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Isogeometric Reissner–Mindlin shell analysis with exactly calculated director vectors

  • An isogeometric Reissner-Mindlin shell derived from the continuum theory is presented. The geometry is described by NURBS surfaces. The kinematic description of the employed shell theory requires the interpolation of the director vector and of a local basis system. Hence, the definition of nodal basis systems at the control points is necessary for the proposed formulation. The control points are in general not located on the shell reference surface and thus, several choices for the nodal values are possible. The proposed new method uses the higher continuity of the geometrical description to calculate nodal basis system and director vectors which lead to geometrical exact interpolated values thereof. Thus, the initial director vector coincides with the normal vector even for the coarsest mesh. In addition to that a more accurate interpolation of the current director and its variation is proposed. Instead of the interpolation of nodal director vectors the new approach interpolates nodal rotations. Account is taken for the discrepancy between interpolated basis systems and the individual nodal basis systems with an additional transformation. The exact evaluation of the initial director vector along with the interpolation of the nodal rotations lead to a shell formulation which yields precise results even for coarse meshes. The convergence behavior is shown to be correct for k-refinement allowing the use of coarse meshes with high orders of NURBS basis functions. This is potentially advantageous for applications with high numerical effort per integration point. The geometrically nonlinear formulation accounts for large rotations. The consistent tangent matrix is derived. Various standard benchmark examples show the superior accuracy of the presented shell formulation. A new benchmark designed to test the convergence behavior for free form surfaces is presented. Despite the higher numerical effort per integration point the improved accuracy yields considerable savings in computation cost for a predefined error bound.
Author:Wolfgang Dornisch, Sven Klinkel, Bernd Simeon
URN (permanent link):urn:nbn:de:hbz:386-kluedo-44479
Publisher:Elsevier B.V.
Document Type:Preprint
Language of publication:English
Publication Date:2012/10/08
Year of Publication:2012
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2016/09/12
Tag:Interpolation of the Director; Isogeometric Analysis; NURBS; Reissner-Mindlin Shell
Number of page:22
Source:This is the peer reviewed version of the following article: Dornisch, W, Klinkel, S, and Simeon, B (2013): Isogeometric Reissner– Mindlin shell analysis with exactly calculated director vectors. Comput. Methods Appl. Mech. Engrg. 253, 491–504, which has been published in final form at doi: 10.1016/j.cma.2012.09.010. (c)2012. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Faculties / Organisational entities:Fachbereich Maschinenbau und Verfahrenstechnik
DDC-Cassification:6 Technik, Medizin, angewandte Wissenschaften / 620 Ingenieurwissenschaften und Maschinenbau
Licence (German):Zweitveröffentlichung