一枚小可爱Dimensionless foundation stiffness, F
R e l a t i v e b u c k l i n g l o a d , P c r /P E
8This discrepancy may have been induced by model-
ing the core material as a Winkler foundation in which
the elastic springs represent the core. To verify that the
discrepancy is caused by the simplifying assumptions of the elastic foundation approach, a second finite-element analysis was performed with reduced constituent Figure 8. Convergence of relative buckling load using finite-difference method.
Figure 9. Comparisons of relative buckling load results from different methods for variations in foundation stiffness.
240 pisions
Dimensionless foundation stiffness, F
R e l a t i v e b u c k l i n g l o a d , P c r /P
E Dimensionless foundation stiffness,
F R e l a t i v e b u c k l i n g l o a d , P c r /P E 7
9
properties. The Poisson’s ratios of the aluminum face-skin and foam core,νb and νf , were set to 0, and Young’s modulus of the foam,E f 11, was set to approximately 0(10?4) psi. This reduction of the material properties elim-inates the effects of the Poisson’s ratios and the longitu-dinal stiffness of the core. Figure 9 shows a comparison of the second set of finite-element results with the Rayleigh-Ritz and finite-difference methods. Excellent agreement is observed between the finite-element analy-sis using the reduced material properties and the results from the Rayleigh-Ritz and finite-difference methods.
Effect of Debond Length on Buckling Load In a second parametric study, the debond ratio μ was varied from 0 (fully bonded) to 1 (fully debonded) for a fixed value of F = 30.0 (K = 12500psi). The limiting value of μ = 0 yields the buckling load for a sandwich panel strip with no debonds, and a value of μ = 1 yields the Euler buckling load P E for a fully debonded faceskin.The results are presented in figure 10 in terms of the nor-malized buckling load P cr /P FULL , which is the ratio of the buckling load pided by the buckling load of a beam fully supported by an elastic foundation (ref.10):(22)
where n is the number of half sine waves required to give the lowest buckling load, depending upon the parameters.
Fifty terms in the Rayleigh-Ritz method and
360gridpoints in the finite-difference method were used in this study. In the finite-element analysis, two sets of constituent properties were again used. Set 1 used isotro-pic properties and Set 2 used reduced constituent proper-ties (νf 12 =νb 12 = 0,E f 11≈ 0). The results in figure 10show that the normalized buckling load decreases as μincreases, indicating that the buckling load for the unsup-ported skin decreases as the debonded length increases.The results from the isotropic plane-strain finite-element analysis are about 10–20 percent higher (depending on the debond length) than those predicted by the Rayleigh-Ritz and finite-difference methods. This suggests that the simplifying assumptions on Poisson’s ratio and the longi-tudinal stiffness of the core can substantially affect buck-ling load predictions. However, excellent agreement is observed once these properties are reduced.
Effect of Transverse Shear on Buckling Load Transverse shear effects were found to be insignifi-cant for the studies performed in this paper. From equa-tion (4.76) in reference (ref.10), the buckled fully bonded faceskin is calculated to have a wavelength of 2.68 in. for the largest K considered in this study (12500 psi). This corresponds to a l d /t b ratio of 13.4,which is estimated to contribute less than 2-percent error for the buckling load of the debonded faceskin using ref-erence (ref.15). Therefore, transverse shear effects were not considered in the Rayleigh-Ritz and finite-difference analyses.
P FULL n 2
π2
E b I L 2--------------kL 2
n 2π
2-----------+=n 12…,,=()Figure 10. Comparisons of normalized buckling load results from different methods for various debond ratios and F =30.0.
Debond ratio, μ
N o r m a l i z e d b u c k l i n g l o a d , P c r /P F U L L
≈ 0)
Conclusions
Three numerical methods were used to analyze the buckling of a debonded aluminum faceskin on a sand-wich panel with a foam core. The Rayleigh-Ritz and finite-difference methods were used to study a 1-D beam-on-elastic-foundation model that represents a strip of a sandwich panel with a through-the-width debond. The results were compared with the buckling loads cal-culated from a 2-D finite-element analysis using 4-noded quadrilateral plane-strain elements. Two parametric stud-ies were performed to evaluate the effects of the elastic foundation stiffness and debond length. Results from the three analytical methods were compared and discussed. As expected, the results showed that the buckling load increases with increasing core foundation stiffness and decreases with increasing debond length.
The Rayleigh-Ritz method was shown to be superior to the finite-difference method in obtaining the buckling loads because it requires less computational time and exhibits fast convergence. However, both the Rayleigh-Ritz and finite-difference methods assumed a Winkler core foundation and, thus, ignored the Poisson’s ratio and longitudinal stiffness effects of the core material. Results from the Rayleigh-Ritz method and the finite-difference method, which are based on the elastic foundation approach, show lower buckling loads than those pre-dicted by the 2-D plane-strain finite-element analysis, which models the sandwich foam core as an isotropic material. When the core is forced to behave as a Winkler foundation so that the Poisson’s ratios of the core are set to 0 and its longitudinal stiffness is reduced to be infini-tesimally small, the finite-element analysis agrees with the results from the Rayleigh-Ritz and finite-difference methods. Therefore, to accurately predict the buckling load of a debonded sandwich panel with sandwich foam cores, a finite-element model that includes the Poisson’s ratio and longitudinal core stiffness should be used. NASA Langley Research Center
Hampton, V A 23681-0001
October 16, 1995
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