads to control meshes with different number and location of the control points. The aim is to avoid shear locking due to the coupling of shear strains and curvature since the compatibility requirement for pure bending is then fulfilled. The accuracy and efficiency of this method are investigated for different examples. In addition, the results are compared to the analytical solutions. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)