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Effect of Simplified Spar Cap and Rib Cap Modeling
Effects occurs by modeling the spar caps with beam or rod elements with or without considering element offsets are similar to those discussed in the section above. Due to smaller cross-section of the spar caps relative to the cross-section of the whole wing box this effects causes only marginal discrepancies of the bending and torsion angle and thus of the elastic angle of attack. If spar stiffeners are considered as isotropic layer in the wall thickness of the skin parts the bending stiffness increases causing 0.8% smaller elastic angle of attack. The deviation [Aael] that results from neglecting the element offsets varies between -0.46% and -0.54% (see fig. 4). A static aeroelastic response was calculated for wing structure with spar caps modeled with bar elements without element offset. The converged angle of attack
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Fig. 6 Deviations of equilibrium state angle of attack for different variants of modeling simplification |
aEqSt of this structure is only 0.11% smaller compared to the reference structure. How can be seen from results in table 4 the influence of rib caps on the bending and torsional deformation is marginal resulting in deviations of elastic angle of attack being between 0.02% and 0.2%. Therefore, the influence of these stiffening components on the deformation behavior and thus on the aerodynamics of the wing can be neglected.
1.2.1 Conclusions
Within the first part of the work, a simple method was presented to calculate global parameters, which enables to estimate the effect of uncertainties of structural models on the deformation behavior and thus on the aerodynamic properties of the wing structure. This method was applied to investigate the impact of modeling uncertainty on the structural and aeroelastic response of the wing of a wide-body transport aircraft. The results of the study yield a rather good agreement between the deviation trends of the structure subjected to modeling uncertainty, which are calculated for a static loading and the discrepancy of aerodynamic properties of the wing obtained by a coupled analysis. As mentioned above, the elastic angle of attack ael, employed as evaluation parameter is dominated by the bending deformation of the wing structure. Since the top and bottom covers have the greatest contribution to the bending stiffness of the wing, the simplified modeling of stringers has the major effect on the accuracy of the structural model. The deviations of converged angle of attack aEqSt, used as performance criterion to evaluate the accuracy of the coupled analysis varies between 0.2% and 1.44% for different degrees of modeling detail (see fig. 6).
As shown on the sample of simplified boundary conditions, the higher deviations of twist and bending angle must not as well produce higher discrepancy of converged angle of attack. In fact the deviations has to be transformed in flight direction using the interrelationship give in equation (2) to estimate the resulting effect of the discrepancies within both deformations on the load distribution.
