Thermal Buckling Analysis of Porous Conical Shell on Elastic Foundation

Journal of Solid Mechanics

مقاله 4، دوره 13، شماره 1، خرداد 2021، صفحه 37-53   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/jsm.2020.1884938.1524

نویسندگان

M Gheisari؛ M.M Najafizadeh^* ؛ A. R Nezamabadi؛ S Jafari؛ P Yousefi

Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran

چکیده

In this research, the thermal buckling analysis of a truncated conical shell made of porous materials on elastic foundation is investigated. The equilibrium equations and the conical shell`s stability equations are obtained  by using the Euler`s and the Trefftz equations .Properties of the materials used in the conical shell are considered as porous foam made of steel, which is characterized by its non-uniform distribution of porous materials along the thickness direction. Initially, the displacement field relation based on the classical model for double-curved shell is expressed in terms of the Donnell`s assumptions. Non-linear strain-displacement relations are obtained according to the von Kármán assumptions by applying the Green-Lagrange strain relationship. Then, performing the Euler equations leads obtaining nonlinear equilibrium equations of cylindrical shell. The stability equations of conical shell are obtained based on neighboring equilibrium benchmark (adjacent state). In order to solve the stability equations, primarily, due to the existence of axial symmetry, we consider the cone crust displacement as a sinusoidal geometry, and then, using the generalized differential quadrature method, we solve them to obtain the critical temperature values of the buckling Future. In order to validate the results, they compare with the results of other published articles. At the end of the experiment, various parameters such as dimensions, boundary conditions, cone angle, porosity parameter and elastic bed coefficients are investigated on the critical temperature of the buckling.

کلیدواژه‌ها

Thermal buckling؛ Truncated conical shell؛ Porous

مراجع

[1] Eslami M.R., Ziaii A.R., Ghorbanpour A., 1996, Thermoelastic buckling of thin cylindrical shells based on improved donnell equations, Journal of Thermal Stresses 19: 299-316.
[2] Najafizadeh M.M., Hasani A., Khazaeinejad P., 2009, Mechanical stability of functionally graded stiffened cylindrical shells, Applied Mathematical Modelling 33: 1151-1157.
[3] Tornabene F., Viola E., Inman D.J., 2009, 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures, Journal of Sound and Vibration 328: 259-290.
[4] Tornabene F., 2009, Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution, Computer Methods in Applied Mechanics and Engineering 198: 2911-2935.
[5] Bagherizadeh E., Kiani Y., Eslami M.R., 2011, Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation, Composite Structures 93: 3063-7301.
[6] Bagherizadeh E., Kiani Y., Eslami M.R., 2012, Thermal buckling of functionally graded material cylindrical shells on elastic foundation, AIAA Journal 50: 500-503.
[7] Sofiyev A.H., Kuruoglu N., 2013, Torsional vibration and buckling of the cylindrical shell with functionally graded coatings surrounded by an elastic medium, Composites Part B 45: 1133-1142.
[8] Dung D.V., Hoa L.K., 2013, Nonlinear buckling and postbuckling analysis of eccentrically stiffened functionally graded circular cylindrical shells under external pressure, Thin-Walled Structures 63: 117-124.
[9] Dung D.V., Hoa L.K., 2013, Research on nonlinear torsional buckling and post-buckling of eccentrically stiffened functionally graded thin circular cylindrical shells, Composites Part B 51: 300-309.
[10] Dung D.V., Hoa L.K., 2015, Semi-analytical approach for analyzing the nonlinear dynamic torsional buckling of stiffened functionally graded material circular cylindrical shells surrounded by an elastic medium, Applied Mathematical Modelling 39: 6951-6967.
[11] Sabzikar Boroujerdy M., Naj R., Kiani Y., 2014, Buckling of heated temperature dependent FGM cylindrical shell surrounded by elastic medium, Theoretical and Applied Mechanics 52(4): 869-881.
[12] Castro S., Mittelstedt C., Monteiro F., Arbelo M., Ziegmann G., Degenhardt R., 2014, Linear buckling predictions of unstiffened laminated composite cylinders and cones under various loading and boundary conditions using semi-analytical models, Composite Structures 118: 303-315.
[13] Dung D.V., Nam V.H., 2014, Nonlinear dynamic analysis of eccentrically stiffened functionally graded circular cylindrical thin shells under external pressure and surrounded by an elastic medium, European Journal of Mechanics - A/Solids 46: 42-53.
[14] Dung D.V., Hoa L.K., 2015, Research on nonlinear torsional buckling and post-buckling of eccentrically stiffened FGMcylindrical shell in thermal environment, Composites Part B 69: 378-388.
[15] Asadi H., Kiani Y., Aghdam M.M., Shakeri M., 2016, Enhanced thermal buckling of laminated composite cylindrical shells with shape memory alloy, Applied Composite Materials 50: 243-256.
[16] Tung H.V., 2014, Nonlinear thermomechanical stability of shear deformable FGM shallow spherical shells resting on elastic foundations with temperature dependent properties, Composite Structures 114: 107-116.
[17] Tornabene F., Viola E., 2013, Static analysis of functionally graded doubly-curved shells and panels of revolution, Meccanica 48: 901-930.
[18] Bich D.H., Dung D.V., Nam V.H., 2013, Nonlinear dynamic analysis of eccentrically stiffened imperfect functionally graded doubly curved thin shallow shells, Composite Structures 96: 384-395.
[19] Tornabene F., Fantuzzi N., Viola E., Reddy J.N., 2014, Winkler-Pasternak foundation effect on the static and dynamic analyses of laminated doubly-curved and degenerate shells and panels, Composites Part B 57: 269-296.
[20] Tornabene F., Fantuzzi N., Viola E., Batra R.C., 2015, Stress and strain recovery for functionally graded free-form and doublycurved sandwich shells using higher-order equivalent single layer theory, Composite Structures 119: 67-89.
[21] Tornabene F., Fantuzzi N., Bacciocchi M., Viola E., Reddy J.N., 2017, A numerical investigation on the natural frequencies of FGM sandwich shells with variable thickness by the local generalized differential quadrature method, Applied Sciences 7(131): 1-39.
[22] Tornabene F., Viola E., 2009, Free vibrations of four-parameter functionally graded parabolic panels and shells of revolution, European Journal of Mechanics - A/Solids 28: 991-1013.
[23] Tornabene F.,Viola E., 2009, Free vibration analysis of functionally graded panels and shells of revolution, Meccanica 44: 255-281.
[24] Mecitoglu Z., 1996, Vibration characteristics of a stiffened conical shell, Journal of Sound and Vibration 197(2): 191-206.
[25] Rao S.S., Reddy E.S., 1981, Optimum design of stiffened conical shells with natural frequency constraints, Composite Structures 14(1-2): 103-110.
[26] Sofiyev A.H., 2007, Thermoelastic stability of functionally graded truncated conical shells, Composite Structures 77: 56-65.
[27] Sofiyev A.H., 2010, The buckling of FGM truncated conical shells subjected to combined axial tension and hydrostatic pressure, Composite Structures 92: 488-498.
[28] Sofiyev A.H., 2015, Buckling analysis of freely-supported functionally graded truncated conical shells under external pressures, Composite Structures 132: 746-758.
[29] Sofiyev A.H., 2010, The buckling of FGM truncated conical shells subjected to axial compressive load and resting on Winkler- Pasternak foundations, International Journal of Pressure Vessels and Piping 87: 753-761.
[30] Naj R., Boroujerdy M.S., Eslami M.R., 2008, Thermal and mechanical instability of functionally graded truncated conical shells, Thin-Walled Structures 46: 65-78.
[31] Bich D.H., Phuong N.T., Tung H.V., 2012, Buckling of functionally graded conical panels under mechanical loads, Composite Structures 94: 1379-1384.
[32] Torabi J., Kiani Y., Eslami M.R., 2013, Linear thermal buckling analysis of truncated hybrid FGM conical shells, Composites Part B 50: 265-272.
[33] Sofiyev A.H., Kuruoglu N., 2013, Nonlinear buckling of an FGM truncated conical shells surrounded by an elastic medium, International Journal of Pressure Vessels and Piping 107: 38-49.
[34] Dung D.V., Hoa L.K., Nga N.T., Anh L.T.N., 2013, Instability of eccentrically stiffened functionally graded truncated conical shells under mechanical loads, Composite Structures 106: 104-113.
[35] Bahadori R., Najafizadeh M.M., 2015, Free vibration analysis of two-dimensional functionally graded axisymmetric cylindrical shell on Winkler–Pasternak elastic foundation by first-order shear deformation theory and using navier-differential quadrature solution methods, Applied Mathematical Modelling 39(16): 4877-4894.