# 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... 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) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

# Separate control meshes for displacements and rotations for a shear locking free isogeometric Reissner‐Mindlin plate

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### Abstract

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)

### Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Dec 1, 2017

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