Aeroelastic Problems of Low Aspect Ratio Wings: Part I. Structural Analysis

A method is presented for calculating influence coefficients in multispar wings of any plan form. Shear deflexion, chordwise bending and taper are taken into account. All the bending material is concentrated at the rib and spar booms and the skin is assumed to carry only shear. The method is particularly useful in the early stages of design as it is rapid and gives a good internal load distribution. The choice of the method, the assumptions made, and the idealization of the structure are discussed. The structure is reduced to a system of beams and torque boxes, the latter connected to the beams by vertical shear at their corner nodes. The internal forces are first expressed as functions of the displacements at the nodes by means of stiffness coefficients. Next the equations of equilibrium, at each node, are established. Finally the conditions of compatibility are brought in. The solution of this system of equations gives the matrix of influence coefficients. Wherever vertical loads only are applied it is possible to solve for the moment equations of straight beams separately from the remainder of the structure, hence from the stiffness matrix. For convenience, these straight beams are organized into sub‐matrices whose moment equations are ‘reduced’. The specific end conditions also allow further reductions. The internal loads can be obtained by substituting the influence coefficients back into the sub‐matrices and by considering the equilibrium of the beams. The angular displacements of the nodes may also be calculated in a similar manner by using the ‘reduced’ rows from the sub‐matrices.