Thermal buckling and post-buckling analysis of geometrically imperfect FGM clamped tubes on nonlinear elastic foundation. (English) Zbl 1481.74206
Summary: Present research deals with the thermal buckling and post-buckling analysis of the geometrically imperfect functionally graded tubes on nonlinear elastic foundation. Imperfect FGM tube with immovable clamped-clamped end conditions is subjected to thermal environments. Tube under different types of thermal loads, such as heat conduction, linear temperature change, and uniform temperature rise is analyzed. Material properties of the FGM tube are assumed to be temperature dependent and are distributed through the radial direction. Displacement field satisfies the tangential traction free boundary conditions on the inner and outer surfaces of the FGM tube. The nonlinear governing equations of the FGM tube are obtained by means of the virtual displacement principle. The equilibrium equations are based on the nonlinear von Kármán assumption and higher order shear deformation circular tube theory. These coupled differential equations are solved using the two-step perturbation method. Approximate solutions are provided to estimate the thermal post-buckling response of the perfect/imperfect FGM tube as explicit functions of the various thermal loads. Numerical results are provided to explore the effects of different geometrical parameters of the FGM tube subjected to different types of thermal loads. The effects of power law index, springs stiffness of elastic foundation, and geometrical imperfection parameter of tube are also included.
Keywords:
thermal buckling; post-buckling; imperfect FGM tube; nonlinear elastic medium; two-step perturbation method; thermal environmentReferences:
| [1] | Timoshenko, S. P.; Gere, J. M., Theory of Elastic Stability (1961), McGraw-Hill: McGraw-Hill New York |
| [2] | Brush, D. O.; Almorth, B. O., Buckling of Bars, Plates and Shells (1975), Mc. Graw-Hill: Mc. Graw-Hill New York · Zbl 0352.73040 |
| [3] | Shen, H. S., A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells (2013), John Wiley & Sons Inc: John Wiley & Sons Inc Singapore · Zbl 1292.74001 |
| [4] | Eslami, M. R., Buckling and Postbuckling of Beams, Plates, and Shells (2018), Springer: Springer Switzerland · Zbl 1405.74002 |
| [5] | Emam, S. A., A static and dynamic analysis of the postbuckling of geometrically imperfect composite beams, Compo. Struct., 90, 247-253 (2009) |
| [6] | Kiani, Y.; Eslami, M. R., Thermal buckling analysis of functionally graded material beams, Int. J. Mech. Mater. Des., 6, 229-238 (2010) |
| [7] | Kiani, Y.; Taheri, S.; Eslami, M. R., Thermal buckling of piezoelectric functionally graded material beams, J. Therm. Stress., 34, 835-850 (2011) |
| [8] | Kiani, Y.; Rezaei, M.; Taheri, S.; Eslami, M. R., Thermo-electrical buckling of piezoelectric functionally graded material Timoshenko beams, Int. J. Mech. Mater. Des., 7, 185-197 (2011) |
| [9] | Shen, H. S., A novel technique for nonlinear analysis of beams on two-parameter elastic foundations, Int. J. Struct. Stab. Dyn., 11, 999-1014 (2011) · Zbl 1245.74036 |
| [10] | Ma, L. S.; Lee, D. W., A further discussion of nonlinear mechanical behavior for FGM beams under in-plane thermal loading, Compos. Struct., 93, 831-842 (2011) |
| [11] | Ma, L. S.; Lee, D. W., Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading, Eur. J. Mech. A/Solids, 31, 13-20 (2012) · Zbl 1278.74092 |
| [12] | Fallah, A.; Aghdam, M. M., Thermo-mechanical buckling and nonlinear free vibration analysis of functionally graded beams on nonlinear elastic foundation, Compos.: B, 43, 1523-1530 (2012) |
| [13] | Yaghoobi, H.; Torabi, M., Post-buckling and nonlinear free vibration analysis of geometrically imperfect functionally graded beams resting on nonlinear elastic foundation, Appl. Math. Model., 37, 8324-8340 (2013) · Zbl 1438.74083 |
| [14] | Esfahani, S. E.; Kiani, Y.; Eslami, M. R., Non-linear thermal stability analysis of temperature dependent FGM beams supported on non-linear hardening elastic foundations, Int. J. Mech. Sci., 69, 10-20 (2013) |
| [15] | Zhang, D. G., Thermal post-buckling and nonlinear vibration analysis of FGM beams based on physical neutral surface and high order shear deformation theory, Meccanica, 49, 283-293 (2014) · Zbl 1364.74040 |
| [16] | She, G. L.; Shu, X.; Ren, Y. R., Thermal buckling and post-buckling analysis of piezoelectric FGM beams based on high-order shear deformation theory, J. Therm.Stress., 40, 783-797 (2017) |
| [17] | She, G. L.; Yuan, F. G.; Ren, Y. R., Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory, Appl. Math. Model, 47, 340-357 (2017) · Zbl 1446.74055 |
| [18] | Huang, Y.; Li, X. F., Buckling of functionally graded circular columns including shear deformation, Mater. Des., 31, 3159-3166 (2010) |
| [19] | Huang, Y.; Li, X. F., Bending and vibration of circular cylindrical beams with arbitrary radial nonhomogeneity, Int. J. Mech. Sci., 52, 595-601 (2010) |
| [20] | Babaei, H.; Kiani, Y.; Eslami, M. R., Geometrically nonlinear analysis of shear deformable FGM shallow pinned arches on nonlinear elastic foundation under mechanical and thermal loads, Acta Mech, 229, 3123-3141 (2018) · Zbl 1459.74102 |
| [21] | Babaei, H.; Kiani, Y.; Eslami, M. R., Thermomechanical nonlinear in-plane analysis of fix-ended FGM shallow arches on nonlinear elastic foundation using two-step perturbation technique, Int. J. Mech. Des. (2018) · Zbl 1459.74102 |
| [22] | Babaei, H.; Kiani, Y.; Eslami, M. R., Application of two-steps perturbation technique to geometrically nonlinear analysis of long FGM cylindrical panels on elastic foundation under thermal load, J. Therm. Stress., 41, 847-865 (2018) |
| [23] | Babaei, H.; Kiani, Y.; Eslami, M. R., Geometrically nonlinear analysis of functionally graded shallow curved tubes in thermal environment, Thin Walled Struct., 132, 48-57 (2018) |
| [24] | Babaei, H.; Kiani, Y.; Eslami, M. R., Thermally induced large deflection analysis of shear deformable FGM shallow curved tubes using perturbation method, ZAMM - J. Appl. Math. Mech. (2018) · Zbl 1459.74102 |
| [25] | Shen, H. S., Thermal postbuckling behavior of functionally graded cylindrical shells with temperature-dependent properties, Int. J. Solids Struct., 41, 1961-1974 (2004) · Zbl 1106.74352 |
| [26] | Bagherizadeh, E.; Kiani, Y.; Eslami, M. R., Mechanical buckling of functionally graded material cylindrical shells surrounded by pasternak elastic foundation, Compos. Struct., 93, 3063-3071 (2011) |
| [27] | Bagherizadeh, E.; Kiani, Y.; Eslami, M. R., Thermal buckling of functionally graded material cylindrical shells on elastic foundation, AIAA J, 50, 500-503 (2012) |
| [28] | Boroujerdy, M. S.; Naj, R.; Kiani, Y., Buckling of heated temperature dependent FGM cylindrical shell surrounded by elastic medium, J. Theor. Appl. Mech., 52, 869-881 (2014) |
| [29] | Fu, Y.; Zhong, J.; Shao, X.; Chen, Y., Thermal postbuckling analysis of functionally graded tubes based on a refined beam model, Int. J. Mech. Sci., 96, 58-64 (2015) |
| [30] | Shen, H. S., Functionally Graded Materials Nonlinear Analysis of Plates and Shells (2009), CRC Press: CRC Press Boca Raton |
| [31] | Zhang, P.; Fu, Y., A higher-order beam model for tubes, Eur. J. Mech. A/Solids., 38, 12-19 (2013) · Zbl 1347.74054 |
| [32] | Ghiasian, S. E.; Kiani, Y.; Eslami, M. R., Dynamic buckling of suddenly heated or compressed FGM beams resting on nonlinear elastic foundation, Compos. Struct, 106, 225-234 (2013) |
| [33] | Dehrouyeh-Semnani, A. M., On the thermally induced nonlinear response of functionally graded beams, Int. J. Eng. Sci., 125, 53-74 (2018) · Zbl 1423.74235 |
| [34] | Zhong, J.; Fu, Y.; Wan, D.; Li, Y., Nonlinear bending and vibration of functionally graded tubes resting on elastic foundations in thermal environment based on a refined beam model, Appl. Math. Model., 40, 1-14 (2016) |
| [35] | Shen, H. S., Thermal postbuckling of shear deformable FGM cylindrical shells surrounded by an elastic medium, J. Eng. Mech., 94, 372-383 (2009) |
| [36] | Reddy, J. N., Mechanics of Laminated Composite Plates and Shells, Theory and Application (2003), CRC Press: CRC Press Boca Raton |
| [37] | Shen, H. S.; Wang, Z. X., Nonlinear analysis of shear deformable FGM beams resting on elastic foundations in thermal environments, Int. J. Mech. Sci., 81, 195-206 (2014) |
| [38] | Shen, H. S., Thermal postbuckling analysis of imperfect reissner-mindlin plates on softening nonlinear elastic foundations, J. Eng. Math., 33, 259-270 (1998) · Zbl 0938.74030 |
| [39] | Hetnarski, R. B.; Eslami, M. R., Thermal Stresses, Advanced Theory and Applications (2009), Springer Verlag: Springer Verlag Amesterdam · Zbl 1165.74004 |
| [40] | She, G. L.; Yuan, F. G.; Ren, Y. R., Nonlinear analysis of bending, thermal buckling and post-buckling for functionally graded tubes by using a refined beam theory, Compos. Struct., 165, 74-82 (2017) |
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