Stress analysis in an isotropic hyperbolic rotating disk fitted with rigid shaft. (English) Zbl 1479.74019
Summary: The purpose of this paper is to present study of stresses distribution and displacement in an isotropic hyperbolic rotating disk fitted with rigid shaft and having variable density parameter by using transition theory. It has been seen that the convergent disk made of rubber material requires a higher angular speed at the inner surface as compared to aluminum alloy material on the initial yielding stage, but for the fully plastic stage divergent disk requires higher angular speed at the inner surface as compared to a uniform/convergent disk. With the introduction of density parameter, the values of angular speed increase in the inner surface the initial/fully plastic stage. The convergent disk made of rubber material requires maximum radial stress at the inner surface as compared to aluminum alloy material. With the increasing value of density parameter, the radial stress increases in the intermediate surface of the hyperbolic rotating disk. Results have been discussed numerical and depicted graphically.
MSC:
| 74C15 | Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) |
| 74K30 | Junctions |
| 74G10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics |
Keywords:
finite Euler-Almansi strain; yielding stage; angular speed; stress distribution; rubber material; density parameterReferences:
| [1] | Sokolnikoff, IS, Mathematical theory of elasticity (1956), New York: McGraw - Hill Book Co., New York · Zbl 0070.41104 |
| [2] | Swainger K.H.: Analysis of deformation. Chapman & Hall London. Macmillan, USA,V.III,fluidity,67-68,83(1956) · Zbl 0075.32701 |
| [3] | Seth, BR, Transition theory of elastic—plastic deformation, creep and relaxation, Nature, 195, 896-897 (1962) · doi:10.1038/195896a0 |
| [4] | Seth, BR, Measure concept in mechanics, Int. J. Non-linear Mech., 1, 1, 35-40 (1966) · doi:10.1016/0020-7462(66)90016-3 |
| [5] | Timoshenko, S.; Goodier, JN, Theory of elasticity (1970), New York: McGraw-Hill Book Company, New York · Zbl 0266.73008 |
| [6] | Reddy, TY; Srinath, H., Elastic stresses in a rotating anisotropic annular disk of variable thickness and variable density, Int. J. Mech. Sci., 16, 1, 85-89 (1974) · doi:10.1016/0020-7403(74)90078-2 |
| [7] | Güven, U., Elastic-plastic stress distribution in a rotating hyperbolic disk with rigid inclusion, Int. J. Mech. Sci., 40, 1, 97-109 (1998) · Zbl 0899.73269 · doi:10.1016/S0020-7403(97)00036-2 |
| [8] | Chakrabart, J., Theory of Plasticity (1998), New York: McGraw-Hill Book Company, New York |
| [9] | Apatay, T.; Eraslan, AN, Elastic deformation of rotating parabolic discs: analytical solutions, J. Faculty Eng. Archit. Gazi Univ., 18, 115-135 (2003) |
| [10] | Eraslan, A.N.: Elastoplastic deformations of rotating parabolic solid disks using Tresca’s yield criterion. Eur. J. Mech. Solids 22(6), 861-874 (2003) · Zbl 1032.74578 |
| [11] | Thakur,P.: Some problems in elastic, plastic and creep transition. Ph.D. Thesis, 13- 27(2006) |
| [12] | Vivio, F.; Vullo, V., Elastic stress analysis of rotating converging conical disks subjected to thermal load and having variable density along the radius, Int. J. Solids Struct., 44, 24, 7767-7784 (2007) · Zbl 1167.74571 · doi:10.1016/j.ijsolstr.2007.05.013 |
| [13] | Bayat, M.; Saleem, M.; Sahari, BB; Hamouda, AMS, Analysis of functionally graded rotating disks with variable thickness, Mech. Res. Commun., 35, 4, 283-309 (2008) · Zbl 1258.74131 · doi:10.1016/j.mechrescom.2008.02.007 |
| [14] | Nie, GJ; Batra, RC, Stress analysis and material tailoring in isotropic linear thermoelastic incompressible functionally graded rotating disks of variable thickness, Compos. Struct., 92, 2, 720-729 (2010) · doi:10.1016/j.compstruct.2009.08.052 |
| [15] | Calderale, PM; Vivio, F.; Vullo, V., Thermal stresses of rotating hyperbolic disks as particular case of non-linearly variable thickness disks, J. Thermal Stress., 35, 7, 877-891 (2012) · doi:10.1080/01495739.2012.720164 |
| [16] | Peng, XL; Li, XF, Effects of gradient on stress distribution in rotating functionally graded solid disks, J. Mech. Sci. Technol., 26, 4, 1483-1492 (2012) · doi:10.1007/s12206-012-0339-1 |
| [17] | Vivio, F.; Vullo, V.; Cifani, P., Theoretical stress analysis of rotating hyperbolic disk without singularities subjected to thermal load, J. Thermal Stress., 37, 1, 117-136 (2014) · doi:10.1080/01495739.2013.839526 |
| [18] | Deepak, D.; Garg, M.; Gupta, VK, Creep behavior of rotating FGM disc with linear and hyperbolic thickness profiles, Kragujevac J. Sci., 37, 35-48 (2015) |
| [19] | Yıldırım, V., Analytic solutions to power-law graded hyperbolic rotating discs subjected to different boundary conditions, Int. J. Eng. Appl. Sci., 8, 1, 38-52 (2016) |
| [20] | Yıldırım, V., A parametric study on the centrifugal force-induced stress and displacements in power-law graded hyperbolic discs, Latin Am. J. Solids Struct., 15, 3, 1-16 (2018) |
| [21] | Jalali, M. H., Shahriari, B.: Elastic stress analysis of rotating functionally graded annular disk of variable thickness using finite difference method. Math. Probl. Eng. 2018,1-11. doi:10.1155/2018/1871674(2018) · Zbl 1426.74200 |
| [22] | Yıldırım, V., Closed-form formulas for hyperbolically tapered rotating disks made of traditional materials under combined thermal and mechanical loads, Int. J Eng. Appl. Sci. (IJEAS)., 10, 1, 73-92 (2018) |
| [23] | Salehian,M. , Shahriari,B. , Yousefi M.:Investigating the effect of angular acceleration of the rotating disk having variable thickness and density function on shear stress and tangential displacement.Journal of the Brazilian Society of Mechanical Sciences and Engineering.41(31),2-11(2019) |
| [24] | Singh, R.; Saxena, R.; Khanna, K.; Gupta, V., Creep response of rotating composite discs having exponential hyperbolic linear and constant thickness profiles, Defence Sci. J., 70, 2, 292-298 (2020) · doi:10.14429/dsj.70.14913 |
| [25] | Sethi, M.; Thakur, P., Elasto-plastic deformation in isotropic material disk with shaft subjected to load and variable density, J. Rubber Res., 23, 1, 69-78 (2020) · doi:10.1007/s42464-020-00038-8 |
| [26] | Thakur, P, Kumar, N., Sukhvinder.:Elasto-plastic density variation in a deformable disk. Struct. Integr. Life.20(1),27-32(2020) |
| [27] | Thakur, P.; Sethi, M.; Gupta, N.; Gupta, K., Effect of density parameter in a disk made of orthotropic material and rubber, J. Rubber Res., 25, 2, 193-201 (2020) · doi:10.1007/s42464-020-00049-5 |
| [28] | Thakur, P.; Sethi, M., Elasto-plastic deformation in an orthotropic spherical shell subjected to temperature gradient, Math. Mech. Solids., 25, 1, 26-34 (2020) · Zbl 1446.74169 · doi:10.1177/1081286519857128 |
| [29] | Thakur, P.; Sethi, M., Creep deformation and stress analysis in a transversely material disc subjected to rigid shaft, Math. Mech. Solids., 25, 1, 17-25 (2020) · Zbl 1446.74159 · doi:10.1177/1081286519857109 |
| [30] | Lin, W.F.: Elastic analysis for rotating functionally graded annular disk with exponentially-varying profile and properties. Math. Probl. Eng. doi:10.1155/2020/2165804(2020) · Zbl 1459.74063 |
| [31] | Thakur, P., Sethi, M., Gupta, N., Gupta, K.:Thermal effects in rectangular plate made of rubber, copper and glass materials. J. Rubber Res. doi:10.1007/S42464-020-00080-6 (2021) |
| [32] | Thakur, P.; Kumar, N.; Sethi, M., Elastic-plastic stresses in a rotating disc of transversely isotropic material fitted with a shaft and subjected to thermal gradient, Meccanica., 56, 1165-1175 (2021) · Zbl 1516.74016 · doi:10.1007/s11012-021-01318-2 |
| [33] | Thakur, P., Sethi, M., Kumar, N., Gupta, N., Kumar, A., Sood, S.:Thermal effects in a rotating disk made of rubber and magnesium materials and having variable density. J. Rubber Res. DOI: 10.1007/s42464-021-00107-6(2021) |
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