Large Elastic Strain of The Elastomeric Torus Shell (Rubber Coupling) under the Combined Action of Torques and Centrifugal Forces
Authors: Belkin A.E., Duradzhi V.Yu. | Published: 14.07.2021 |
Published in issue: #8(737)/2021 | |
Category: Mechanical Engineering and Machine Science | Chapter: Machine Science | |
Keywords: shell of revolution, constrained torsion, large strain, hyperelastic material, Treloar potential, elastic coupling element |
The article considers solving the problem of large axisymmetric deformations of elastomeric torus shells of revolution, loaded with jointly acting torques, axial and centrifugal forces. The task is posed due to the calculation of rubber elements of couplings. The calculations are performed according to the momentless shell theory by solving a nonlinear one-dimensional boundary value problem using the shooting method, as well as in a three-dimensional formulation using the finite element method. The calculation results are presented both for convex and concave torus shells. The load characteristics are compared for free and constrained torsion. The dependence of axial reactions in supports on torque and centrifugal forces has been investigated.
References
[1] Rivlin R.S. Torsion of a rubber cylinder. J. Appl. Phys., 1947, vol. 18, no. 5, pp. 444–449, doi: https://doi.org/10.1063/1.1697674
[2] Rivlin R.S. A note on the torsion of an incompressible highly-elastic cylinder. Math. Proc. Camb. Philos. Soc., 1949, vol. 45, no. 3, pp. 485–487, doi: https://doi.org/10.1017/S0305004100025135
[3] Gent A.N., Rivlin R.S. Experiments on the mechanics of rubber II: the torsion, inflation and extension of a tube. Proc. Phys. Soc. B, 1952, vol. 65, no. 7, pp. 487–501, doi: https://doi.org/10.1088/0370-1301/65/7/304
[4] Ogden R.W., Chadwick P. On the deformation of solid and tubular cylinders of incompressible isotropic elastic materials. J. Mech. Phys. Solids, 1972, vol. 20, no. 2, pp. 77–90, doi: https://doi.org/10.1016/0022-5096(72)90032-4
[5] Horgan C.O., Polignone D.A. A note on the pure torsion of a circular cylinder for a compressible nonlinearly elastic material with nonconvex strain-energy. J. Elasticity, 1994, vol. 37, no. 2, pp. 167–178.
[6] Suphadon N., Busfield J.J.C. Elastic behaviour of rubber cylinders under combined torsion and tension loading. Plast. Rubber Compos., 2009, vol. 38, no. 8, pp. 337–342, doi: https://doi.org/10.1179/146580109X12473409436788
[7] Sokolova M.Yu., Chikov V.S. A description of solid cylinders finite strains at torsion. Izvestiya TulGU. Estestvennye nauki [News of the Tula State University. Natural Sciences], 2013, no. 2-1, pp. 109–118. (In Russ.).
[8] Belkin A.E., Dashtiev I.Z., Kostromitskikh A.V. Determining polyurethane elastic parameters at large strains using torsion and tensile test results. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [BMSTU Journal of Mechanical Engineering], 2016, no. 8, pp. 3–10, doi: http://dx.doi.org/10.18698/0536-1044-2016-8-3-10 (in Russ.).
[9] Ryakhovskiy O.A. Razrabotka konstruktsiy, issledovaniya, raschety i standartizatsiya muft s nemetallicheskimi uprugimi elementami. Diss. dok. tekh. nauk [Construction development, study, calculation and standardization of couplings with non-metallic elastic elements. Doc. tech. sci. diss.]. Moscow, Bauman MVTU Publ., 1985. 302 p.
[10] Tribel’skiy I.A. Raschetno-eksperimental’nye metody proektirovaniya slozhnykh rezinokordnykh konstruktsiy uzlov agregatov i mashin. Dis. dok. tekh. nauk [Computational-experimental design methods for complex rubber-cord structural nodes of aggregates and machines. Doc. tech. sci. diss.]. Omsk, OmGTU Publ., 2009. 396 p.
[11] Biderman T.V. Rotation of rotary shell from high-elasticity material at strong deformations. Raschety na prochnost’, 1989, no. 27, pp. 237–244. (In Russ.).
[12] Golovanov A.I., Sultanov L.U. Matematicheskie modeli vychislitel’noy nelineynoy mekhaniki deformiruemykh sred [Mathematical models of computational nonlinear mechanics of deformable medium]. Kazan’, Kazanskiy gos. un-t Publ., 2009. 464 p.
[13] Biderman V.L. Raschet rezino-metallicheskikh i rezinokordnykh elementov mashin. Diss. dok. tekh. nauk [Calculation of rubber-metallic and rubber-cord machine elements. Doc. tech. sci. diss.]. Moscow, NII shinnoy promyshlennosti Publ., 1958. 372 p.
[14] Treloar L.R.G. The physics of rubber elasticity. Oxford, 1949. (Russ. ed.: Fizika uprugosti kauchuka. Moscow, IL Publ., 1953. 240 p.)
[15] Valishvili N.V. Metody rascheta obolochek vrashcheniya na ETsVM [Computer calculation methods for rotation shells]. Mosow, Mashinostroenie Publ., 1976. 278 p.
[16] Mikhaylov Yu.K., Ivanov B.S. Mufty s nemetallicheskimi elementami [Couplings with non-metallic elements]. Leningrad, Mashinostroenie Publ., 1987. 145 p.
[17] Belkin A.E., Biderman T.V. Numerical study on torsion durability of rotation shells. Raschety na prochnost’, 1983, no. 24, pp. 148–155. (In Russ.).