Thin-walled structures, i.e. the wing-upper-skin panels, are prone to buckling accompanied by a significantly large out-of-plane deflection. The computational efficiency of the conventional finite element based full-order method is not satisfactory for nonlinear buckling problems of the structure. In this work, the skin panels on the upper surface of the wing butt box are selected using a sub-modeling technique based on the nonlinear structural analysis. A reduced-order method is proposed to trace the geometrically nonlinear response of the single and double-curved skin panels in a stepwise manner. A predictor-corrector strategy is developed using the Koiter-perturbation-theory based reduced-order model and Newton iterations. The high-efficiency of the proposed method is validated by comparing the number of path-following steps and iterations with the full-order method. A fairly large step size is achieved to significantly reduce the computational cost in a nonlinear buckling analysis. The influence of the number of closely-spaced modes on the numerical accuracy and efficiency of the proposed reduced-order method is also studied. Different boundary condition, location, and thickness of the wing-upper-skin panel, are considered to further demonstrate the favorable performance of the proposed method.

中文翻译：

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存在屈曲时机翼上蒙皮板几何非线性分析的降阶方法


薄壁结构，即机翼上蒙皮面板，容易发生屈曲，并伴有明显较大的平面外偏转。传统的基于有限元的全阶方法对于结构的非线性屈曲问题的计算效率并不令人满意。在这项工作中，使用基于非线性结构分析的子建模技术选择机翼对接盒上表面的蒙皮面板。提出了一种降阶方法来逐步追踪单曲和双曲蒙皮面板的几何非线性响应。使用基于 Koiter 扰动理论的降阶模型和牛顿迭代开发了预测校正策略。通过与全阶方法比较路径跟踪步数和迭代次数，验证了该方法的高效性。实现相当大的步长以显着降低非线性屈曲分析中的计算成本。还研究了紧密间隔模式的数量对所提出的降阶方法的数值精度和效率的影响。考虑不同的边界条件、位置和机翼上蒙皮面板的厚度，以进一步证明该方法的良好性能。