Local Refinement in Isogeometric Analysis of Detailed Tire Models

Abstract

AbstractIsogeometric 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.