Shear buckling of a composite drive shaft under torsion Mahmood M. Shokrieh a, * , Akbar Hasani a , Larry B. Lessard b a Composites Research Laboratory, Mechanical Engineering Department, Iran University of Science and Technology, Narmak, Tehran 16844, Iran b Mechanical Engineering Department, McGill University, 817 Sherbrooke St.W., Montreal, Qc, Canada H3A 2K6 Abstract In this research the torsional stability of a composite drive shaft torsion is studied. Composite materials are considered as the suitable choice for manufacturing long drive shafts. The applications of this kind of drive shafts are developed in various products such as cars, helicopters, cooling towers, etc. From the design point of view, local and global torsional instability of drive shafts limits the capability for them to transfer torque. After reviewing the closed form solution methods to calculate the buckling torque of composite drive shafts, a finite element analysis is performed to study their behavior. Furthermore, to evaluate the results obtained by the finite element method, a comparison with experimental and analytical results is presented. A case study of the effects of boundary conditions, fiber orien- tation and stacking sequence on the mechanical behavior of composite drive shafts is also performed. Finally, the reduction of the torsional natural frequency of a composite drive shaft due to an increase of applied torque is studied. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Composite drive shafts; Finite element analysis; Buckling 1. Introduction The general stability of drive shafts under torsion has been studied by many researchers. Greenhill [1] for the first time in 1883 presented a solution for torsional stability of long solid shafts. This method of solution can be extended for calculating of the first torsional buckling mode of a hollow shaft. The first and oldest buckling analysis of thin-walled cylinders under torsion was presented by Schwerin [2] in 1924. However, his analysis did not show a good agreement with experi- mental results. In 1931 Kubo and Sezawa [3] presented a theory for calculating the torsional buckling of tubes and also re- ported on experimental results for rubber models. However, this theory did not show an agreement with experimental results. Lundquist [4] performed extensive experiments on the strength of aluminum shafts under torsion reported in 1932. There was still no analytical solution until 1933 for simulation of the buckling behavior of drive shafts, so experimental results were the only basis for the research of Donell [5]. In 1934 he presented a theoretical solution for the instability of drive shafts under torsion. He used the theory of thin-wall shells for analysis and evaluated his theory with available experimental results, which included about fifty tests. These studies showed that the torsional failure load measured by experiments is always less than that obtained by theory. The main reason is the initial eccentricity of the shafts in the experiments. All of the above mentioned researchers were limited their re- search to isotropic materials. A general theory for isotropic shells was presented for the first time by Ambartsumyan [6] and Dong et al. [7] in 1964. Ho and Cheng [8] performed a general analysis on the buckling of non-homogeneous anisotropic thin-wall cylinders under combined axial, radial and torsional loads by considering four boundary conditions. Chehil and Cheng [9] studied the elastic buckling of composite thin-wall shell cylinders under torsion based on the large deflection theory of shells. Tennyson [10] using a theoretical method studied the classical linear elastic buckling of non-isotropic com- posite cylinders, ‘‘perfect’’ and ‘‘imperfect’’, under dif- ferent loading conditions. He compared his results with experiments. Bauchau and Krafchack [11] in 1988 * Corresponding author. Fax: +98-21-200-0016. E-mail address: shokrieh@iust.ac.ir (M.M. Shokrieh). 0263-8223/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0263-8223(03)00214-9 Composite Structures 64 (2004) 63–69 www.elsevier.com/locate/compstruct