Analytical theory for an approach calculation of non-balanced composite box beams

For aeroelastic problems, optimization of the behavior of box beams, carried out in composite materials, can lead to the construction of structures whose longitudinal axis is not necessarily the orthotropic axis of the materials. These beams present couplings such as Flexion–Torsion or Traction–Torsion. In this study, we propose an analytical theory which allows these structures to be dimensioned with extreme accuracy and without using complicated calculations. The method developed, based on a weak hypothesis on the field of deformations, makes it possible to obtain from simple analytical calculations, the stresses and displacement in a cross-section for normal load F→x, flexion moments M→y, Mz and torsion moments M→x. It is then possible using the laminated plates theory, to determine the stresses in each layer. The results obtained correspond perfectly to those found in a 3D Finite Element model, calculated using CATIA–ELFINI software. On the central part of the beams, the relative differences noticed between these two methods on the calculation of stress, strain and rigidities are negligible. Near the embedded section, warping is very important and the relative error is great.