Abstract
The present research develops a general formulation for thermo-elastic analysis of a functionally graded thick shell of revolution with arbitrary curvature and variable thickness subjected to thermo-mechanical loading by using higher-order shear deformation theory. Mechanical properties except Poisson’s ratio are assumed to vary along a two-dimensional coordinate system with arbitrary functional distribution. Given that the thick shell is divided into some virtual disks and replacing various variable terms by their constant values, a set of differential equations for constant thickness are obtained for each virtual disk. By applying continuity conditions between the virtual disks, the general solution of the thick shell is obtained. The final relations are derived in general state for every arbitrary structure and material property distributions. Although previous publications presented a general formulation for thick shells of revolution, to the best of the authors’ knowledge, a closed-form solution is not provided.
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References
Kang, J.H.: Field equations, equations of motion, and energy functionals for thick shells of revolution with arbitrary curvature and variable thickness from a three-dimensional theory. Acta Mech. 188, 21–37 (2007)
Hu, X.X., Sakiyama, T., Matsuda, H., Morita, C.: Vibration analysis of twisted conical shells with tapered thickness. Int. J. Eng. Sci. 40, 1579–1598 (2002)
Arefi, M.: Nonlinear thermoelastic analysis of thick-walled functionally graded piezoelectric cylinder. Acta Mech. 224, 2771–2783 (2013)
Safari, A., Tahani, M., Hosseini, S.M.: Two-dimensional dynamic analysis of thermal stresses in a finite-length FG thick hollow cylinder subjected to thermal shock loading using an analytical method. Acta Mech. 220, 299–314 (2011)
Van-Dung, D., Hoa, L.K., Nga, N.T., Anh, L.T.N.: Instability of eccentrically stiffened functionally graded truncated conical shells under mechanical loads. Compos. Struct. 106, 104–113 (2013)
Rad, M.H.G., Shahabian, F., Hosseini, S.M.: A meshless local Petrov–Galerkin method for nonlinear dynamic analyses of hyper-elastic FG thick hollow cylinder with Rayleigh damping. Acta Mech. 226, 1497–1513 (2015)
Boresi, A.P., Paslay, P.R.: Elasticity in Engineering Mechanics. Wiley, Hoboken (2011)
Venkataramana, J.: Thermal stresses in heterogeneous thick isotropic shells. Nucl. Eng. Des. 30, 369–378 (1974)
Panferov, I.V.: Stresses in a transversely isotropic conical elastic pipe of constant thickness under a thermal load. J. Appl. Math. Mech. 56, 410–415 (1992)
Gro\(\beta \)-Weege, J., Weichert, D.: Elastic–plastic shells under variable mechanical and thermal loads. Int. J. Mech. Sci. 34, 863–880 (1992)
Obata, Y., Noda, N.: Two-dimensional unsteady thermal stresses in a partially heated plate made of functionally graded material. In: Proceedings of thermal stress, Rochester Institute of Technology, Rochester, pp. 735–738, 1997
Reddy, J.N., Chin, C.D.: Thermo-mechanical analysis of functionally graded cylinders and plates. J. Therm. Stress. 21, 593–626 (1998)
Ootao, Y., Tanigawa, Y., Nakamura, T.: Optimization of material composition of FGM hollow circular cylinder under thermal loading: a neural network approach. Compos. Part B Eng. 30, 415–422 (1999)
Tarn, J.Q.: Exact solutions for functionally graded anisotropic cylinders subjected to thermal and mechanical loads. Int. J. Solids Struct. 38, 8189–8206 (2001)
Tutuncu, N., Ozturk, M.: Exact solutions for stresses in functionally graded pressure vessels. Compos. Part B Eng. 32(8), 683–686 (2001)
Jabbari, M., Sohrabpour, S., Eslami, M.R.: Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads. Int. J. Press. Vessel. Pip. 79, 493–497 (2002)
Liew, K.M., Kitipornchai, S., Zhang, X.Z., Lim, C.W.: Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders. Int. J. Solids Struct. 40, 2355–2380 (2003)
Jane, K.C., Wu, Y.H.: A generalized thermoelasticity problem of multilayered conical shells. Int. J. Solids Struct. 41, 2205–2233 (2004)
Jabbari, M., Bahtui, A., Eslami, M.R.: Axisymmetric mechanical and thermal stresses in thick long FGM cylinders. J. Therm. Stress. 29, 643–663 (2006)
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, 7767–7784 (2007)
Argeso, H., Eraslan, A.N.: On the use of temperature-dependent physical properties in thermomechanical calculations for solid and hollow cylinders. Int. J. Therm. Sci. 47, 136–146 (2008)
Sladek, J., Sladek, V., Solek, P., Wen, P.H., Atluri, S.N.: Thermal analysis of Reissner–Mindlin shallow shells with FGM properties by the MLPG. Comput. Model. Eng. Sci. 30, 77–97 (2008)
Nejad, M.Z., Rahimi, G.H., Ghannad, M.: Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system. Mechanika 3, 18–26 (2015)
Jabbari, M., Meshkini, M., Eslami, M.R.: Mechanical and thermal stresses in a FGPM hollow cylinder due to non-axisymmetric loads. J. Solid. Mech. 3, 19–41 (2011)
Ray, S., Loukou, A., Trimis, D.: Evaluation of heat conduction through truncated conical shells. Int. J. Therm. Sci. 57, 183–191 (2012)
Alashti, R.A., Khorsand, M., Tarahhomi, M.H.: Three-dimensional asymmetric thermo-elastic analysis of a functionally graded rotating cylindrical shell. J. Theor. Appl. Mech. 51, 143–158 (2013)
Bîrsan, M., Sadowski, T., Pietras, D.: Thermoelastic deformations of cylindrical multi-layered shells using a direct approach. J. Therm. Stress. 36, 749–789 (2013)
Aziz, A., Torabi, M.: Thermal stresses in a hollow cylinder with convective boundary conditions on the inside and outside surfaces. J. Therm. Stress. 36, 1096–1111 (2013)
Dai, H.L., Dai, T.: Analysis for the thermoelastic bending of a functionally graded material cylindrical shell. Meccanica 49, 1069–1081 (2014)
Nejad, M.Z., Jabbari, M., Ghannad, M.: A semi-analytical solution for elastic analysis of rotating thick cylindrical shells with variable thickness using disk form multilayers. Sci. World J. (2014). doi:10.1155/2014/932743
Nejad, M.Z., Jabbari, M., Ghannad, M.: A semi-analytical solution of thick truncated cones using matched asymptotic method and disk form multilayers. Arch. Mech. Eng. 61, 495–513 (2014)
Nejad, M.Z., Jabbari, M., Ghannad, M.: Elastic analysis of rotating thick cylindrical pressure vessels under non-uniform pressure: linear and non-linear thickness. Period. Polytech. Mech. Eng. 59, 65–73 (2015)
Sabik, A., Kreja, I.: Thermo-elastic non-linear analysis of multilayered plates and shells. Compos. Struct. 130, 37–43 (2015)
Nejad, M.Z., Jabbari, M., Ghannad, M.: Elastic analysis of axially functionally graded rotating thick cylinder with variable thickness under non-uniform arbitrarily pressure loading. Int. J. Eng. Sci. 89, 86–99 (2015)
Nejad, M.Z., Jabbari, M., Ghannad, M.: Elastic analysis of FGM rotating thick truncated conical shells with axially-varying properties under non-uniform pressure loading. Compos. Struct. 122, 561–569 (2015)
Alsubari, S., Ali, J.S.M., Aminanda, Y.: Hygrothermoelastic analysis of anisotropic cylindrical shells. Compos. Struct. 131, 151–159 (2015)
Jabbari, M., Nejad, M.Z., Ghannad, M.: Thermo-elastic analysis of axially functionally graded rotating thick truncated conical shells with varying thickness. Compos. Part B-Eng 96, 20–34 (2016)
Jabbari, M., Nejad, M.Z., Ghannad, M.: Thermo-elastic analysis of axially functionally graded rotating thick cylindrical pressure vessels with variable thickness under mechanical loading. Int. J. Eng. Sci. 96, 1–18 (2015)
Kugler, S., Fotiu, P.A., Murin, J.: Thermo-elasticity in shell structures made of functionally graded materials. Acta Mech. 227, 1307–1329 (2016)
Xin, L., Dui, G., Yang, S., Zhang, J.: An elasticity solution for functionally graded thick-walled tube subjected to internal pressure. Int. J. Mech. Sci. 89, 344–349 (2014)
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Nejad, M.Z., Jabbari, M. & Ghannad, M. A general disk form formulation for thermo-elastic analysis of functionally graded thick shells of revolution with arbitrary curvature and variable thickness. Acta Mech 228, 215–231 (2017). https://doi.org/10.1007/s00707-016-1709-z
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DOI: https://doi.org/10.1007/s00707-016-1709-z