Torsion of Poroelastic Shaft with Hollow Elliptical Section

Document Type: Research Paper


Department of Mechanical Engineering, Islamic Azad University, South Tehran Branch, Iran


In this paper torsion of hollow Poroelastic shaft with Elliptical section is developed. Using the boundary equation scheme. It looks for a stress function where satisfied Poisson equation and vanishes on boundary. It also analyzed stress function and warping displacement for the hollow elliptical section in Poroelastic shaft. At the end, the result of elastic and poroelastic shaft in warping displacement and stress function is compared.


[1] Timoshenko S.P., Goodier J.N., 1970, Theory of Elasticity, New York:, McGraw-Hill.
[2] Timoshenko S.P., 1953, History of Strength of Materials, New York:, McGraw-Hill.
[3] Baron F. M ., 1942,Torsion of multi-connected thin-walled cylinders, Journal of Applied Mechanics 9:72-74.
[4] Li Z.., Ko J. M., Ni Y. Q., 2000, Torsional rigidity of reinforced concrete bars with arbitrary sectional shape, Finite Elements in Analysis and Design 35:349-361.
[5] Mejak G ., 2000, Optimization of cross-section of hollow prismatic bars in torsion, Communications in Numerical Methods in Engineering 16:687-695.
[6] Jiang W. G ., Henshall J. L ., 2002 , A coupling cross-section finite element model for torsion analysis of prismatic bars, European Journal of Mechanics A-solids 21: 513-522.
[7] Louis Angelo M ., Ryan M ., 2007 , Torsion of a rectangular prismatic bar: Solution using a power fit model, Philippine Engineering Journal 28(1) : 77-98.
[8] Doostfatemeh A., Hematiyan M.. R ., Arghavan S., 2009 , Closed-form approximate formulations for torsional analyses of hollow tube with straight and circular edges, Journal of Mechanics 25:401-409.
[9] Courant R., 1943 , Variational methods for the solution of problems of equilibrium and vibration, Bulletin of the American Mathematical Society 49(1):1-23.
[10] Timoshenko S.P., 1956, Strength of Materials, Berkshire (England) ,Van Nostrand.
[11] Quinlan P.M., 1964, The torsion of an irregular polygon, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 282 :208-227.
[12] Muskhelishvilli N.I., 1953, Some Basic Problems of the Mathematical Theory of Elasticity, Groningen ,Holland.
[13] Booker J.R., Kitipornchai S., 1971, Torsion of multilayered rectangular section, Journal of the Engineering Mechanics Division ASCE 97:1451-1468.
[14] Kuo Y.M., Conway H.D., 1973 ,The torsion of composite tubes and cylinders, International Journal of Solids and Structures 9(12):1553-1565.
[15] Kuo Y.M., Conway H..D., 1974, Torsion of cylinders with multiple reinforcement, Journal of the Engineering Mechanics Division ASCE 100:221-234.
[16] Kuo Y.M., Conway H.D., 1974, Torsion of composite rhombus cylinder, Journal of Applied Mechanics 41(1):302-303.
[17] Kuo Y.M., Conway H.D., 1980, Torsion of reinforced square cylinder, Journal of the Engineering Mechanics Division 106 :1341-1347.
[18] Packham B.A., Shail R.., 1978 , St. venant torsion of composite cylinders, Journal of Elasticity 8(4):393-407.
[19] Ripton R.,1998 , Optimal fiber configurations for maximum torsional rigidity, Archive for Rational Mechanics and Analysis 144(1):79-106.
[20] Chen T., Benveniste Y., Chuang P.C , 2002 , Exact solutions in torsion of composite bars: thickly coated neutral inhomogeneities and composite cylinder assemblages, Proceedings of the Royal Society A : Mathematical, Physical and Engineering Science 458(2023):1719-1759.
[21] Ely J.F., Zienkiewicz O.C., 1960, Torsion of compound bars a relaxation solution, International Journal of Mechanical Sciences 1(4):356-365.
[22] Herrmann L.R., 1965 , Elastic torsional analysis of irregular shapes, Journal of the Engineering Mechanics Division 91(6): 11-20.
[23] Jaswon M.A., Ponter A.R., 1963, An integral equation solution of the torsion problem, Proceedings of the Royal Society A: Mathematical Physical and Engineering Science 273:237-246.
[24] Kasikadelis J.T., Sapountzakis E.J, 1986 , Torsion of composite bars by boundary element method, Journal of Engineering Mechanics 111(9):1197-1210.
[25] Sapountzakis E.J., 2000 , Solution of non-uniform torsion of bars by an integral equation method, Computer and Structures 77(6):659-667.
[26] Sapountzakis E.J., 2001 , Nonuniform torsion of multi-material composite bars by the boundary element method, Computer and Structures 79(32):2805-2816.
[27] Koizumi M., 1993 ,The concept of FGM, Ceram Trans Function Grad Mater 34(1):3-10.
[28] Plunkett R., 1965 , Torsion of inhomogeneous elastic prismatic bars, Journal of Engineering for Industry 87:391-392.
[29] Rooney F.J., Ferrari M., 1995, Torsion and flexure of inhomogeneous elements, Engineering of Composite 5(7):901-911.
[30] Rooney F.J., Ferrari M., 1999, On the St. venant problems for inhomogeneous circular bars, Journal of Applied Mechanics 66(2):32-44.
[31] Horgan C.O., Chan A..M., 1999, Torsion of functionally graded isotropic linearly elastic bars, Journal of Elasticity 52(2):181-199.
[32] Tarn J.G., 2008, Chang HH. Torsion of cylindrically orthotropic elastic circular bars with radial inhomogeneity: some exact solutions and end effects, International Journal of Solids and Structures 45(1):303-319.
[33] Rooney F.J ., Ferrari M.,1995,Torsion and flexure of inhomogeneous elements, Composites Engineering 5: 901-911.
[34] Biot M..A., 1962 , Generalized theory of acoustic propagation in porous dissipative media, Journal of the Acoustical Society of America 34: 1254-1264.
[35] Biot M.A., 1972, Theory of finite deformation of porous solid, Indiana University Mathematics Journal 21:597-620.
[36] Biot M..A., 1982, Generalized Lagrangian equations of non-linear reaction- diffusion, Chemical Physics 66:11-26.
[37] Arghavan S., Hematiyan, M..R., 2009, Torsion of functionally graded hollow tubes, European Journal Mechanics A/Solids 28(3): 551-559.
[38] Batra R..C, 2006, Torsion of a functionally graded cylinder, The American Institute of Aeronautics and Astronautics 44 (6):1363-1365.
[39] Horgan C.O, 2007, On the torsion of functionally graded anisotropic linearly elastic bars, Journal of Applied Mathematics 72 (5): 556-562.
[40] Rooney F.J, Ferrari M., 1995, Torsion and flexure of inhomogeneous elements, Composites Engineering 5 (7):901-911.
[41] Udea M., Nishimura T., Sakate T, 2002, Torsional analysis of functionally graded materials., Advances in Mechanics of Structures and Materials, Proceedings of 17th Australian Conference (ACMS17), Tayor and Francis, Queensland, Australia.
[42] Yaususi T., Shigeyasu A., 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] Sofiyev A..H, 2005, The torsional buckling analysis of cylindrical shells with material non-homogeneity in thickness direction under impulsive loading, Structural Engineering and Mechanics an International Journal 19(2):231-236.
[44] Sofiyev A.H., 2003, Torsional buckling of cross-ply laminated orthotropic composite cylindrical shells subject to dynamic loading, European Journal of Mechanics A/Solids 22:943-951.
[45] Sadd M. H.,. 2009, Elasticity Theory, Application, and Numerics, Department of Mechanical Engineering and Applied Mechanics University of Rhode Island.