Torsion of cylindrically poroelasic circular shaft with radial inhomogeneity .some exact solutions for extruder

محورهای موضوعی : Smart & Advanced Materials

محمد فرید خان سمنی ¹ (Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran)
فرانک خان سمنی ² (Department of Engineering, Zanjan University, Zanjan, Iran)

تاریخ دریافت : 1396/04/30 تاریخ پذیرش : 1396/04/30 تاریخ انتشار : 1395/04/11

کلید واژه: Torsion, FGM and poroelastic shaft, Radial inhomogeneity, extruder,

چکیده مقاله :

Torsion of elastic and poroelastic circular shaft of radially inhomogeneous, cylindrically orthotropic materials is studied with emphasis on the end effects example for extruder. To examine the conjecture of Saint-Venant’s torsion, we consider torsion of circular shaft with one end fixed and the other end free on which tractions that results in a pure torque are prescribed arbitrarily over the free end surface. Exact solutions that satisfy the prescribed boundary conditions point by point over the entire boundary surfaces are derived in a unified manner for cylindrically orthotropic shafts with or without radial inhomogeneity and for their coun- terparts of Saint-Venant’s torsion. Stress diffusion due to the end effect is examined in the light of the exact solutions.The present study enables us to assess Saint-Venant’s principle as applied to anisotropic, non-homogeneous poroelastic bodies in general and to evaluate the stress diffusion in torsion of radially inhomogeneous, cylindrically orthotropic cylinders in particular. The following conclusions can be drawn from the analysis

منابع و مأخذ:

[1] S.-P. Timoshenko.,J.-N. Goodier , Theory of elasticity, third ed.McGraw-Hill, New York.1970.

[2] S.-P.Timoshenko., History of strength of materials, McGraw-Hill, New York.1953.

[3]F.-M.Baron, Torsion of Multi-Connected Thin-Walled Cylinders, J. Appl.1942. Mech, Vol. 9, pp. 72-74.

[4] Li.-Z.Ko, J. M. and Y.- Q. Ni, 2000,TorsionalRigidity of Reinforced Concrete Bars with Arbitrary Sectional Shape, Finite Elem. Anal .Des., Vol. 35, pp. 349-361.

[5]G.Mejak, 2000 ,Optimization of cross-section of hollow prismatic bars in torsion, Communications in Numerical Methods in Engineering, Vol. 16, pp. 687-695.

[6] K. Sezawa, K. Kubo, 1931,The buckling of a cylindrical shell under torsion, Aero Research Inst, Tokyo Imperial University, Report No. 176.

[7]E.Lundquist, 1932, Strength tests on thin-walled duralumin cylinders in torsion. NACA No. 427.

[8] A.Doostfatemeh, M.-R.Hematiyan, and S.Arghavan, 2009,Closed-form approximate formulations for torsional analyses of hollow tube with straight and circular edges, Journal of Mechanics, Vol. 25, pp. 401-409.

[9]R. Courant, 1943,Variational methods for the solution of problems of equilibrium and vibration, Bull Am Math Soc; 49(1):1–23.

[10]S.-P. Timoshenko, 1956,Strength of materials.thirded, Berkshire (England): Van Nostrand.

[11] P.-M. Quinlan, 1964,Thetorsion of an irregular polygon,Proc Royal SocLondSer A Math PhysSci; 282(1389):208–27.

[12]N.-I. Muskhelishvilli, 1953 .Some basic problems of the mathematical theory of elasticity. Groningen (Holland): P. Noordhoff.

[13]J.-R. Booker, S. Kitipornchai, 1971,Torsion of multilayered rectangular section, J EngMechDiv ASCE; 97(EM5):1451–68.

[14]Y.-M. Kuo, H.-D.Conway, 1973,The torsion of composite tubes and cylinders, I JSS; 9(12):1553–65.

[15]Y.-M. Kuo, H.-D.Conway, 1974,Torsion of cylinders with multiple reinforcement ,JEngMechDiv ASCE; 100(EM2):221–34.

[16] Y.-M. Kuo, H.-D.Conway, 1974,Torsion of composite rhombus cylinder, J ApplMech; 31(2):302–3.

[17] Y.-M.  Kuo, H.-D.Conway, 1980, Torsion of reinforced square cylinder, J EngMechDiv ASCE; 106(EM6):1341–7.

[18]B.-A.Packham, R.-St. Shail, 1978 ,Venant torsion of composite cylinders, J Elasticity; 8(4):393–407.

[19] R. Ripton, 1998 ,Optimal fiber configurations for maximum torsional rigidity, Arch Ration Mech Anal; 144(1):79–106.

[20]T.Chen, Y. Benveniste, 2002, Chuang PC, Exact solutions in torsion of composite bars: thickly coated neutral inhomogeneities and composite cylinder assemblages, Proc Math PhysEngSci; 458(2023):1719–59.

[21] J.-F. Ely,O.-C.Zienkiewicz, 1960 ,Torsion of compound bars – a relaxation solution,Int J MechSci; 1(4):356–65.

[22]L.-R. Herrmann, 1965,Elastic torsional analysis of irregular shapes, J EngMechDiv ASCE (EM6):11–9.

[23] M.-A. Jaswon, A.-R., Ponter, 1963,An integral equation solution of the torsion problem,Proc Roy SocLondSer A Math PhysSci; 273(1353):237–46.

[24]J.-T.Kasikadelis, E.-J.Sapountzakis, 1986,Torsion of composite bars by boundary element method, J EngMech; 111(9):1197–210.

[25]E.-J.Sapountzakis, 2000,Solution of non-uniform torsion of bars by an integral equation method,ComputStruct; 77(6):659–67.

[26] E.-J. Sapountzakis, 2001, Nonuniform torsion of multi-material composite bars by the boundary element method, ComputStruct; 79(32):2805–16.

[27] M. Koizumi, 1993,The concept of FGM. Ceram Trans Function Grad Mater; 34(1):3–10.

[28]R., Plunkett, 1965,Torsion of inhomogeneous elastic prismatic bars, J EngInd; 87:391–2.

[29] F.-J. Rooney, M. Ferrari, 1995, Torsion and flexure of inhomogeneous elements, Compos Eng; 5(7):901–11.

[30] F.-J. Rooney, M. Ferrari, 1999, On the St. Venant problems for inhomogeneous circular bars,  JApplMech; 66(2):32–44.

[31]C.-O.Horgan, A.-M.Chan, 1999,Torsion of functionally graded isotropic linearly elastic bars, J Elasticity; 52(2):181–99.

[32] J.-G. Tarn, H.-H.Chang, 2008, Torsion of cylindrically orthotropic elastic circular bars with radial inhomogeneity: some exact solutions and end effects,Int J Solids Struct; 45(1):303–19.

[33] F.-J. Rooney, M. Ferrari, 1995, Torsion and flexure of inhomogeneous elements, CompositesEngineering 5, 901–911.

[34]M.-A. Biot, 1962, Generalized theory of acoustic propagation in porous dissipative media, Journal of the Acoustical Society of America 34, 1254-1264.

[35] M.-A. Biot, 1972, Theory of finite deformation of porous solid. Indiana University Mathematics Journal 21, 597-620.

[36]M.-A.Biot, 1982, Generalized Lagrangian equations of non-linear reaction-diffusion, Chemical Physics 66, 11-26.

[37] S. Arghavan, M.-R.Hematiyan, 2009,Torsion of functionally graded hollow tubes, European Journal Mechanics A/Solids 28 (3), 551–559.

[38] R.-C. Batra, 2006,Torsion of a functionally graded cylinder, AIAA Journal 44 (6), 1363–1365.

 [39] C.-O.Horgan, 2007,On the torsion of functionally graded anisotropic linearly elastic bars, IMA Journal of Applied Mathematics 72 (5), 556–562.

[40] F.-J. Rooney, M. Ferrari, 1995,Torsion and flexure of inhomogeneous elements , Composites Engineering 5 (7), 901–911.

[41] M. Udea, T. Nishimura, T. Sakate, 12–14 June 2002,Torsional analysis of functionally graded materials. In: Lao, Y.-C. Chowdhury, S.-H.Fragomeni, S. (Eds.), Advances in Mechanics of Structures and Materials: Proceedings of 17th

Australian Conference (ACMS17) .Tayor and Francis ,Queensland, Australia, pp. 533–538.

[42]T.Yaususi, A. Shigeyasu, 2000, Torsional characteristics of hemp palm branch with triangular cross-section (2-composite bar), The Japan Society of Mechanical Engineers 66 (649), 1806–1811.

[43] M.-F.Khansanami ,M. Jabbari ,Torsion of poroelastic shaft with hollow elliptical section, JSM Journal of solid Mechanics Vol.8, No.1 (2016)pp.1-11

 

[44] H.-sadd.Martin,2009,  Elasticity theory, application and numeric, second ed .Department of mechanical engineering and applied mechanics university of Rhode Island, 229-232