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.

用详细的数值模型估算加劲板的屈曲阻力可以提供高保真度的结果，但是对于飞机结构的初步设计阶段，这是不切实际的，因为需要进行多次迭代或敏感性分析。对于此设计阶段，分析解决方案变得更可取。为此，开发了一种近似封闭形式的解决方案，以估计带有反对称交叉层和角层层合的欧米茄纵梁的加劲板的临界皮肤局部屈曲载荷。这是使用创新的基于能量的均质化方法获得的，该方法可得出等效的弯曲刚度矩阵。该研究进一步检验了两个关键参数对上述部分各向异性皮肤的屈曲载荷的分析估计的影响。第一个参数涉及必须为皮肤纵梁接合处假定的适当边界条件的选择。数学模型考虑了两个连续的欧米茄纵梁之间的皮肤部分。加强板的其余部分由等效的横向和旋转弹簧代替，这些弹簧用作弹性边缘支撑。弹性约束是通过考虑欧米茄纵梁的弯曲和扭转刚度的两种独特方法确定的。作为第二参数，Rayleigh-Ritz方法考虑了两个不同的偏转函数（三角函数和多项式）。目的是确定弹性约束刚度和挠度函数的适当组合，以使反对称交叉层和角度层皮肤层压的情况产生更准确的屈曲结果。最后，通过将获得的分析结果与各自的数值进行比较来评估获得的分析结果。比较表明，对于边界条件和挠度函数的一定组合，可以获得令人满意的相关性。强调了有关派生屈曲解的准确性，差异和局限性的讨论和结论。