Minimum weight design of a wing box subjected to bending
Aircraft wing is one of the best examples of an efficient structural design. A variety of structural arrangements are possible to satisfy design goals. The endeavour is always to arrive at a minimum weight of a wing structure for a given set of design conditions. The main load carrying structure of a wing is the torsion box formed by front spar, rear spar, and top spar & bottom skins. In the preliminary design stages an effect is made to arrive at an efficient design of this box –structure. The load carrying capacity of this box structure is largely controlled by the buckling of the compression cover plate. In order to get a minimum weight design of such a box the compression cover skin and its support arrangements are to be selected so as to give highest buckling stress. In this project an ideal box beam representative of a wing torsion box will be considered for a detailed analysis. The box beam subjected to a bending moment, various structural arrangements will be considering in order maximising the buckling stress. An analytical formulation is developed to obtain the minimum weight of the box design charts will be developed based on this formulation. A FEM & FEA route will be employed to correlate with the analytical predictions.
Aircraft structure is one of the finest examples of optimum structural design. Beginning with Wright brothers first flight the covering was of fabric material for the aircraft. With the advancement of our structural concepts fabrics gave way to stressed skin design which continues even today. Airframe is essentially a semi-monologue structure: a thin skin of orthogonally stiffened to resist the externally applied load by developing internal stresses distributed uniformly over large areas. These skins are very efficient in carrying in plane tensile loads. But they are relatively weak in carrying compression and shear loading thin skin structures are prone to the phenomenon of buckling. This practically restricts their ultimate load carrying capacity. Aircraft wings, fuselage and control surfaces primarily resist externally applied load by beam action. In flight the wing top surface too is subjected to compression. In fact the static design limiting consideration is the buckling and subsequent failure of stiffened skins of the airframe. In a multiple load path compressive load carrying structural component, once buckling initiates in any one of the elements, other elements are not develop their full load carrying potential. There for an efficient and minimum weight design, a multiple load path structure must be designed to fail simultaneously at the design ultimate load. For an efficient design of a transport aircraft wing to have a minimum weight for a given design ultimate bending moment the wing top skin must be sized to have the highest buckling stress possible. A uniformly thick skin without any lateral support cannot develop high buckling stress. A number of support arrangements are utilized to maximize the buckling stress. Typically in a transport aircraft wing, transverse supports are provided by the ribs and this enhances the buckling stress of the wing top skin. A typical longitudinal section of a wing is shown below
A rear aircraft wing buckling analysis will require a numerical solution approach through a FEM and FEA route. On the other hand closed form analytical solution is possible only for simplified geometry and simple loading condition. These closed form solution are extremely important to develop our understanding of the structural response of the wing structure. With this view in focus, we will consider only the torsion box of the wing structure to be carrying the entire wing loading. This is the box formed by the front spur, the rear spur and the top and bottom skin covers. In an actual wing this box is of variable cross section designed to carry varying bending moment...
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