Formulation of three-dimensional joint constraints using the absolute nodal coordinates

摘要

A wide variety of mechanical and structural multibody systems consist of very flexible components subject to kinematic constraints. The widely used floating frame of reference formulation that employs linear models to describe the local deformation leads to a highly nonlinear expression for the inertia forces and can be applied to only small deformation problems. This paper is concerned with the formulation and computer implementation of spatial joint constraints and forces using the large deformation absolute nodal coordinate formulation. Unlike the floating frame of reference formulation that employs a mixed set of absolute reference and local elastic coordinates, in the absolute nodal coordinate formulation, global displacement and slope coordinates are used. The nonlinear kinematic constraint equations and generalized force expressions are expressed in terms of the absolute global displacements and slopes. In particular, a new formulation for the sliding joint between two very flexible bodies is developed. A surface parameter is introduced as an additional new variable in order to facilitate the formulation of this sliding joint. The constraint and force expressions developed in this paper are also expressed in terms of generalized Cholesky coordinates that lead to an identity inertia matrix. Several examples are presented in order to demonstrate the use of the formulations developed in the paper. [References: 13]