Skip to main content
SpringerLink
Log in

Nonlinear thermo-mechanical stability of eccentrically stiffened functionally graded material sandwich doubly curved shallow shells with general sigmoid law and power law according to third-order shear deformation theory

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In this paper, the nonlinear analysis of stability of functionally graded material (FGM) sandwich doubly curved shallow shells is studied under thermo-mechanical loads with material properties obeying the general sigmoid law and power law of four material models. Shells are reinforced by the FGM stiffeners and rest on elastic foundations. Theoretical formulations are derived by the third-order shear deformation theory (TSDT) with the von Kármán-type nonlinearity taking into account the initial geometrical imperfection and smeared stiffener technique. The explicit expressions for determining the critical buckling load, the post-buckling mechanical, and the thermal load-deflection curves are obtained by the Galerkin method. Two iterative algorithms are presented. The effects of the stiffeners, the thermal element, the distribution law of material, the initial imperfection, the foundation, and the geometrical parameters on buckling and post-buckling of shells are investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hutchison, J. W. and He, M. Y. Buckling of cylindrical sandwich shells with metal foam cores. International Journal of Solids and Structures, 37, 6777–6794 (2000)

    Article  MATH  Google Scholar 

  2. Ferreira, A. J. M., Barbosa, J. T., Marques, A. T., and de Sá, J. C. Nonlinear analysis of sandwich shells: the effect of core plasticity. Computers and Structures, 76, 337–346 (2000)

    Article  Google Scholar 

  3. Wang, C. M. Vibration frequencies of simply supported polygonal sandwich plates via Kirchhoff solutions. Journal of Sound and Vibration, 190, 255–260 (1996)

    Article  Google Scholar 

  4. Wang, C. M., Ang, K. K., and Yan, L. Free vibration of skew sandwich plates with laminated facings. Journal of Sound and Vibration, 235, 317–340 (2000)

    Article  Google Scholar 

  5. Pilipchuk, V. N., Berdichevsky, V. L., and Ibrahim, R. A. Thermo-mechanical coupling in cylindrical bending of sandwich plates. Composite Structures, 92, 2632–2640 (2010)

    Article  Google Scholar 

  6. Zenkour, A. M. A comprehensive analysis of functionally graded sandwich plates: part 1, deflection and stresses. International Journal of Solids and Structures, 42, 5224–5242 (2005)

    Article  MATH  Google Scholar 

  7. Zenkour, A. M. A comprehensive analysis of functionally graded sandwich plates: part 2, buckling and free vibration. International Journal of Solids and Structures, 42, 5243–5258 (2005)

    Article  MATH  Google Scholar 

  8. Zenkour, A. M. and Sobhy, M. Thermal buckling of various types of FGM sandwich plates. Composite Structures, 93, 93–102 (2010)

    Article  Google Scholar 

  9. Shen, H. S. and Li, S. R. Postbuckling of sandwich plates with FGM face sheets and temperaturedependent properties. Composites: Part B, 39, 332–344 (2008)

    Article  Google Scholar 

  10. Xia, X. K. and Shen, H. S. Vibration of post-buckled sandwich plates with FGM face sheets in a thermal environment. Journal of Sound and Vibration, 314, 254–274 (2008)

    Article  Google Scholar 

  11. Wang, Z. X. and Shen, H. S. Nonlinear analysis of sandwich plates with FGM face sheets resting on elastic foundations. Composite Structures, 93, 2521–2532 (2011)

    Article  Google Scholar 

  12. Wang, Z. X. and Shen, H. S. Nonlinear dynamic response of sandwich plates with FGM face sheets resting on elastic foundations in thermal environments. Ocean Engineering, 57, 99–110 (2013)

    Article  Google Scholar 

  13. Shariyat, M. Nonlinear dynamic thermo-mechanical buckling analysis of the imperfect sandwich plates based on a generalized three-dimensional high-order global-local plate theory. Composite Structures, 92, 72–85 (2010)

    Article  Google Scholar 

  14. Alipour, M. M. and Shariyat, M. Analytical stress analysis of annular FGM sandwich plates with non-uniform shear and normal tractions, employing a zigzag-elasticity plate theory. Aerospace Science and Technology, 32, 235–259 (2014)

    Article  Google Scholar 

  15. Dozio, L. Natural frequencies of sandwich plates with FGM core via variable-kinematic 2-D Ritz models. Composite Structures, 96, 561–568 (2013)

    Article  Google Scholar 

  16. Tung, H. V. Thermal and thermo-mechanical post-buckling of FGM sandwich plates resting on elastic foundations with tangential edge constraints and temperature dependent properties. Composite Structures, 131, 1028–1039 (2015)

    Article  Google Scholar 

  17. Sofiyev, A. H. and Kuruoglu, N. Torsional vibration and buckling of the cylindrical shell with functionally graded coatings surrounded by an elastic medium. Composites: Part B, 45, 1133–1142 (2013)

    Article  Google Scholar 

  18. Sofiyev, A. H. The vibration and buckling of sandwich cylindrical shells covered by different coatings subjected to the hydrostatic pressure. Composite Structures, 117, 124–134 (2014)

    Article  Google Scholar 

  19. Sofiyev, A. H. and 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)

    Article  Google Scholar 

  20. Sofiyev, A. H. and Kuruoglu, N. Effect of a functionally graded interlayer on the non-linear stability of conical shells in elastic medium. Composite Structures, 99, 296–308 (2013)

    Article  Google Scholar 

  21. Seidi, J., Khalili, S. M. R., and Malekzadeh, K. Temperature-dependent buckling analysis of sandwich truncated conical shells with FG facesheets. Composite Structures, 131, 682–691 (2015)

    Article  Google Scholar 

  22. Dey, T. and Ramachandra, L. S. Buckling and postbuckling response of sandwich panels under non-uniform mechanical edge loadings. Composites: Part B, 60, 537–545 (2014)

    Article  Google Scholar 

  23. Barush, M. and Singer, J. Effect of eccentricity of stiffeners on the general instability of stiffened cylindrical shells under hydrostatic pressure. Journal of Mechanical Engineering Science, 5, 23–27 (1963)

    Article  Google Scholar 

  24. Khalil, M. R., Olson, M. D., and Anderson, D. L. Nonlinear dynamic analysis of stiffened plates. Composite Structures, 29, 929–941 (1988)

    Article  MATH  Google Scholar 

  25. Shen, P. C. and Dade, C. Dynamic analysis of stiffened plates and shells using spline Gauss collocation method. Composite Structures, 36, 623–629 (1990)

    Article  MATH  Google Scholar 

  26. Patel, S. N., Datta, P. K., and Sheikh A. H. Buckling and dynamic instability analysis of stiffened shell panels. Thin-Wall Structure, 44, 321–333 (2006)

    Article  Google Scholar 

  27. Najafizadeh, M. M. and Heydari, H. R. An exact solution for buckling of functionally graded circular plates based on higher order shear deformation plate theory under uniform radial compression. International Journal of Mechanical Sciences, 50, 603–612 (2008)

    Article  MATH  Google Scholar 

  28. Bich, D. H., Dung, D. V., and Nam, V. H. Nonlinear dynamical analysis of eccentrically stiffened functionally graded cylindrical panels. Composite Structures, 94, 2465–2473 (2012)

    Article  Google Scholar 

  29. Dung, D. V. and Hoa, L. K. 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 (2015)

    Article  MathSciNet  Google Scholar 

  30. Brush, D. D. and Almroth, B. O. Buckling of Bars, Plates and Shells, McGraw-Hill, New York (1975)

    MATH  Google Scholar 

  31. Reddy, J. N. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton (2004)

    MATH  Google Scholar 

  32. Reddy, J. N. A refined nonlinear theory of plates with transverse shear deformation. International Journal of Solids and Structures, 20, 881–896 (1984)

    Article  MATH  Google Scholar 

  33. Reddy, J. N. and Chin, C. D. Thermo-elastical analysis of functionally graded cylinders and plates. Journal of Thermal Stress, 21, 593–626 (1988)

    Article  Google Scholar 

  34. Shariat, B. A. S. and Eslami, M. R. Buckling of thick functionally graded plates under mechanical and thermal loads. Composite Structures, 78, 433–439 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics, Mechanics and Informatics, Vietnam National University, Hanoi, 100000, Vietnam

    D. V. Dung

  2. Faculty of Civil Engineering, University of Transport Technology, Hanoi, 100000, Vietnam

    D. T. Dong

Authors
  1. D. V. Dung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. T. Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. T. Dong.

Additional information

Project supported by the Vietnam National Foundation for Science and Technology Development (No.107.02-2015.11)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dung, D.V., Dong, D.T. Nonlinear thermo-mechanical stability of eccentrically stiffened functionally graded material sandwich doubly curved shallow shells with general sigmoid law and power law according to third-order shear deformation theory. Appl. Math. Mech.-Engl. Ed. 38, 191–216 (2017). https://doi.org/10.1007/s10483-017-2166-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-017-2166-9

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation