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《Chinese Quarterly of Mechanics》 2008-03
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Mechanical Analysis of Coiling Process of an Elastic Rod

LIU Yan-zhu Dept.Engineering Mechanics,Shanghai Jiaotong University,Shanghai 200030,China XUE Yun School of Mechanical and Automation Engineering,Shanghai Institute of Technology,Shanghai 200233,China  
The deformation of an elastic rod under the unilateral constraint of a cylinder was discussed as a simplified model of the coiling process of an element of extendable space mast in astronautic technique. The process from a straight rod to a helical rod,at last to connected planar rings is a spatial large deforma- tion of the rod.Therefore the hypothesis of small deformation cannot be applied in analysis.Considering the existence of constraint force,the Kirchhoff equations of a rod without distributed force cannot be ap- plied too.The nonlinear differential equations of equilibrium of a rod constrained by a cylinder were estab- lished with Euler angles as attitude variables of the cross section.Some first integrals were applied to de- termine the internal forces and torques.Assume that the coiling process is slowly and the inertial effects are neglected.Consequently the helical configuration with continuously variable parameters can be treated as the quasi-equilibrium state in the coiling process.The necessary axial compressive force and torque in the coiling process were derived as the functions of the pitching angle of helix.The stability of the helical rod in coiling process was analyzed in first approximation.It is shown that the stability conditions cannot be satisfied when the rod has hinged constraints on both ends and the relative twist is restricted to zero. The stable helical equilibrium in whole coiling process can be realized only when the relative twist of the rod is admissible by the constraints.The necessary compressive force and torque to ensure the stability of coiling process were suggested.
【Fund】: 国家自然科学基金(10472067)
【CateGory Index】: O317
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