Analysis of Nonlinear Multi-Body Systems with Elastic Couplings * Olivier A. Bauchau and Dewey H. Hodges Georgia Institute of Technology, School of Aerospace Engineering. Atlanta, Georgia, 30332, USA. Abstract This paper is concerned with the dynamic analysis of nonlinear multi-body sys- tems involving elastic members made of laminated, anisotropic composite materials. The analysis methodology can be viewed as a three-step procedure. First, the sec- tional properties of beams made of composite materials are determined based on an asymptotic procedure that involves a two-dimensional finite element analysis of the cross-section. Second, the dynamic response of nonlinear, flexible multi-body systems is simulated within the framework of energy-preserving and energy-decaying time in- tegration schemes that provide unconditional stability for nonlinear systems. Finally, local three-dimensional stresses in the beams are recovered, based on the stress resul- tants predicted in the previous step. Numerical examples are presented and focus on the behavior of multi-body systems involving members with elastic couplings. Keywords: Flexible multi-body systems; Composite materials; Elastic couplings. 1 Introduction This paper is concerned with the dynamic analysis of flexible, nonlinear multi-body systems, i.e. a collection of bodies in arbitrary motion with respect to each other while each body is undergoing large displacements and rotations with respect to a frame of reference attached to the body. The strain within each elastic body is assumed to remain small. The paper focuses on structures made of laminated composite materials and exhibiting elastic couplings. The elastic bodies are modeled using the finite element method. The use of beam elements will be demonstrated for multi-body systems. The location of each node is represented by its Cartesian coordinates in an inertial frame, and the rotation of the cross-section at each node is represented by a finite rotation tensor expressed in the same inertial frame. The kinematic constraints among the various bodies are enforced via the Lagrange multiplier * Multibody System Dynamics, 3, 1999, pp 168-188. 1