Hierarchical refinement in isogeometric analysis for flexible multibody impact simulations

Abstract

Detailed impact simulations in flexible multibody systems can be simulated based on reduced isogeometric analysis (IGA) models. However, a precise simulation of an impact requires a high element resolution in the contact area. Usually in IGA, global refinement methods are used, which are easy to implement. However, in the literature, also the use of hierarchical local refinement is proposed. The local refinement generates fewer countable degrees of freedom compared to an equivalent global refinement. Numerous application areas can be found in the literature, such as contact simulations, where the computational effort is reduced by local refinement. In this work, we introduce the inclusion of hierarchically refined IGA models within the floating frame of reference formulation. Thereby, the hierarchically refined IGA model is reduced and applied in impact simulations. In two application examples, we simulate the impact of two- and three-dimensional spheres and compare with an analytical solution. The focus here is on the comparison of calculation times and accuracy of globally and locally refined reference models. The third application example consists of two flexible double pendulums and is devoted to systems in which the bodies undergo both arbitrary rigid body motions and small elastic deformations.