Stress-strain state of thick-walled anisotropic cylindrical shells under thermal power load, protected by the functionally graded material
Keywords:thick-walled anisotropic cylindrical shell, stress-strain state, three-dimensional formulation, functionally graded material
In the article the stress-strain state of thick-walled structurally anisotropic composite cylindrical shells under thermal power load, which are protected by a functionally graded material, are analysed. Based on the interrelations of the spatial theory of elasticity, a system of inhomogeneous differential equations in three-dimensional formulation, which describes the stress-strain state of thick-walled anisotropic cylindrical shells, was obtained. To reduce the dimensionality of this system, the Bubnov-Galerkin analytical method was used. Thus, the obtained one-dimensional system of twelve equations of normal Cauchy form was implemented using the numerical method of discrete orthogonalization. To represent the possibilities of the proposed approach, there were used stress-strain states of two, four and five-layered anisotropic cylindrical shells of fibrous composites, protected from temperature by a layer of transversely isotropic functionally graded material.
Bazhenov V.A., Semeniuk M.P., Trach V.M. (2010), Nelinijne deformuvannia, stijkist' i zakrytychna povedinka anizotropnykh obolonok (Nonlinear deformation, stability and supercritical behavior of anisotropic shells). Kyiv, Karavela, 352 p. [in Ukrainian].
Grigorenko Ya.M., Vasilenko A.T., Pankratova N.D. Zadachi teorii uprugosti neodnorodnyih tel (Problems of the theory of elasticity of inhomogeneous bodies) – Kyiv, Naukova dumka, 1991. - 216 p. [in Russian].
Grigorenko Ya.M., Kryukov N.N. Chislennyie resheniya zadach statiki gibkih sloistyih obolochek s peremennyimi parametrami (Numerical solutions of problems of statics of flexible layered shells with variable parameters) – Kyiv, Naukova dumka, 1988. 264 p. [in Russian].
Lekhnitskyi S.G. Teoriya uprugosti anizotropnogo tela (The theory of elasticity of an anisotropic body). - 2nd ed. - Мoscow: Nauka, 1977. - 415 p. [in Russian].
Novozhilov V.V. Osnovy nelineynoy teorii uprugosti (Fundamentals of the nonlinear theory of elasticity). - L.-M .: OGIZ, 1948. - 211 p. [in Russian].
Trach V.M., Podvorny A.V., Khoruzhiy M.M. Deformuvannya ta stiykistʹ netonkykh anizotropnykh obolonok (Deformation and stability of non-thin anisotropic shells): Monograph. – K.: Karavela, 2019. - 273 p. [in Ukrainian].
Trach V.M., Semenyuk M.P., Podvorny A.V. Vykorystannia 3D metodyky do rozrakhunku napruzhenoho stanu sharuvatykh anizotropnykh tsylindrychnykh obolonok pid diieiu bokovoho tysku. Resursoekonomni materialy, konstruktsii, budivli ta sporudy (The use of 3D techniques to calculate the stress state of layered anisotropic cylindrical shells under lateral pressure load). Resource-saving materials, structures, buildings and constructions: Collection of scientific papers. Issue 37. - NUWEE.- Rivne, 2019.- P.296-306. [in Ukrainian].
Gibson L.J., Ashby M.F., Karam G.N., Wegst U., and Shercliff H.R. Mechanical properties of natural materials. II. Microstructures for mechanical efficiency, Proceedings of the Royal Society of London Series A, 450, 141–162.
Javaheri R. and Eslami M.R. Thermal buckling of functionally graded plates.
AIAA Journal, 40, 2002, рр. 162–169
Podvornyi A. The stability of anisotropic cylindrical shells under torsion in spatial position. ActaSci.Pol. Arch. 19 (1) 2020, 103-109.
Podvornyi A.V., Semenyuk N.P., Trach V.M. Stability of inhomogeneous cylindrical shells under distributed external pressure in a three-dimensional statement // Int. Appl. Mech. – 2017. – 53, N 6. P. 623 – 638.
Reddy J.N. and Chin C.D. Thermoelastical analysis of functionally graded
cylinders and plates, Journal of Thermal Stresses, 21, 593–626
Semenyuk, N.P., Trach, V.M., Podvornyi, A.V. Spatial Stability of Layered Anisotropic Cylindrical Shells Under Compressive Loads. International Applied Mechanics. №2, 2019.
Semenyuk, N.P., Trach, V.M., Podvornyi, A.V. Stability of cylindrical anisotropic shells under axial pressure in three-dimensional statement. Strength of Materials and Theory of Structures, issue 94, KNUBA (2015), pp. 192–206.
Shahsiah R. And Eslami M.R. Thermal buckling of functionally graded cylindrical shell, Journal of Thermal Stresses, 26, 2003, 277–294.
Shen, Hui-Shen Functionally graded materials: nonlinear analysis of plates and shells. - CRC Press Taylor & Francis Group, Boca Raton London New York, 2009, - 266p.
Shen, Hui-Shen Postbuckling of axially-loaded FGM hybrid cylindrical shells in thermal environments, Composites Science and Technology, 65, 2005, 1675–1690.
Touloukian Y.S. Thermo physical Properties of High Temperature Solid Materials, McMillan, New York.
Copyright (c) 2020 Mykola Semenyuk, Volodymyr Trach, Andrii Podvornyi
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.