A novel reduced‐order modeling method with two‐step strategy is proposed for nonlinear buckling analysis of axially compressed thin‐walled cylinder. The nonlinear response analysis up until the buckling point is achieved quickly by solving the small‐scale reduced‐order model, accounting for the geometrically nonlinear behavior. The buckling point is determined accurately using an efficient buckling detection algorithm, where the stiffness information of the reduced‐order model is extrapolated based on an eigenvalue analysis until a singular tangent stiffness is obtained. Then, the nonlinear buckling fiber angle optimization scheme of laminated composite cylinders is constructed in the MATLAB's MultiStart scheme with gradient‐based algorithms. The proposed two‐step reduced‐order modeling strategy is adopted to calculate the nonlinear buckling objection function at a much lower cost. Numerical results for axially compressed cylinders with various geometric imperfection fields demonstrate the good performance of the proposed strategy in both nonlinear buckling analyses and lamination optimizations.

中文翻译：

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非线性屈曲分析和几何缺陷圆柱体优化的新型降阶建模方法

提出了一种新颖的两步降阶建模方法，用于轴向压缩薄壁圆筒的非线性屈曲分析。通过求解小规模的降阶模型，可以快速解决直至屈曲点的非线性响应，并考虑了几何非线性行为。使用有效的屈曲检测算法可以准确地确定屈曲点，其中基于特征值分析推断降阶模型的刚度信息，直到获得奇异的切线刚度。然后，在MATLAB的MultiStart方案中使用基于梯度的算法构造了层压复合材料圆柱体的非线性屈曲纤维角度优化方案。采用拟议的两步降阶建模策略以较低的成本计算非线性屈曲反对函数。具有各种几何缺陷场的轴向压缩圆柱体的数值结果证明了该策略在非线性屈曲分析和叠层优化中的良好性能。