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**Nonlinear stability of functionally graded material (FGM) sandwich cylindrical shells reinforced by FGM stiffeners in thermal environment.**
*(English)*
Zbl 1365.74112

Summary: In this paper, Donnell’s shell theory and smeared stiffeners technique are improved to analyze the postbuckling and buckling behaviors of circular cylindrical shells of stiffened thin functionally graded material (FGM) sandwich under an axial loading on elastic foundations, and the shells are considered in a thermal environment. The shells are stiffened by FGM rings and stringers. A general sigmoid law and a general power law are proposed. Thermal elements of the shells and reinforcement stiffeners are considered. Explicit expressions to find critical loads and postbuckling load-deflection curves are obtained by applying the Galerkin method and choosing the three-term approximate solution of deflection. Numerical results show various effects of temperature, elastic foundation, stiffeners, material and geometrical properties, and the ratio between face sheet thickness and total thickness on the nonlinear behavior of shells.

### MSC:

74K25 | Shells |

74D05 | Linear constitutive equations for materials with memory |

74G60 | Bifurcation and buckling |

74E30 | Composite and mixture properties |

74F05 | Thermal effects in solid mechanics |

### Keywords:

functionally graded material (FGM); stiffened cylindrical shell; sandwich; thermal environment
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\textit{D. V. Dung} et al., AMM, Appl. Math. Mech., Engl. Ed. 38, No. 5, 647--670 (2017; Zbl 1365.74112)

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### References:

[1] | Shen, H. S., Postbuckling analysis of pressure-loaded functionally graded cylindrical shells in thermal environments, Engineering Structures, 25, 487-497, (2003) |

[2] | Li, Z. M.; Shen, H. S., Post-buckling of 3D braided composite cylindrical shells under combined external pressure and axial compression in thermal environments, International Journal of Mechanical Sciences, 50, 719-731, (2008) · Zbl 1264.74064 |

[3] | Huang, H.; Han, Q., Buckling of imperfect functionally graded cylindrical shells under axial compression, European Journal of Mechanics-A/Solids, 27, 1026-1036, (2008) · Zbl 1151.74356 |

[4] | Huang, H.; Han, Q., Nonlinear elastic buckling and postbuckling of axially compressed functionally graded cylindrical shells, International Journal of Mechanical Sciences, 51, 500-507, (2009) |

[5] | Huang, H.; Han, Q., Nonlinear buckling and postbuckling of heated functionally graded cylindrical shells under combined axial compression and radial pressure, International Journal of NonLinear Mechanics, 44, 209-218, (2009) · Zbl 1203.74044 |

[6] | Wu, L.; Jiang, Z.; Liu, J., Thermoelastic stability of functionally graded cylindrical shells, Composite Structures, 70, 60-68, (2005) |

[7] | Shariyat, M.; Asgari, D., Non-linear thermal buckling and postbuckling analyses of imperfect variable thickness temperature-dependent bidirectional functionally graded cylindrical shells, International Journal of Pressure Vessels and Piping, 111, 310-320, (2013) |

[8] | Bahtui, A.; Eslami, M. R., Couple thermoelasticity of functionally graded cylindrical shells, Mechanics Research Communications, 34, 1-8, (2007) · Zbl 1192.74086 |

[9] | Bagherizadeh, E.; Kiani, Y.; Eslami, M. R., Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation, Composite Structures, 93, 3063-3071, (2011) |

[10] | Singer, J.; Baruch, M.; Harari, O., On the stability of eccentrically stiffened cylindrical shells under axial compression, International Journal of Solids and Structures, 3, 445-470, (1967) |

[11] | Shen, H. S.; Zhou, P.; Chen, T. Y., Post-buckling analysis of stiffened cylindrical shells under combined external pressure and axial compression, Thin-Walled Structures, 15, 43-63, (1993) |

[12] | Reddy, J. N.; Starnes, J. H., General buckling of stiffened circular cylindrical shells according to a layerwise theory, Computers and Structures, 49, 605-616, (1993) · Zbl 0797.73019 |

[13] | Ji, Z. Y.; Yeh, K. Y., General solution for nonlinear buckling of nonhomogeneous axial symmetric ring-and stringer-stiffened cylindrical shells, Computers and Structures, 34, 585-591, (1990) · Zbl 0712.73040 |

[14] | Zeng, T.; Wu, L., Postbuckling analysis of stiffened braided cylindrical shells under combined external pressure and axial compression, Composite Structures, 60, 455-466, (2003) |

[15] | Jiang, L.; Wang, Y.; Wang, X., Postbuckling analysis of stiffened circular cylindrical panels using differential quadrature element method, Thin -Walled Structures, 46, 390-398, (2008) |

[16] | Sadeghifar, M.; Bagheri, M.; Jafari, A. A., Buckling analysis of stringer-stiffened laminated cylindrical shells with non-uniform eccentricity, Archive of Applied Mechanics, 81, 875-886, (2011) · Zbl 1271.74100 |

[17] | Bich, D. H.; Dung, D. V.; Nam, V. H.; Phuong, N. T., Nonlinear static and dynamic buckling analysis of imperfect eccentrically stiffened functionally graded circular cylindrical thin shells under axial compression, International Journal of Mechanical Science, 74, 190-200, (2013) |

[18] | Dung, D. V.; Nam, V. H., 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, (2014) · Zbl 1406.74471 |

[19] | Najafizadeh, M. M.; Hasani, A.; Khazaeinejad, P., Mechanical stability of functionally graded stiffened cylindrical shells, Applied Mathematical Modelling, 33, 1151-1157, (2009) · Zbl 1168.74392 |

[20] | Dung, D. V.; Hoa, L. K., Nonlinear buckling and post-buckling analysis of eccentrically stiffened functionally graded circular cylindrical shells under external pressure, Thin-Walled Structures, 63, 117-124, (2013) |

[21] | Dung, D. V.; Hoa, L. K.; Nga, N. T., On the stability of functionally graded truncated conical shells reinforced by functionally graded stiffeners and surrounded by an elastic medium, Composite Structures, 108, 77-90, (2014) |

[22] | Shen, H. S., Thermal postbuckling analysis of imperfect stiffened laminated cylindrical shells, International Journal of Non-Linear Mechanics, 32, 259-275, (1997) · Zbl 0890.73027 |

[23] | Shen, H. S., Post-buckling analysis of imperfect stiffened laminated cylindrical shells under combined external pressure and thermal loading, International Journal of Mechanical Science, 40, 339-355, (1998) · Zbl 0904.73019 |

[24] | Wang, X.; Oguamanam, D. C. D.; Hansen, J. S., Layout optimization of stiffeners in stiffened composite plates with thermal residual stresses, Finite Elements in Analysis and Design, 40, 1233-1257, (2004) |

[25] | Golmakani, M. E.; Kadkhodayan, M., Large deflection thermoelastic analysis of functionally graded stiffened annular sector plates, International Journal of Mechanical Sciences, 69, 94-106, (2013) |

[26] | Dung, D. V.; Hoa, L. K., Nonlinear torsional buckling and postbuckling of eccentrically stiffened FGM cylindrical shells in thermal environment, Composites: Part B, 69, 378-388, (2015) |

[27] | Zenkour, A. M.; Alghamdi, N. A., Thermoelastic bending analysis of functionally graded sandwich plates, Journal of Materials Science, 43, 2574-2589, (2008) |

[28] | Zenkour, A. M.; Alghamdi, N. A., Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads, Mechanic of Advanced Materials and Structures, 17, 419-432, (2010) |

[29] | Zenkour, A. M.; Sobhy, M., Thermal buckling of various types of FGM sandwich plates, Composite Structures, 93, 93-102, (2010) |

[30] | Wang, Z. X.; Shen, H. S., Nonlinear analysis of sandwich plates with FGM face sheets resting on elastic foundations, Composite Structures, 93, 2521-2532, (2011) |

[31] | Thai, H. T.; Nguyen, T. K.; Vo, T. P.; Lee, J., Analysis of functionally graded sandwich plates using a new first-order shear deformation theory, European Journal of Mechanics-A/Solids, 45, 211-225, (2014) · Zbl 1406.74455 |

[32] | Sofiyev, A. H.; Kuruoglu, N., Parametric instability of shear deformable sandwich cylindrical shells containing an FGM core under static and time dependent periodic axial loads, International Journal of Mechanical Sciences, 101/102, 114-123, (2015) |

[33] | Sofiyev, A. H., Influences of shear stresses on the dynamic instability of exponentially graded sandwich cylindrical shells, Composites: Part B, 77, 349-362, (2015) |

[34] | Seidi, J.; Khalili, S. M. R.; Malekzadeh, K., Temperature-dependent buckling analysis of sandwich truncated conical shells with FG facesheets, Composite Structures, 131, 682-691, (2015) |

[35] | Dung, D. V.; Hoa, L. K.; Thuyet, B. T.; Nga, N. T., Buckling analysis of functionally graded material (FGM) sandwich truncated conical shells reinforced by FGM stiffeners filled inside by elastic foundations, Applied Mathematics and Mechanics (English Edition), 37, 879-902, (2016) · Zbl 1345.74075 |

[36] | Volmir, A. S. Stability of Elastic Systems (in Russian), Science Edition, Moscow (1963) |

[37] | Chi, S. H.; Chung, Y. L., Mechanical behavior of functionally graded material plates under transverse load, part 1, analysis, International Journal of Solids and Structures, 43, 3657-3674, (2006) · Zbl 1121.74396 |

[38] | Brush, D. O. and Almroth, B. O. Buckling of Bars, Plates and Shells, McGraw-Hill, New York (1975) · Zbl 0352.73040 |

[39] | Reddy, J. N. Mechanics of Laminated Composite Plates and Shells, Theory and Analysis, CRC Press, Boca Raton (2004) · Zbl 1075.74001 |

[40] | Huang, H.; Han, Q., Nonlinear dynamic buckling of functionally graded cylindrical shells subjected to time-dependent axial load, Composite Structures, 92, 593-598, (2010) |

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