Abstract
We proposed an original method to investigate the problem of torsion of anisotropic cross-section. We implemented an energy method to calculate the stress function represented by infinite series of trigonometric functions adapted to rectangular cross-section. After validation, we implemented a parametric sensitivity study to investigate the influence of the cross-section aspect ratio and the anisotropy level on the stress function, the strain energy density and the torsion stiffness. The process showed a fast convergence with a very good accuracy. The model showed a potential interest for the experimental identification of anisotropic material properties.
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References
Allen D.N.: Relaxation Methods. McGraw-Hill, London (1955)
Benveniste Y.: A new approach to the application of Mori–Tanaka’s theory in composite materials. Mech. Mat. 6, 147–157 (1987)
Ely J.F., Zienkiewicz O.C.: Torsion of compounds bars—a relaxation solution. Int. J. Mech. Sci. 1, 356–365 (1960)
Estivalèzes E., Couteau B., Darmana R.: 2D calculation method based on composite beam theory for the determination of local homogenized stiffnesses of long bones. J. Biomech. 34(2), 277–283 (2001)
Herrman L.R.: Elastic analysis of irregular shaped prismatic beams by the method of finite elements. J. Eng. Mech. Div. Prc. ASCE 94(EM4), 965–983 (1968)
Horgan C.O., Chan A.M.: Torsion of functionally graded isotropic linearly elastic bars. J. Elast. 52, 181–199 (1999)
Lekhnitshii S.G.: Theory of Elasticity of an Anisotropic Body. Mir Publishers, Moscow (1981)
Meirovitch L.: Elements of Vibration Analysis. McGraw-Hill, New York (1975)
Manson, W.E., Herrman, L.R.: Elastic Analysis of Irregular Shaped Prismatic Beams by the Method of Finite Elements. Davis, Dept. Civ. Eng. University of California, Tech. Report no 67-1 (1967)
Muskhelishvilli N.I.: Some Basic Problems of the Mathematical Theory of Elasticity, pp. 561. Noordhoff, Groningen (1953)
Pereira, J.C.: Contribution à l’étude du comportement mécanique des structures en matériaux composites: caractéristiques homogénéisées des poutres composites, comportement dynamique des coques composites. PhD thesis, INSA Lyon, France (1995)
Rooney F.J., Ferrari M.: Tension, bending and flexure of functionally graded cylinders. Int. J. Solids Struct. 38, 413–421 (2001)
Shaw, F.S.: The torsion of solid and hollow prisms in the elastic and plastic range by relaxation methods. Austral. Counc. Aeronaut., Sydney, 92 p, Report ACA-11, 38 (1944)
Sokolnikoff I.S.: Mathematical Theory of Elasticity. McGraw-Hill, USA (1956)
Southwell R.V.: Relaxation Methods in Theoretical Physics, pp. 85. Clarendon press, Oxford (1946)
Swider P., Jacquet-Richardet G., Pereira J.C.: Interactions between numerical and experimental approaches in composite structure dynamics. Compos. Struct. 43(2), 127–135 (1998)
Timoshenko S., Goodier J.N.: 1934 reissued 1987. Theory of Elasticity. McGraw-Hill, USA (1934)
Zienkiewicz O.C., Cheung Y.K.: Finite elements in the solution of field problems. Engineer 8, 507–510 (1965)
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Swider, P., Briot, J. & Estivalèzes, E. A solution of torsional problem by energy method in case of anisotropic cross-section. Arch Appl Mech 81, 801–808 (2011). https://doi.org/10.1007/s00419-010-0450-7
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DOI: https://doi.org/10.1007/s00419-010-0450-7