Journal of Computational Applied Mechanics

Bi-Directional Thermo-Elastic Analysis of Pressurized Thick Cylindrical Shell with Nonlinear Variable Thickness

Document Type : Research Paper

Authors

1 Department of Mechanical Engineering, Yasouj University, Yasouj, Iran

2 Mechanical Engineering Department, Yasouj University, P. O. Box: 75914-353, Yasouj, Iran

3 Department of Solid Mechanics, Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran,

Abstract

In this paper, a thermo-elastic analysis is presented to obtain stresses, displacements, and the thermal field in the axisymmetric clamped–clamped rotating thick cylindrical shell with nonlinear variable thickness. This shell is subjected to mechanical and thermal load in two dimensions. The governing equations are formulated as a set of non-homogeneous ordinary differential equations with variable coefficients. The system of partial differential equations is semi-analytically solved by using multi-layer method (MLM). The solution of equations is obtained by applying boundary conditions and ensuring continuity between the layers. The problem is also solved, using the finite element method (FEM). The obtained results of the disk form multi-layers method (MLM) are compared with those of FEM.

Keywords

Main Subjects

[1]          C. Wang, J. N. Reddy, K. Lee, 2000, Shear deformable beams and plates: Relationships with classical solutions, Elsevier.
[2]          P. Fatehi, M. Z. Nejad, Effects of material gradients on onset of yield in FGM rotating thick cylindrical shells, International Journal of Applied Mechanics, Vol. 6, No. 4, pp. 1450038, 2014.
[3]          M. Z. Nejad, A. Rastgoo, A. Hadi, Exact elasto-plastic analysis of rotating disks made of functionally graded materials, International Journal of Engineering Science, Vol. 85, pp. 47-57, 2014.
[4]          Z. Mazarei, M. Z. Nejad, A. Hadi, Thermo-elasto-plastic analysis of thick-walled spherical pressure vessels made of functionally graded materials, International Journal of Applied Mechanics, Vol. 8, No. 4, pp. 1650054, 2016.
[5]          M. Z. Nejad, M. D. Kashkoli, Time-dependent thermo-creep analysis of rotating FGM thick-walled cylindrical pressure vessels under heat flux, International Journal of Engineering Science, Vol. 82, pp. 222-237, 2014.
[6]          A. R. Shahani, F. Kiarasi, Numerical and experimental envestigation on post-buckling‎ behavior of stiffened cylindrical shells with cutout subject to‎ uniform axial compression, Journal of Applied and Computational Mechanics, Vol. 9, No. 1, pp. 25-44, 2023.
[7]          M. Z. Nejad, N. Alamzadeh, A. Hadi, Thermoelastoplastic analysis of FGM rotating thick cylindrical pressure vessels in linear elastic-fully plastic condition, Composites Part B-Engineering, Vol. 154, pp. 410-422, 2018.
[8]          T. Taghizadeh, M. Z. Nejad, M. D. Kashkoli, Thermo-elastic creep analysis and life assessment of thick truncated conical shells with variable thickness, International Journal of Applied Mechanics, Vol. 11, No. 9, pp. 1950086, 2019.
[9]          A. Farajpour, A. Rastgoo, Size-dependent static stability of magneto-electro-elastic CNT/MT-based composite nanoshells under external electric and magnetic fields, Microsystem Technologies, Vol. 23, pp. 5815-5832, 2017.
[10]        M. D. Kashkoli, K. N. Tahan, M. Z. Nejad, Creep damage and life assessment of thick cylindrical pressure vessels with variable thickness made of 304L austenitic stainless steel, Steel and Composite Structures, Vol. 32, No. 6, pp. 701, 2019.
[11]        M. Z. Nejad, T. Taghizadeh, S. J. Mehrabadi, S. Herasati, Elastic analysis of carbon nanotube-reinforced composite plates with piezoelectric layers using shear deformation theory, International Journal of Applied Mechanics, Vol. 9, No. 1, pp. 1750011, 2017.
[12]        T. Ebrahimi, M. Z. Nejad, H. Jahankohan, A. Hadi, Thermoelastoplastic response of FGM linearly hardening rotating thick cylindrical pressure vessels, Steel and Composite Structures, Vol. 38, No. 2, pp. 189-211, 2021.
[13]        M. D. Kashkoli, K. N. Tahan, M. Z. Nejad, Time-dependent thermomechanical creep behavior of FGM thick hollow cylindrical shells under non-uniform internal pressure, International Journal of Applied Mechanics, Vol. 9, No. 6, pp. 1750086, 2017.
[14]        M. H. Dindarloo, L. Li, Vibration analysis of carbon nanotubes reinforced isotropic doubly-curved nanoshells using nonlocal elasticity theory based on a new higher order shear deformation theory, Composites Part B-Engineering, Vol. 175, pp. 107170, 2019.
[15]        N. K. Lamba, Impact of memory-dependent response of a thermoelastic thick solid cylinder, Journal of Applied and Computational Mechanics, Vol. 9, No. 4, pp. 1135-1143, 2023.
[16]        M. Dehghan, M. Z. Nejad, A. Moosaie, Thermo-electro-elastic analysis of functionally graded piezoelectric shells of revolution: Governing equations and solutions for some simple cases, International Journal of Engineering Science, Vol. 104, pp. 34-61, 2016.
[17]        M. Z. Nejad, P. Fatehi, Exact elasto-plastic analysis of rotating thick-walled cylindrical pressure vessels made of functionally graded materials, International Journal of Engineering Science, Vol. 86, pp. 26-43, 2015.
[18]        M. Kashkoli, K. N. Tahan, M. Nejad, Time-dependent creep analysis for life assessment of cylindrical vessels using first order shear deformation theory, Journal of Mechanics, Vol. 33, No. 4, pp. 461-474, 2017.
[19]        A. Amiri Delouei, A. Emamian, S. Karimnejad, Y. Li, An exact analytical solution for heat conduction in a‎ functionally graded conical shell, Journal of Applied and Computational Mechanics, Vol. 9, No. 2, pp. 302-317, 2023.
[20]        A. Sofiyev, N. Fantuzzi, Analytical solution of stability and vibration problem of clamped cylindrical shells containing functionally graded layers within shear deformation theory, Alexandria Engineering Journal, Vol. 64, pp. 141-154, 2023.
[21]        M. Nejad, Z. Hoseini, A. Niknejad, M. Ghannad, Steady-state creep deformations and stresses in FGM rotating thick cylindrical pressure vessels, Journal of Mechanics, Vol. 31, No. 1, pp. 1-6, 2015.
[22]        Y.-W. Zhang, G.-L. She, Nonlinear primary resonance of axially moving functionally graded cylindrical shells in thermal environment, Mechanics of Advanced Materials and Structures, pp. 1-13, 2023.
[23]        C. Ipek, Vibration analysis of shear deformable cylindrical shells made‎ of heterogeneous anisotropic material with clamped edges, Journal of Applied and Computational Mechanics, Vol. 9, No. 3, pp. 861-869, 2023.
[24]        M. D. Kashkoli, M. Z. Nejad, Time-dependent creep analysis and life assessment of 304 L austenitic stainless steel thick pressurized truncated conical shells, Steel and Composite Structures, Vol. 28, No. 3, pp. 349-362, 2018.
[25]        M. D. Kashkoli, M. Z. Nejad, Time-dependent thermo-elastic creep analysis of thick-walled spherical pressure vessels made of functionally graded materials, Journal of Theoretical and applied Mechanics, Vol. 53, No. 4, pp. 1053-1065, 2015.
[26]        I. Panferov, Stresses in a transversely isotropic conical elastic pipe of constant thickness under a thermal load, Journal of Applied Mathematics and Mechanics, Vol. 56, No. 3, pp. 410-415, 1992.
[27]        H. Xiang, Z. Shi, T. Zhang, Elastic analyses of heterogeneous hollow cylinders, Mechanics Research Communications, Vol. 33, No. 5, pp. 681-691, 2006.
[28]        M. Arefi, G. H. Rahimi, Thermo elastic analysis of a functionally graded cylinder under internal pressure using first order shear deformation theory, Scientific Research and Essays, Vol. 5, No. 12, pp. 1442-1454, 2010.
[29]        M. Z. Nejad, G. H. Rahimi, Deformations and stresses in rotating FGM pressurized thick hollow cylinder under thermal load, Scientific Research and Essays, Vol. 4, No. 3, pp. 131-140, 2009.
[30]        L. Xin, G. Dui, S. Yang, D. Zhou, Solutions for behavior of a functionally graded thick-walled tube subjected to mechanical and thermal loads, International Journal of Mechanical Sciences, Vol. 98, pp. 70-79, 2015.
[31]        M. Z. Nejad, G. H. Rahimi, M. Ghannad, Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system, Mechanika, Vol. 77, No. 3, pp. 18-26, 2009.
[32]        A. Yasinskyy, L. Tokova, Inverse problem on the identification of temperature and thermal stresses in an FGM hollow cylinder by the surface displacements, Journal of Thermal Stresses, Vol. 40, No. 12, pp. 1471-1483, 2017.
[33]        M. Ghannad, M. Z. Nejad, Elastic analysis of pressurized thick hollow cylindrical shells with clamped-clamped ends, Mechanika, Vol. 85, No. 5, pp. 11-18, 2010.
[34]        J.-H. Kang, 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 Mechanica, Vol. 188, No. 1-2, pp. 21-37, 2007.
[35]        M. Z. Nejad, M. Jabbari, M. Ghannad, A semi-analytical solution of thick truncated cones using matched asymptotic method and disk form multilayers, Archive of Mechanical Engineering, Vol. 61, No. 3, pp. 495--513, 2014.
[36]        M. Ghannad, G. H. Rahimi, M. Z. Nejad, Determination of displacements and stresses in pressurized thick cylindrical shells with variable thickness using perturbation technique, Mechanika, Vol. 18, No. 1, pp. 14-21, 2012.
[37]        B. Sundarasivarao, N. Ganesan, Deformation of varying thickness of conical shells subjected to axisymmetric loading with various end conditions, Engineering Fracture Mechanics, Vol. 39, No. 6, pp. 1003-1010, 1991.
[38]        I. Mirsky, G. Herrmann, Axially symmetric motions of thick cylindrical shells, 1958.
[39]        F. Witt, Thermal stress analysis of conical shells, Nuclear Structural Engineering, Vol. 1, No. 5, pp. 449-456, 1965.
[40]        H. R. Eipakchi, S. Khadem, G. H. Rahimi S, Axisymmetric stress analysis of a thick conical shell with varying thickness under nonuniform internal pressure, Journal of Engineering Mechanics, Vol. 134, No. 8, pp. 601-610, 2008.
[41]        M. Ghannad, M. Z. Nejad, Elastic solution of pressurized clamped-clamped thick cylindrical shells made of functionally graded materials, Journal of Theoretical and Applied Mechanics, Vol. 51, No. 4, pp. 1067-1079, 2013.
[42]        K. Jane, Y. Wu, A generalized thermoelasticity problem of multilayered conical shells, International Journal of Solids and Structures, Vol. 41, No. 9-10, pp. 2205-2233, 2004.
[43]        M. Ghannad, M. Z. Nejad, G. H. Rahimi, Elastic solution of axisymmetric thick truncated conical shells based on first-order shear deformation theory, Mechanika, Vol. 79, No. 5, pp. 13-20, 2009.
[44]        Y. Obata, N. Noda, Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material, Journal of Thermal Stresses, Vol. 17, No. 3, pp. 471-487, 1994.
[45]        M. Ghannad, G. H. Rahimi, M. Z. Nejad, Elastic analysis of pressurized thick cylindrical shells with variable thickness made of functionally graded materials, Composites Part B-Engineering, Vol. 45, No. 1, pp. 388-396, 2013.
[46]        H. R. Eipakchi, Third-order shear deformation theory for stress analysis of a thick conical shell under pressure, Journal of Mechanics of Materials and Structures, Vol. 5, No. 1, pp. 1-17, 2010.
[47]        G. Cao, Z. Chen, L. Yang, H. Fan, F. Zhou, Analytical study on the buckling of cylindrical shells with arbitrary thickness imperfections under axial compression, Journal of Pressure Vessel Technology, Vol. 137, No. 1, pp. 011201, 2015.
[48]        M. Z. Nejad, M. Jabbari, M. Ghannad, Elastic analysis of axially functionally graded rotating thick cylinder with variable thickness under non-uniform arbitrarily pressure loading, International Journal of Engineering Science, Vol. 89, pp. 86-99, 2015.
[49]        Ö. Civalek, Vibration analysis of laminated composite conical shells by the method of discrete singular convolution based on the shear deformation theory, Composites Part B-Engineering, Vol. 45, No. 1, pp. 1001-1009, 2013.
[50]        M. Z. Nejad, M. Jabbari, M. Ghannad, Elastic analysis of rotating thick cylindrical pressure vessels under non-uniform pressure: linear and non-linear thickness, Periodica Polytechnica Mechanical Engineering, Vol. 59, No. 2, pp. 65-73, 2015.
[51]        S. Ray, A. Loukou, D. Trimis, Evaluation of heat conduction through truncated conical shells, International Journal of Thermal Sciences, Vol. 57, pp. 183-191, 2012.
[52]        M. Z. Nejad, M. Jabbari, M. Ghannad, Elastic analysis of FGM rotating thick truncated conical shells with axially-varying properties under non-uniform pressure loading, Composite Structures, Vol. 122, pp. 561-569, 2015.
[53]        M. Jabbari, M. Z. Nejad, M. Ghannad, Thermoelastic analysis of rotating thick truncated conical shells subjected to non-uniform pressure, Journal of Solid Mechanics, Vol. 8, No. 3, pp. 466-481, 2016 .
[54]        M. Jabbari, M. Z. Nejad, M. Ghannad, Stress analysis of rotating thick truncated conical shells with variable thickness under mechanical and thermal loads, Journal of Solid Mechanics, Vol. 9, No. 1, pp. 100-114, 2017.
[55]        A. A. Hamzah, H. K. Jobair, O. I. Abdullah, E. T. Hashim, L. A. Sabri, An investigation of dynamic behavior of the cylindrical shells under thermal effect, Case Studies in Thermal Engineering, Vol. 12, pp. 537-545, 2018.
[56]        M. D. Kashkoli, K. N. Tahan, M. Z. Nejad, Thermomechanical creep analysis of FGM thick cylindrical pressure vessels with variable thickness, International Journal of Applied Mechanics, Vol. 10, No. 1, pp. 1850008, 2018.
[57]        H. Gharooni, M. Ghannad, M. Z. Nejad, Thermo-elastic analysis of clamped-clamped thick FGM cylinders by using third-order shear deformation theory, Latin American Journal of Solids and Structures, Vol. 13, pp. 750-774, 2016.
[58]        M. Jabbari, M. Z. Nejad, M. Ghannad, Thermo-elastic analysis of axially functionally graded rotating thick truncated conical shells with varying thickness, Composites Part B-Engineering, Vol. 96, pp. 20-34, 2016.
[59]        J. Lai, C. Guo, J. Qiu, H. Fan, Static analytical approach of moderately thick cylindrical ribbed shells based on first-order shear deformation theory, Mathematical Problems in Engineering, Vol. 2015, 2015.
[60]        M. Z. Nejad, M. Jabbari, M. Ghannad, A general disk form formulation for thermo-elastic analysis of functionally graded thick shells of revolution with arbitrary curvature and variable thickness, Acta Mechanica, Vol. 228, pp. 215-231, 2017.
[61]        F. Aghaienezhad, R. Ansari, M. Darvizeh, On the stability of hyperelastic spherical and cylindrical shells subjected to external pressure using a numerical approach, International Journal of Applied Mechanics, Vol. 14, No. 10, pp. 2250094, 2022.
[62]        O. Ifayefunmi, D. Ruan, Buckling of stiffened cone–cylinder structures under axial compression, International Journal of Applied Mechanics, Vol. 14, No. 7, pp. 2250075, 2022.
[63]        M. Y. Ariatapeh, M. Shariyat, M. Khosravi, Semi-analytical large deformation and three-dimensional stress analyses of pressurized finite-length thick-walled incompressible hyperelastic cylinders and pipes, International Journal of Applied Mechanics, Vol. 15, No. 1, pp. 2250100, 2023.
[64]        S. Mannani, L. Collini, M. Arefi, Mechanical stress and deformation analyses of pressurized cylindrical shells based on a higher-order modeling, Defence Technology, Vol. 20, pp. 24-33, 2023.
[65]        M. Ghannad, M. P. Yaghoobi, 2D thermo elastic behavior of a FG cylinder under thermomechanical loads using a first order temperature theory, International Journal of Pressure Vessels and Piping, Vol. 149, pp. 75-92, 2017.
[66]        S. Vlachoutsis, Shear correction factors for plates and shells, International Journal for Numerical Methods in Engineering, Vol. 33, No. 7, pp. 1537-1552, 1992.
Journal of Computational Applied Mechanics
Volume 55, Issue 1
January 2024
Pages 125-143
  • Receive Date: 10 November 2023
  • Revise Date: 01 December 2023
  • Accept Date: 01 December 2023