Trivariate Isogeometric Analysis for Flexible Multibody Dynamics

Abstract

Isogeometric analysis (IGA) has been a fundamental step forward in the computational mechanics for the past few years, which maintains the accuracy of the description of computational domain geometry throughout the analysis process. However, the research on IGA in the area of flexible multibody dynamics is little and mainly concentrates on the univariate or bivariate NURBS geometry. This paper applies the trivariate IGA to the flexible multibody dynamics and proposes a continuum mechanics-based method to construct the system dynamic equations within the framework of IGA. A significant feature of this method is that it only employs the position coordinates of the control points as the system variables. To solve the large rotation and deformation coupled problems without introducing any rotation angles, the Green-Lagrange strain tensor is adopted. The evaluation of the elastic force and its Jacobian is easy and accurate by exploiting the appropriate mathematical transformation. In addition, the mass matrix and the generalized gravity force remain constant, and the centrifugal and Coriolis inertia forces equal zero. A numerical experiment is conducted using a thin-plate pendulum, which proves the feasibility and effectiveness of this method.