Finite Element Incremental Approach and Exact Rigid Body Inertia

[+] Author and Article Information
A. A. Shabana

Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL 60607-7022

J. Mech. Des 118(2), 171-178 (Jun 01, 1996) (8 pages) doi:10.1115/1.2826866 History: Received September 01, 1994; Revised December 01, 1995; Online December 11, 2007


In the dynamics of multibody systems that consist of interconnected rigid and deformable bodies, it is desirable to have a formulation that preserves the exactness of the rigid body inertia. As demonstrated in this paper, the incremental finite element approach, which is often used to solve large rotation problems, does not lead to the exact inertia of simple structures when they rotate as rigid bodies. Nonetheless, the exact inertia properties, such as the mass moments of inertia and the moments of mass, of the rigid bodies can be obtained using the finite element shape functions that describe large rigid body translations by introducing an intermediate element coordinate system. The results of application of the parallel axis theorem can be obtained using the finite element shape functions by simply changing the element nodal coordinates. As demonstrated in this investigation, the exact rigid body inertia properties in case of rigid body rotations can be obtained using the shape function if the nodal coordinates are defined using trigonometric functions. The analysis presented in this paper also demonstrates that a simple expression for the kinetic energy can be obtained for flexible bodies that undergo large displacements without the need for interpolation of large rotation coordinates.

Copyright © 1996 by The American Society of Mechanical Engineers
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