APPLICATION OF THE ABSOLUTE NODAL CO-ORDINATE FORMULATION TO MULTIBODY SYSTEM DYNAMICS

Abstract

The floating frame of reference formulation is currently the most widely used approach in flexible multibody simulations. The use of this approach, however, has been limited to small deformation problems. In this investigation, the computer implementation of the newabsolute nodal co-ordinate formulationand its use in the small and large deformation analysis of flexible multibody systems that consist of interconnected bodies are discussed. While in the floating frame of reference formulation a mixed set of absolute reference and local elastic co-ordinates are used, in the absolute nodal co-ordinate formulation only absolute co-ordinates are used. In the absolute nodal co-ordinate formulation, new interpretation of the nodal co-ordinates of the finite elements is used. No infinitesimal or finite rotations are used as nodal co-ordinates from beams and plates, instead, global slopes are used to define the element nodal co-ordinates. Using this interpretation of the element co-ordinates, beams and plates can be considered as isoparametric elements, and as a result, exact modelling of the rigid body dynamics can be obtained using the element shape function and the absolute nodal co-ordinates. Unlike the floating frame of reference approach, no co-ordinate transformation is required in order to determine the element inertia. The mass matrix of the finite elements is a constant matrix, and therefore, the centrifugal and Coriolis forces are equal to zero when the absolute nodal co-ordinate formulation is used. Another advantage of using the absolute nodal co-ordinate formulation in the dynamic simulation of multibody systems is its simplicity in imposing some of the joint constraints and also its simplicity in formulating the generalized forces due to spring-damper elements. The results obtained in this investigation show an excellent agreement with the results obtained using the floating frame of reference formulation when large rotation–small deformation problems are considered.