Thin-walled laminated composite structures are being used extensively in aerospace, naval, transportation and civil engineering industries. These structures are often subjected to aggressive service conditions, such as elevated temperatures, which lead to thermally induced deformations, buckling or post-buckling. Since these structures retain considerable post-buckling strength beyond the thermal buckling load, it is quite advantageous to make use of the post-buckling characteristics in practical design. Most of the investigations on thermal post-buckling analysis have been devoted to thin structures, [1,2] in which the elastic and thermal properties are considered to be temperature independent.

Actually, the material properties of the constituents of laminated composite structures depend, generally, on the temperature field imposed. The investigation of thermal post-buckling of laminated composites, considering material degradation using finite element methods, and the static buckling of composite and sandwich plates using layer-wise plate theories are presented in [3,4].

The aim of this paper is the development of a path following algorithm to compute the critical thermal buckling and the post-buckling equilibrium path using an asymptotic numerical method [5]. Temperature-dependent elastic and thermal properties are considered. A power law distribution in terms of temperature is used and the structure is assumed to be subjected to uniform temperature change. Power series expansions of the displacement and the temperature are developed and the homotopy method coupled with the finite element method is used for numerical solution.

An asymptotic numerical algorithm is elaborated herein to solve the resulting nonlinear thermal problem with a reasonable computational cost. This algorithm combines the perturbation technique and the finite element. After getting the thermal buckling bifurcation point, the nonlinear equilibrium equations were employed to get the post-buckling configurations. The effects of temperature dependent properties, structure's geometry and boundary conditions on the thermal buckling and post-buckling behaviors were evaluated. It is observed that the thermal buckling strength has been reduced significantly when the temperature-dependent properties are taken into consideration. On the other hand, the temperature-dependent material effect lowered the critical buckling temperatures and increased the post-buckling deflections.

The developed methodological approach is efficient and can easy account for various linear and nonlinear temperature dependent models and can be applied to various multilayered composite structures.

References

[1] Singh, G., Venkateswara Rao, G., Iyengar, N.G.R., Thermal post buckling behavior of rectangular antisymmetric cross-ply composite plates, Acta Mechanica (1993), 98, 39-50. 

[2] Singha, M.K., Ramachandra, L.S., Bandyopadhyay, J.N., Vibration behavior of thermally stressed composite skew plate, Journal of Sound and Vibration (2006), 296, 1093–1102.

[3] L.W. Chen and L.Y. Chen, Thermal post buckling behaviors of laminated composite plates with temperature-dependent properties, Composite Structures 19 (1991), 267-283.

[4] M. Shariyat, Thermal buckling analysis of rectangular composite plates with temperature-dependent properties based on a layerwise theory, Thin-Walled Structure 45 (2007), 439–52.

[5] F. Abdoun, L. Azrar, E.M. Daya, and M. Potier-Ferry, "Forced vibrations of viscoelastic structures by an Asymptotic Numerical Method” Computers & Structures, (2009), Volume 87, Issues 1-2, Pages 91-100,

[6] H-S Shen, Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties, International Journal of Mechanical Sciences 49 (2007) 466–478.