Local Refinement in Isogeometric Analysis of Complex Tire Models. Issue 1 (25th January 2021)

• Record Type: Journal Article
• Authors: Israfilova, Alina; Garcia, Mario A.; Kaliske, Michael
• Other Names: Kuhl D. guestEditor.; Meister A. guestEditor.; Ricoeur A. guestEditor.; Wünsch O. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 20:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-01-25
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202000147
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: The capability of Non‐Uniform Rational B‐Splines (NURBS) to exactly represent conic sections exactly makes Isogeometric Analysis (IGA) an attractive alternative to classical Finite Element Method (FEM) for tire simulation. Application of NURBS as basis functions for geometry representation simplifies the generation of the computational mesh that can be directly obtained from the software for graphical design. NURBS‐based approximations of the field variables lead to higher convergence rates and allow higher continuity across the element boundaries. Moreover, the tensor structure of these functions permits the usage of additional advanced refinement techniques. The contribution at hand focuses on the application of hierarchically nested basis functions in tire analysis. The developed framework is based on the introduction of the global multilevel Bézier extraction operator [1]. This approach allows local refinement in the existing isoparametric FEM code without violating its architecture. Within the introduced framework, material models developed for standard FEM can be retained. Special attention is paid to the modelling of rebar elements within the framework of IGA and local refinement in particular. The from standard FEM adopted unconventional method avoids the drawbacks of smeared formulations common in tire numerical analysis and does not require an explicit definition of the reinforcing bars [2]. An additional check of the volumetric content of rebar in the material allows the compatibility of the employed concept with locally improved meshes. Numerical simulations for rolling tires using IGA are presented. The complex multilevel composite structure of tire‐models is obtained by means of CAD‐software. All simulations are performed under the consideration of steady‐state rolling within the Arbitrary Lagrangian‐Eulerian (ALE) description including finite deformations. A benchmark study of IGA and FEM for tire analysis closes this presentation.