An approximate closed-form buckling solution for the local skin buckling of stiffened plates with omega stringers: The case of antisymmetric cross-ply and angle-ply laminations

Abstract

Estimating the buckling resistance of stiffened plates with detailed numerical models can provide high fidelity results, but for the preliminary design phase of aircraft structures this is impractical, since numerous iterations or sensitivity analyses are required. Analytical solutions become preferable for this design phase. To this end, an approximate closed-form solution is developed to estimate the critical skin local buckling load of stiffened plates with omega stringers with antisymmetric cross-ply and angle-ply lamination. This is obtained using an innovative energy-based homogenization method that yields to an equivalent bending stiffness matrix. The research further examines the influence of two key parameters to the analytical estimation of the buckling load of the fore mentioned partially anisotropic skin. The first parameter concerns the selection of the appropriate boundary conditions that must be assumed for the skin-stringer junction. The mathematical model considers the part of the skin between two consecutive omega stringers. The rest of the stiffened plate is replaced by equivalent transverse and rotational springs, which act as elastic edge supports. The elastic restraints are determined with two distinctive approaches considering the bending and torsional stiffness of the omega stringers. As a second parameter two different deflection functions (trigonometric and polynomial) are considered for the Rayleigh-Ritz method. Aim is to determine the appropriate combination of elastic restrain stiffness and deflection function that yield to more accurate buckling results for the cases of antisymmetric cross-ply and angle-ply skin laminations. Finally, the obtained analytical results are evaluated by comparing them with the respective numerical. The comparison showed that a satisfactory correlation can be achieved, for a certain combination of boundary conditions and deflection functions. Discussion and conclusions regarding the accuracy, discrepancies and limitations of the derived buckling solution are highlighted.