Search

Isogeometric Analysis (IGA) and its unconventional basis functions bring undeniable benefits to the numerical analysis of solid bodies with a complex geometrical shape such as pneumatic tires. This approach erases barriers between the stage of design and the computational environment. Preservation of the exact geometrical description of the real body and the nature of functions at hand allow for higher precision of simulations for different physical phenomena. This contribution is aimed to show further developments in the framework for rolling simulation of tires using IGA. The large support of Non‐Uniform Rational B‐Splines (NURBS) provides continuous variable fields along the contact patch. Truncated hierarchical B‐splines (THB‐splines), implemented into an in‐house Finite Element Analysis (FEA) code, improve the modeling of tires by locally refining the contact zone. Global extraction operators bring the hierarchical concept as close as possible to a standard FEA code structure, flattening the set of nested layers of mesh into a sequence of single‐level elements. Furthermore, an algorithm for the computation of the accelerations at material points based on the relative velocities is adapted. The outlook of this development is the intention to use this algorithm in possible combination with analytical models for the in‐situ estimation of forces and to capture certain mechanical behavior which often are not tracked in experiments or hard and too costly to reproduce. The sampling procedure within the hierarchically nested basis is elaborated with attention to required adjustments for the nested parent‐child layered analytical meshes created via the introduction of the selective global multilevel extraction operators. Numerical simulations of rolling tires at steady‐state using IGA are presented. The evaluation and comparison of the developed framework are done using uniformly refined and locally refined models in IGA as well as classical FEA models. [ABSTRACT FROM AUTHOR]

• Isogeometric analysis with high order continuity for tire analysis is presented. • Unclamped B-splines define a circle with high accuracy and full continuity. • Derivatives of B-spline basis functions are computed efficiently. • Steady-state rolling in IGA considers higher order gradients straightforwardly. • Comparison and validation by means of experiments. The analysis of rolling tires using numerical methods sheds light on the understanding of complex phenomena, while reducing the amount of experimental tests, which are used to calibrate and validate the models. Among different approaches, the finite element method is often used in tire industry, due to its capabilities of describing structural behavior, where material properties and an accurate geometry are required. Isogeometric Analysis offers an efficient and exact geometrical description of bodies, in contrast e.g. to linear finite elements, which is fundamental for the circular shape of a tire. In this contribution, a novel framework for tire analysis is presented. Closed unclamped B-splines are employed for a fully continuous description of geometry and field variables. The overall high-order continuity of the model allows the analysis to be less sensitive with respect to the applied discretization which becomes obvious in comparison to standard FEA models. The rolling phenomenon is described by an Arbitrary L agrangian –E ulerian approach with a direct computation of second order gradients due to the use of higher order basis functions. This novel framework is validated by experiments using a passenger car tire, where accelerations are registered. This versatile approach can be employed for the comparison and evaluation of analytical approaches. A discussion of the results of numerical simulations, significant remarks and an outlook on further research directions close this presentation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]