## 3 Design of the Skin and the Stringers
### Selection and Design of the Stringers  
The aerodynamic surface of the MLE is provided by the above-mentioned skin of CFRP. Its laminate was designed with comparatively low bending stiffness in the circumferential direction, i.e., along the cross-section contour, to allow the change of shape required for the morphing function. In the span-wise direction, however, considerable bending stiffness is required to limit the deformation of the contour due to the aerodynamic loads. Otherwise, the target shapes would not be met and the aerodynamic performance of the MLE would not be acceptable. Therefore, the skin was stiffened by additional span-wise stringers. Depending on how the stringers are joined to the skin, they could lead to a local stiffening of the skin and thus to uneven deformation of the MLE, which would also reduce the aerodynamic performance. Figure 8 schematically shows the leading-edge contours in the cruise and high-lift configurations (Figure 8 left) as well as the implied change of curvature and positioning of the stringers along the cross-sections' contour (Figure 8 right). The stringer locations were defined where the change in curvature is minimal, limiting the effect of any local stiffening they may cause. Figure 8: Curvature analysis for placement of stringers (schematic); (**a**) abscissa: Location along the MLE-contour; blue: Curvature along contour S4, red: Curvature along contour S5, grey: Difference between S4 and S5 curvatures, grey squares: Selected locations for stringers 2 to 5 (region of stringer 1 does not change curvature very much anyhow); (**b**) Blue curve is S4, red curve is S5 (not to scale). As shown in Figure 9, the stringers are formed by the inner part of the skin-laminate itself. While this is more complicated with respect to manufacturing than adhesive bonding of separate stringers, it avoids much of the local stiffening that would be caused by the bonding flanges. However, the skin's laminate mostly contains fibres oriented approximately in the circumferential direction. To provide sufficient span-wise bending stiffness, the stringers therefore require further reinforcement. In principle, this could readily be achieved by adding CFRP-plies with fibres oriented along the stringers. However, the span-wise coefficients of thermal expansion (CTE) of skin and stringers would then be very different. In the temperature range considered for the MLE (i.e., down to \(-45\)\({}^{\circ}\)C), this would lead to unacceptable transverse (i.e., span-wise) residual stresses in the skin. This is demonstrated by finite element analyses of the skin and CFRP-stringers in conjunction with applying [PERSON]'s failure criterion (see Section 3.1). The skin consists of a symmetric and balanced laminate with fibres oriented mostly in the \(+5^{\circ}\) and \(-5^{\circ}\) direction (relative to the flight direction). Its span-wise CTE is ca. \(18\times 10^{-6}\)\(1/\)K. The reinforced CFRP-stringers assumed initially possessed the following lay-up: \([-85^{\circ},85^{\circ},\)\(-45^{\circ},\)\(45^{\circ},\)\(5^{\circ},\)\(-5^{\circ},\)\(-5^{\circ},\)\(5^{\circ}]_{\text{S}}\) (expressed in the same coordinate system as the skin laminate, i.e., \(90^{\circ}\) corresponds to the span-wise direction, which is longitudinal to the stringers and perpendicular to the flight direction). The corresponding CTE in the span-wise direction is only \(1.15\times 10^{-6}\)\(1/\)K. As the temperature is reduced, the skin itself would contract in the span-wise direction much more than the stringers. Since it is connected to the stringers and its contraction would thus largely be prevented, residual stresses would occur in the span-wise direction, i.e., roughly perpendicular to its fibres. Evaluation of the above mentioned IRF shows that these residual stresses would be critical with respect to causingply-failure, especially when additional stresses due to morphing also occur.