Torsional Stresses Near the Bonded Interface of a Tube-to-Tube Connected Cylindrically Orthotropic Circular Shaft with Radial Inhomogeneity
Tóm tắt
This study uncovers the stress distributions on or adjacent to the bonded interface connecting two sections in a circular shaft subjected to torsional shear loads on the surfaces of both ends. The material in each section is considered to be cylindrically orthotropic with radial inhomogeneity. The derived results in explicit expressions enable us to investigate the trends of variations in stress near the connecting interface due to the varying degree of material anisotropy, forms of end loads, and material inhomogeneity. According to the numerical results of the examples, when both end surfaces are subjected to radially power-distributed torsional shear loads, the interfacial influences on stress distributions will be strongly dependent on the degree of material anisotropy, and the maximum magnitudes of the torsional stresses near the interface can be effectively alleviated by properly introducing a radial inhomogeneity into the material and adjusting the forms of the end torsional loads, even though the end surfaces are sufficiently far from the interface. When one designs the structure of a tube-to-tube connected shaft subjected to torsional loads, besides paying attention to the maximum magnitude of the interfacial longitudinal shear stress, the transverse shear stress adjacent to the interface has to be considered, especially when one section possesses strong anisotropy.
Tài liệu tham khảo
Solkolnikoff, I.S.: Mathematical Theory of Elasticity. McGraw-Hill, New York (1956)
Lekhnitskii, S.G.: Theory of Elasticity of an Anisotropic Body. Holden-Day, San Francisco (1963)
Lekhnitskii, S.G.: Theory of Elasticity of an Anisotropic Body, 2nd edn. Mir, Moscow (1981)
Ting, T.C.T.: New solutions to pressuring, shearing, torsion and extension of a circular tube or bar. Proc. R. Soc. A 455, 3527–3542 (1999)
Dong, S.B., Kosmatka, J.B., Lin, H.C.: On Saint-Venant’s problem for an inhomogeneous, anisotropic cylinder—Part I: Methodology for Saint-Venant solutions. J. Appl. Mech. 68(3), 376–381 (2000)
Tarn, J.Q.: Exact solutions for functionally graded anisotropic cylinders subjected to thermal and mechanical loads. Int. J. Solids Struct. 38, 8189–8206 (2001)
Tarn, J.Q.: A state space formalism for anisotropic elasticity. Part two: Cylindrical anisotropy. Int. J. Solids Struct. 39, 5157–5172 (2002)
Tarn, J.Q., Chang, H.H.: Extension, torsion, bending, pressuring and shearing of piezoelectric circular cylinders with radial inhomogeneity. J. Intell. Mater. Syst. Struct. 16, 631–641 (2005)
Chen, T., Wei, C.J.: Saint-Venant torsion of anisotropic shafts: Theoretical framework, extremal bounds and affine transformations. Q. J. Mech. Appl. Math. 58, 269–287 (2005)
Iesan, D.: On the torsion of inhomogeneous and anisotropic bars. Math. Mech. Solids 17(8), 848–859 (2012)
Ecsedi, I.: Some analytical solutions for Saint-Venant torsion of non-homogeneous anisotropic cylindrical bars. Mech. Res. Commun. 52, 95–100 (2013)
Sun, X.S., Tan, V.B.C., Chen, Y., Tan, L.B., Jaiman, R.K., Tay, T.E.: Stress analysis of multi-layered hollow anisotropic composite cylindrical structures using the homogenization method. Acta Mech. 225, 1649–1672 (2014)
Goldstein, R.V., Gorodtsov, V.A., Lisovenko, D.S., Volkov, M.A.: Two-layered tubes from cubic crystals: Auxetic tubes. Phys. Status Solidi B, Basic Solid State Phys. 254(12), 1600815 (2017)
Goldstein, R.V., Gorodtsov, V.A., Lisovenko, D.S.: Mesomechanics of multiwall carbon nanotubes and nanowhiskers. Phys. Mesomech. 12(1–2), 38–53 (2009)
Goldstein, R.V., Gorodtsov, V.A., Lisovenko, D.S., Volkov, M.A.: Negative Poisson’s ratio for cubic crystals and nano/microtubes. Phys. Mesomech. 17(2), 97–115 (2014)
Goldstein, R.V., Gorodtsov, V.A., Lisovenko, D.S.: Poynting’s effect of cylindrically anisotropic nano/microtubes. Phys. Mesomech. 19(3), 229–238 (2016)
Goldstein, R.V., Gorodtsov, V.A., Lisovenko, D.S., Volkov, M.A.: Auxeticity in nano/microtubes produced from orthorhombic crystals. Smart Mater. Struct. 25, 054006 (2016)
Goldstein, R.V., Gorodtsov, V.A., Lisovenko, D.S.: Chiral elasticity of nano/microtubes from hexagonal crystals. Acta Mech. 229(5), 2189–2201 (2018)
Horgan, C.O.: Some remarks on Saint-Venant’s principle for transversely isotropic composites. J. Elast. 2, 335–339 (1972)
Tarn, J.Q., Chang, H.H.: Torsion of cylindrically orthotropic elastic circular bars with radial inhomogeneity: Some exact solutions and end effects. Int. J. Solids Struct. 45, 303–319 (2008)
Alpdogan, C., Dong, S.B., Taciroglu, E.: A method of analysis for end and transitional effects in anisotropic cylinders. Int. J. Solids Struct. 47, 947–956 (2010)
Lomakin, E.V.: Torsion of rods with elastic properties depending on the stress state type. Mech. Solids 37(4), 23–30 (2002)
Lomakin, E.V.: Torsion of cylindrical bodies with varying strain properties. Mech. Solids 43(3), 502–511 (2008)
Wang, C.H.: Some end effects in a cylindrically orthotropic circular tube of finite length with radial inhomogeneity subjected to torsional loads. Acta Mech. 226, 1707–1723 (2015)
Miller, K.L., Horgan, C.O.: Saint-Venant end effects for plane deformations of elastic composites. Mech. Compos. Mater. Struct. 2, 203–214 (1995)
Sonsino, C.M., Łagoda, T.: Assessment of multiaxial fatigue behaviour of welded joints under combined bending and torsion by application of a fictitious notch radius. Int. J. Fatigue 26, 265–279 (2004)
Portillo, P., Kreiner, J., Lancey, T.: Torsional fatigue behavior of adhesively joined tubes. J. Mater. Process. Technol. 191, 339–341 (2007)
Mahamood, R.M., Akinlabi, E.T., Shukla, M., Pityana, S.: Functionally graded material: An overview. In: Proceedings of the World Congress on Engineering 2012 (WCE 2012), vol. III, London (2012)
Watanabe, Y., Inaguma, Y., Sato, H., Miura-Fujiwara, E.A.: Novel fabrication method for functionally graded materials under centrifugal force: The centrifugal mixed-powder method. Materials 2(4), 2510–2525 (2009)
Korenev, B.G.: Bessel Functions and Their Applications. CRC Press, Boca Raton (2002)
Alshits, V.I., Kirchner, H.O.K.: Cylindrically anisotropic, radially inhomogeneous elastic materials. Proc. R. Soc. Lond. A 457, 671–693 (2001)
Keles, I., Tutuncu, N.: Exact analysis of axisymmetric dynamic response of functionally graded cylinders (or disks) and spheres. J. Appl. Mech. 78(6), 061014 (2011)
Watson, G.N.: A Treatise on the Theory of Bessel Functions. Cambridge University Press, Cambridge (1995)
Michell, J.H.: The uniform torsion and flexure of incomplete tores, with application to helical springs. Proc. Lond. Math. Soc. 31, 130–146 (1899)
Tarn, J.Q., Chen, W.Q.: Connection between static electromagnetoelasticity and anisotropic elasticity and its applications. Int. J. Solids Struct. 43, 4957–4970 (2006)
Chang, H.H., Tarn, J.Q.: A state space formalism and perturbation method for generalized thermoelasticity of anisotropic bodies. Int. J. Solids Struct. 44, 956–975 (2007)
Tarn, J.Q., Chang, H.H.: A refined state space formalism for piezothermoelasticity. Int. J. Solids Struct. 45, 3021–3132 (2008)