Skip to main content
SpringerLink
Log in

Probabilistic thermal stability of laminated composite plates with temperature-dependent properties under a stochastic thermal field

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Probabilistic thermal buckling analysis of composite plates with temperature-dependent properties under stochastic thermal fields is performed by developing a new temperature increment-based algorithm for solving the stochastic nonlinear equation. The temperature distribution is assumed to be a stochastic Gaussian field which leads to spatially varying stochastic mechanical properties. The stochastic thermal field is decomposed by applying the Karhunen–Loeve theorem. The combination of stochastic assumed mode method and polynomial chaos is proposed as an alternative solution for the time-consuming stochastic finite element method. The uncertainty of the critical temperature is studied by considering uncertainty propagation in the temperature distribution. The results portend a reduction in the average of predicted critical buckling temperature and a significant statistical dispersion in the predicted critical temperatures. Besides, the stochastic buckling mode shapes are obtained. Based on the result, uncertainty in temperature distribution leads to a stochastic irregularity in buckling mode shape.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Chiba, R.: Stochastic analysis of heat conduction and thermal stresses in solids: a review. Heat Transfer Phenom. Appl. (2012). https://doi.org/10.5772/50994

    Article  Google Scholar 

  2. Król, P.A.: Random parameters and sources of uncertainty in practical fire safety assessment of steel building structures. PeriodicaPolytechnica Civil Eng. 61(3), 398–411 (2017). https://doi.org/10.3311/PPci.9833

    Article  Google Scholar 

  3. Paudel, D., Hostikka, S.: Propagation of model uncertainty in the stochastic simulations of a compartment fire. Fire Technol. (2019). https://doi.org/10.1007/s10694-019-00841-9

    Article  Google Scholar 

  4. Sasikumar, P., Suresh, R., Gupta, S.: Stochastic finite element analysis of layered composite beams with spatially varying non-Gaussian inhomogeneities. Acta Mech. 225(6), 1503–1522 (2014). https://doi.org/10.1007/s00707-013-1009-9

    Article  MATH  Google Scholar 

  5. Shi, B., Deng, Z.: An efficient reliability method for composite laminates with high-dimensional uncertainty variables. Acta Mech. 232(9), 3509–3527 (2021). https://doi.org/10.1007/s00707-021-03008-2

    Article  MathSciNet  MATH  Google Scholar 

  6. Dey, S., Mukhopadhyay, T., Khodaparast, H.H., Adhikari, S.: Stochastic natural frequency of composite conical shells. Acta Mech. 226(8), 2537–2553 (2015). https://doi.org/10.1007/s00707-013-1009-9

    Article  MathSciNet  MATH  Google Scholar 

  7. Mukhopadhyay, T.: A multivariate adaptive regression splines based damage identification methodology for web core composite bridges including the effect of noise. J. Sandwich Struct. Mater. 20(7), 885–903 (2018). https://doi.org/10.1177/1099636216682533

    Article  Google Scholar 

  8. Dash, P., Singh, B.N.: Static response of geometrically nonlinear laminated composite plates having uncertain material properties. Mech. Adv. Mater. Struct. 22(4), 269–280 (2015). https://doi.org/10.1080/15376494.2012.736056

    Article  Google Scholar 

  9. Kaveh, A., Dadras, A.: An efficient method for reliability estimation using the combination of asymptotic sampling and weighted simulation. ScientiaIranica (2019). https://doi.org/10.24200/sci.2019.21367

    Article  Google Scholar 

  10. Zhang, S., Zhang, L., Wang, Y., Tao, J., Chen, X.: Effect of ply level thickness uncertainty on reliability of laminated composite panels. J. Reinf. Plast. Compos. 35(19), 1387–1400 (2016). https://doi.org/10.1177/0731684416651499

    Article  Google Scholar 

  11. Zhao, W., Liu, W., Yang, Q.: Reliability analysis of ultimate compressive strength for stiffened composite panels. J. Reinf. Plast. Compos. 35(11), 902–914 (2016). https://doi.org/10.1177/0731684416631838

    Article  Google Scholar 

  12. Singh, B.N., Verma, V.K.: Hygrothermal effects on the buckling of laminated composite plates with random geometric and material properties. J. Reinf. Plast. Compos. 28(4), 409–427 (2009). https://doi.org/10.1177/0731684407084991

    Article  Google Scholar 

  13. Lin, S.C.: Buckling failure analysis of random composite laminates subjected to random loads. Int. J. Solids Struct. 37(51), 7563–7576 (2000). https://doi.org/10.1016/S0020-7683(99)00305-4

    Article  MATH  Google Scholar 

  14. Lal, A., Singh, B.N., Kumar, R.: Effects of random system properties on the thermal buckling analysis of laminated composite plates. Comput. Struct. 87(17–18), 1119–1128 (2009). https://doi.org/10.1016/j.compstruc.2009.06.004

    Article  Google Scholar 

  15. Verma, V.K., Singh, B.N.: Thermal buckling of laminated composite plates with random geometric and material properties. Int. J. Struct. Stab. Dyn. 9(02), 187–211 (2009). https://doi.org/10.1142/S0219455409002990

    Article  MATH  Google Scholar 

  16. Singh, B.N., Iyengar, N.G.R., Yadav, D.: Effects of random material properties on buckling of composite plates. J. Eng. Mech. 127(9), 873–879 (2001). https://doi.org/10.1061/(ASCE)0733-9399(2001)127:9(873)

    Article  Google Scholar 

  17. Singh, B.N., Iyengar, N.G.R., Yadav, D.: AC 0 finite element investigation for buckling of shear deformable laminated composite plates with random material properties. Struct. Eng. Mech. 13(1), 53–74 (2002). https://doi.org/10.12989/sem.2002.13.1.053

    Article  Google Scholar 

  18. Nguyen, H.X., Hien, T.D., Lee, J., Nguyen-Xuan, H.: Stochastic buckling behaviour of laminated composite structures with uncertain material properties. Aerosp. Sci. Technol. 66, 274–283 (2017). https://doi.org/10.1016/j.ast.2017.01.028

    Article  Google Scholar 

  19. Kumar, R.R., Mukhopadhyay, T., Pandey, K.M., Dey, S.: Stochastic buckling analysis of sandwich plates: the importance of higher order modes. Int. J. Mech. Sci. 152, 630–643 (2019). https://doi.org/10.1016/j.ijmecsci.2018.12.016

    Article  Google Scholar 

  20. Salim, S., Iyengar, N.G.R., Yadav, D.: Buckling of laminated plates with random material characteristics. Appl. Compos. Mater. 5(1), 1–9 (1998). https://doi.org/10.1023/A:1008878912150

    Article  Google Scholar 

  21. Papadopoulos, V., Charmpis, D.C., Papadrakakis, M.: A computationally efficient method for the buckling analysis of shells with stochastic imperfections. Comput. Mech. 43(5), 687 (2009). https://doi.org/10.1007/s00466-008-0338-3

    Article  Google Scholar 

  22. Singh, B.N., Lal, A., Kumar, R.: Post buckling response of laminated composite plate on elastic foundation with random system properties. Commun. Nonlinear Sci. Numer. Simul. 14(1), 284–300 (2009). https://doi.org/10.1016/j.cnsns.2007.08.005

    Article  MATH  Google Scholar 

  23. Huang, N.N., Tauchert, T.R.: Thermal buckling of clamped symmetric laminated plates. Thin-walled Struct. 13(4), 259–273 (1992). https://doi.org/10.1016/0263-8231(92)90024-Q

    Article  MATH  Google Scholar 

  24. Chen, L.W., Chen, L.Y.: Thermal buckling of laminated composite plates. J. Therm. Stresses 10(4), 345–356 (1987). https://doi.org/10.1080/01495738708927017

    Article  Google Scholar 

  25. Thangaratnam, K.R., Ramachandran, J.: Thermal buckling of composite laminated plates. Comput. Struct. 32(5), 1117–1124 (1989). https://doi.org/10.1016/0045-7949(89)90413-6

    Article  MATH  Google Scholar 

  26. Chen, W.J., Lin, P.D., Chen, L.W.: Thermal buckling behavior of thick composite laminated plates under nonuniform temperature distribution. Comput. Struct. 41(4), 637–645 (1991). https://doi.org/10.1016/0045-7949(91)90176-M

    Article  MATH  Google Scholar 

  27. Shu, X., Sun, L.: Thermomechanical buckling of laminated composite plates with higher-order transverse shear deformation. Comput. Struct. 53(1), 1–7 (1994). https://doi.org/10.1016/0045-7949(94)90123-6

    Article  MATH  Google Scholar 

  28. Sahin, O.S., Avci, A., Kaya, S.: Thermal buckling of orthotropic plates with angle crack. J. Reinf. Plast. Compos. 23(16), 1707–1716 (2004). https://doi.org/10.1177/0731684404040125

    Article  Google Scholar 

  29. Avci, A., Kaya, S., Daghan, B.: Thermal buckling of rectangular laminated plates with a hole. J. Reinf. Plast. Compos. 24(3), 259–272 (2005). https://doi.org/10.1177/1731684405043554

    Article  Google Scholar 

  30. Chen, L.W., Chen, L.Y.: Thermal buckling behavior of laminated composite plates with temperature-dependent properties. Compos. Struct. 13(4), 275–287 (1989). https://doi.org/10.1016/0263-8223(89)90012-3

    Article  MathSciNet  Google Scholar 

  31. Burton, W.S.: Three-dimensional solutions for the thermal buckling and sensitivity derivatives of temperature-sensitive muitilayered angle-ply plates. J. Appl. Mech. 59, 849 (1992). https://doi.org/10.1115/1.2894052

    Article  Google Scholar 

  32. Shen, H.S.: Thermal postbuckling behavior of imperfect shear deformable laminated plates with temperature-dependent properties. Comput. Methods Appl. Mech. Eng. 190(40–41), 5377–5390 (2001). https://doi.org/10.1016/S0045-7825(01)00172-4

    Article  MATH  Google Scholar 

  33. Vosoughi, A.R., Malekzadeh, P., Banan, Mo.R., Banan, Ma.R.: Thermal postbuckling of laminated composite skew plates with temperature-dependent properties. Thin-Walled Structures 49(7), 913–922 (2011). https://doi.org/10.1016/j.tws.2011.02.017

    Article  Google Scholar 

  34. Chen, C.S., Chen, C.W., Chen, W.R., Chang, Y.C.: Thermally induced vibration and stability of laminated composite plates with temperature-dependent properties. Meccanica 48(9), 2311–2323 (2013). https://doi.org/10.1007/s11012-013-9750-7

    Article  MATH  Google Scholar 

  35. Malekzadeh, P., Vosoughi, A.R., Sadeghpour, M., Vosoughi, H.R.: Thermal buckling optimization of temperature-dependent laminated composite skew plates. J. Aerosp. Eng. 27(1), 64–75 (2012). https://doi.org/10.1061/(ASCE)AS.1943-5525.0000220

    Article  Google Scholar 

  36. Bohlooly, M., Mirzavand, B.: A closed-form solution for thermal buckling of cross-ply piezolaminated plates. Int. J. Struct. Stab. Dyn. 16(03), 1450112 (2016). https://doi.org/10.1142/S0219455414501120

    Article  MathSciNet  MATH  Google Scholar 

  37. Shariyat, M.: Thermal buckling analysis of rectangular composite plates with temperature-dependent properties based on a layerwise theory. Thin-walled Struct. 45(4), 439–452 (2007). https://doi.org/10.1016/j.tws.2007.03.004

    Article  Google Scholar 

  38. Zhang, Z., Zhou, W.L., Zhou, D., Huo, R.L., Xu, X.L.: Elasticity solution of laminated beams with temperature-dependent material properties under a combination of uniform thermo-load and mechanical loads. J. Central South Univ. 25(10), 2537–2549 (2018). https://doi.org/10.1007/s11771-018-3934-1

    Article  Google Scholar 

  39. Benyamina, A., Bouderba, B., Saoula, A.: Bending response of composite material plates with specific properties, case of a typical FGM "ceramic/metal&quot thermal environments. PeriodicaPolytechnica Civil Eng. 62(4), 930–938 (2018). https://doi.org/10.3311/PPci.11891

    Article  Google Scholar 

  40. Kamarian, S., Shakeri, M., Yas, M.H.: Thermal buckling optimisation of composite plates using firefly algorithm. J. Exp. Theor. Artif. Intell. 29(4), 787–794 (2017). https://doi.org/10.1080/0952813X.2016.1259267

    Article  Google Scholar 

  41. Kim, Y.W.: Temperature dependent vibration analysis of functionally graded rectangular plates. J. Sound Vib. 284(3–5), 531–549 (2005). https://doi.org/10.1016/j.jsv.2004.06.043

    Article  Google Scholar 

  42. Moskalenko, V.N.: Random temperature fields in plates and shells. Soviet Appl. Mech. 4(9), 6–9 (1968)

    Article  Google Scholar 

  43. Nakamura, T., Fujii, K.: Probabilistic transient thermal analysis of an atmospheric reentry vehicle structure. Aerosp. Sci. Technol 10(4), 346–354 (2006)

    Article  Google Scholar 

  44. Val’kovskaya, V.I., Lenyuk, M.P.: Stochastic nonstationary temperature fields in a solid circular-cylindrical two-layer plate. J. Math. Sci. 79(6), 1483–1487 (1996)

    Article  Google Scholar 

  45. Chiba, R.: Stochastic thermal stresses in an FGM annular disc of variable thickness with spatially random heat transfer coefficients. Meccanica 44(2), 159–176 (2009)

    Article  MathSciNet  Google Scholar 

  46. Samuels, J.C.: Heat conduction in solids with random external temperatures and/or random internal heat generation. Int. J. Heat Mass Transf. 9(4), 301–314 (1966)

    Article  Google Scholar 

  47. Clarke, N.S.: Heat diffusion in random laminates. Q. J. Mech. Appl. Math 37(2), 195–230 (1984)

    Article  Google Scholar 

  48. Ghanem, R.G., Spanos, P.D.: Stochastic finite element method: response statistics in stochastic finite elements: a spectral approach. Springer (1991)

    Book  Google Scholar 

  49. Fish, J., Wu, W.: A nonintrusive stochastic multiscale solver. Int. J. Numer. Meth. Eng. 88(9), 862–879 (2011). https://doi.org/10.1002/nme.3201

    Article  MathSciNet  MATH  Google Scholar 

  50. Parviz, H., Fakoor, M.: Free vibration of a composite plate with spatially varying Gaussian properties under uncertain thermal field using assumed mode method. Physica A 559, 125085 (2020). https://doi.org/10.1016/j.physa.2020.125085

    Article  MathSciNet  Google Scholar 

  51. Parviz, H., Fakoor, M.: Stochastic free vibration of composite plates with temperature-dependent properties under spatially varying stochastic high thermal gradient. Mech. Based Des. Struct. Mach. (2021). https://doi.org/10.1080/15397734.2021.2014863

    Article  Google Scholar 

  52. Fakoor, M., Parviz, H.: Uncertainty propagation in dynamics of composite plates: a semi-analytical non-sampling-based approach. Front. Struct. Civ. Eng. (2020). https://doi.org/10.1007/s11709-020-0658-8

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of New Sciences and Technologies, University of Tehran, 14395-1561, Tehran, Iran

    Hadi Parviz & Mahdi Fakoor

  2. Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Fatemeh Hosseini

Authors
  1. Hadi Parviz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mahdi Fakoor
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fatemeh Hosseini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mahdi Fakoor.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Parviz, H., Fakoor, M. & Hosseini, F. Probabilistic thermal stability of laminated composite plates with temperature-dependent properties under a stochastic thermal field. Acta Mech 233, 1351–1370 (2022). https://doi.org/10.1007/s00707-022-03167-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-022-03167-w

Search

Navigation