Idealization of Stiffened Structural Components

In the following sections, the effects of the different degrees of detail of modeling are discussed. Several types of stiffener idealization are considered and the effect of the simplifications on the structural behavior and aerodynamic properties of the wing is evaluated by calculating structural and static aeroelastic response. The devi­ations of structural response computed for each case are summarized in a test matrix (see fig. 4). In the test matrix, different degrees of modeling detail are considered for stringers, spar caps and rib caps. The levels of modeling detail are represented by realizing the structural member by beam elements or rod elements, or by homo­genizing the stiffeners as isotropic or orthotropic layer. The effect of element offset is also considered for beam and rod elements as well as for the orthotropic material layer. For the main idealizations, the deviation of converged angle of attack from the reference case is plotted in figure 6.

Effects of Simplified Stringer Modeling

Explicit modeling of stringer stiffened top and bottom covers including property as­sociation for stiffening members is very time-consuming especially if the stringer cross-section geometry varies in both chord and span wise directions. Several de­grees of stringer idealization are considered within the present study. A common method to avoid the modeling effort is to create a skin-stringer-"laminate" with iso­tropic skin and orthotropic stringer layers. The benefit of this approach is that only one parameter is required to realize the skin-stringer-structure. This parameter is the area ratio of the skin and summarized stringer cross-sections, commonly given in the literature as 100:50 for thee design of transport aircraft wing structures [7]. The structural model with stringers smeared as an isotropic layer presents the simplest approach concerned in the present study.

Homogenizing discrete stringers over the skin area has two opposite effects on the bending stiffness of the wing box. The first effect is the reduction of the wing box local moment of inertia by neglecting the bending stiffness of the stringers. The second effect is the overestimation of the wing bending stiffness caused by neglect­ing the (offset) distance of the stringer cross-sections relative to the skin surface. The effect of ignoring the bending stiffness of the stiffeners on the bending and tor­sional deformation of the wing can be concerned on the basis of deviations obtained for a FE model with stringers realized with rod elements. For this idealization, the bending angle is increased by only 0.84% due to lower structural stiffness, resulting in 0.87% greater angle of attack. The influence of stringer stiffness on the torsional behavior and in turn on the elastic angle of attack is negligible (see table 4). The marginal impact of stringer bending stiffness on the deformation behavior results in change of geometric angle of attack being only 0.19% (see fig. 6).

In contrast to the effect of the stringer-stiffness, the overestimated contribution of the stringer-cross-sections to the local wing box moments of inertia due to non­considering the correct offset distance dominates the influence on the bending de­formation. How can be seen in table 4 for the deviations obtained for FE models with stringers idealized as isotropic and orthotropic layer without offset, the bending angle decreases by 3.9 — 4%. Because stringers do not contribute to the shear load resistance of skin panels the stringer idealization as an orthotropic material layer enables to reproduce the torsional stiffness of the wing box structure in the way that

is more realistic compared with stringers homogenized as isotropic material. This trend is demonstrated by the smaller deviation of twist ( [AQ] = 1.1%) compared to the simplest model ([A0] = 6.3%). One remarkable effect of greater difference of wing twist is the smaller deviation of elastic angle of attack of the structural model with stringers idealized as isotropic layer ([Aael] = -3.4%) compared with the more realistic approach ([Aael] = -4.1%). The trend predicted by the comparison of the [Aael]-deviation parameters between the both structural models, confirms with the results of static aeroelastic analysis. The deviation of converged angle of attack for the skin-stringer compound realized with orthotropic stringer layer is slightly higher (AaEqSt / aEqSt = -0.82%) as for a simpler structure (AaEqst/aEqSt = -0.71%, see fig. 6).