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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

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Front. Mech. Eng.    2014, Vol. 9 Issue (1) : 41-49    https://doi.org/10.1007/s11465-014-0284-z
RESEARCH ARTICLE
Thermal buckling behavior of laminated composite plates: a finite-element study
Houdayfa OUNIS(),Abdelouahab TATI(),Adel BENCHABANE()
Laboratoire de Génie Energétique et Matériaux (LGEM), Université de Biskra, B.P. 145, Biskra 07000, Algeria
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Abstract

In this paper, the thermal buckling behavior of composite laminated plates under a uniform temperature distribution is studied. A finite element of four nodes and 32 degrees of freedom (DOF), previously developed for the bending and mechanical buckling of laminated composite plates, is extended to investigate the thermal buckling behavior of laminated composite plates. Based upon the classical plate theory, the present finite element is a combination of a linear isoparametric membrane element and a high precision rectangular Hermitian element. The numerical implementation of the present finite element allowed the comparison of the numerical obtained results with results obtained from the literature: 1) with element of the same order, 2) the first order shear deformation theory, 3) the high order shear deformation theory and 4) the three-dimensional solution. It was found that the obtained results were very close to the reference results and the proposed element offers a good convergence speed. Furthermore, a parametrical study was also conducted to investigate the effect of the anisotropy of composite materials on the critical buckling temperature of laminated plates. The study showed that: 1) the critical buckling temperature generally decreases with the increasing of the modulus ratio EL/ET and thermal expansion ratio αT/αL, and 2) the boundary conditions and the orientation angles significantly affect the critical buckling temperature of laminated plates.
Keywords thermal buckling      laminated composite plates      anisotropy      critical buckling temperature      finite-element method      high precision rectangular Hermitian element     
Corresponding Author(s): Adel BENCHABANE   
Issue Date: 16 May 2014
 Cite this article:   
Houdayfa OUNIS,Abdelouahab TATI,Adel BENCHABANE. Thermal buckling behavior of laminated composite plates: a finite-element study[J]. Front. Mech. Eng., 2014, 9(1): 41-49.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-014-0284-z
https://academic.hep.com.cn/fme/EN/Y2014/V9/I1/41
FEM theoryFE detailsNo. nodesDOFReferences
CPThigh-precision triangular354[29]
Semiloof shell432[30]
Hermitian448[31-33]
Lagrangian412[34]
FSDTshear locking free315[21]
plate bending440[20]
serendipity840[6,7]
Lagrangian840[22,23]
Lagrangian945[8,14,16,17]
penalty plate bending945[13,15]
Lagrangian1680[19]
mixed formulation-13[9-12]
HSDTglobal-local shear deformation theory3-[27]
-864[24,25]
without transverse normal deformation981[26]
with transverse normal deformation999[26]
Lagrangian16144[19]
LWTLagrangian--[35]
Hermitian4-[36]
Lagrangian--[37]
mixed interpolation of tensorial components (MITC)4-[38]
Tab.1  Finite elements used to study the thermal buckling behavior of laminated composite plates
Fig.1  Geometry and coordinate systems of rectangular laminated composite plate
boundary conditionsabbreviationsrestrained edges
simply supportedSSSSu=w=∂w∂y=0, x=±a2, v=w=∂w∂x=0, y=±b2
ClampedCCCCu=v=w=∂w∂x=∂w∂y=∂2w∂x∂y=∂2w∂x2=∂2w∂y2=0
clamped-simply supportedCSCSclamped at x=±a2, simply supported at y=±b2
clamped-freeCFCFclamped at x=±a2, free at y=±b2
simply supported-freeSFSFsimply supported at x=±a2, free at y=±b2
Tab.2  Boundary conditions used in this paper
Matsunaga [41]Noor and Burton [42]Zhao et al. [40](mesh-free,5)*Shiau et al. [29](3,6)*present(4,8)*
0.12640.12640.1284 (16 × 16)0.1266 (2 × 2)0.1272 (2 × 2)
0.1273 (18 × 18)0.1265 (4 × 4)0.1265 (4 × 4)
0.1271 (20 × 20)0.1265 (6 × 6)0.1265 (6 × 6)
Tab.3  Minimum critical temperature parameter αT × 10-3 of the simply supported isotropic plate (a/b = 1, a/h = 100, α0 = 1.0 × 10-6, E = 1.0 × 10-6, v = 0.3)
Shi et al. [39](4,6) *Shiau et al. [29](3,6) *present(4,8) *
[0/90/90/0]s--12.26 (12 × 12)12.2616 (4 × 4)12.2610 (8 × 8)12.2610 (12 × 12)12.2716 (4 × 4)12.2617 (8 × 8)12.2612 (12 × 12)
[0/45/-45/90]s--13.71 (12 × 12)13.7744 (4 × 4)13.7582 (8 × 8)13.7519 (12 × 12)13.7388 (4 × 4)13.7354 (8 × 8)13.7357 (12 × 12)
Tab.4  Critical buckling temperature of simply supported composite laminated plates
ΔTcr
0°15°30°45°
present0.7486 × 10-30.1133 × 10-20.1540 × 10-20.1720 × 10-2
Noor and Burton [42]0.7463 × 10-30.1115 × 10-20.1502 × 10-20.1674 × 10-2
err/%0,301,612,522,74
Tab.5  Minimum critical buckling temperature of simply supported angle-ply composite plates
Fig.2  Critical buckling temperature (∆Tcr) vs. modulus ratio EL/ET for (a) CCCC and (b) SSSS boundary conditions
Fig.3  Critical buckling temperature (∆Tcr) vs. modulus ratio EL/ET for (a) CSCS and (b) CFCF boundary conditions
Fig.4  Critical buckling temperature (∆Tcr) vs. modulus ratio EL/ET for SFSF boundary condition
Fig.5  Critical buckling temperature (∆Tcr) vs. thermal expansion ratio αT / αL for CCCC and SSSS boundary conditions
Fig.6  Critical buckling temperature (∆Tcr) vs. thermal expansion ratio αT/αL for (a) CSCS and (b) CFCF boundary conditions
Fig.7  Critical buckling temperature (∆Tcr) vs. thermal expansion ratio αT/αL for SFSF boundary condition
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