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A convective isogeometric element formulation with mixed basis function degrees

  • Employing isogeometric analysis (IGA), the geometry of structures is discretized by non-uniform rational B-splines (NURBS), which simultaneously provide the basis functions for the corresponding analysis as well. Due to the high continuity within patches, a unique local convective basis system, which corresponds to the local geometry directions of the mesh, can be defined in every point. Locking Phenomena, which strongly affect purely displacement-based low order elements, can be counteracted by employing particular methods or higher polynomial degrees; both options increase the resulting computational effort significantly. Using order elevation only in specific directions has the potential to optimize the ratio between locking counteraction and computational costs. In this contribution, the use of directed deformations based on convective basis systems in each control point is proposed for a displacement-based isogeometric formulation with specifically adapted orders. Therefore, distinct meshes for the interpolation of theEmploying isogeometric analysis (IGA), the geometry of structures is discretized by non-uniform rational B-splines (NURBS), which simultaneously provide the basis functions for the corresponding analysis as well. Due to the high continuity within patches, a unique local convective basis system, which corresponds to the local geometry directions of the mesh, can be defined in every point. Locking Phenomena, which strongly affect purely displacement-based low order elements, can be counteracted by employing particular methods or higher polynomial degrees; both options increase the resulting computational effort significantly. Using order elevation only in specific directions has the potential to optimize the ratio between locking counteraction and computational costs. In this contribution, the use of directed deformations based on convective basis systems in each control point is proposed for a displacement-based isogeometric formulation with specifically adapted orders. Therefore, distinct meshes for the interpolation of the displacements in each direction are generated based on the initial geometry. Subsequently, the order of every mesh is elevated in only one direction. Consequently, different possibilities for the combination of order elevations have to be examined. This procedure is conducted for a two-dimensional linear elasticity problem. The benefit of a convective formulation with direction dependent degrees is shown by a comparison to a standard isogeometric formulation. Furthermore, the impact of the directions selected for order elevation on the accuracy of the results is investigated.show moreshow less

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Metadaten
Author: Lisa StammenORCiD, Wolfgang DornischORCiD
URL:https://drive.google.com/file/d/1CYA-jTeVREnLcY2XIY1HuYiYutElGxXE/view
Title of the source (English):Isogeometric Analysis 2022 (IGA 2022) - Book of Abstracts
Editor: Artem Korobenko, John Evans, Ming-Chen Hsu
Document Type:Conference publication not peer-reviewed
Language:English
Year of publication:2022
First Page:103
Faculty/Chair:Fakultät 6 Architektur, Bauingenieurwesen und Stadtplanung / FG Statik und Dynamik
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