Optimum design for buckling of arbitrary shaped ribs under uncertain loadings

Abstract

Typically, aircraft wing structural panels are designed against buckling for a very large number of possible loadings that may occur during the operation of the aircraft. If the optimisation procedure accounts only for a limited number of design loads, the structure may be vulnerable to a specific type of loading that may cause the structure to fail. A novel approach for the optimisation of ribs or plates of arbitrary shapes under uncertain loads is proposed. The geometry of the rib is defined by a single closed spline or several connected splines. The loading distribution is not considered to be uniform but it is allowed to vary within an admissible set, conferring uncertainty to the applied loads. The admissible load space comprises distributed normal and shear loadings that can be represented through a collection of piecewise linear functions defined along the plate boundary. A special procedure is applied to handle the constraint that the loading must be self equilibrating. A minimax strategy is used to deal with the loading variability such that the resulting optimal design is able to withstand an entire class of linear piecewise loadings along the rib boundary. The refinement of the loading representation may be completely independent of the refinement of finite element mesh. The validity of the proposed approach is assessed by applying it to an aeronautical wing rib.