基于非线性有限元降阶方法的网格加筋筒壳结构屈曲承载特性研究

非线性有限元数值计算方法是结构屈曲性能评估的主要手段,然而该方法需要基于精细网格迭代求解,降低结构非线性计算规模是其关键技术之一。采用一种结构非线性有限元降阶方法,对均匀轴向压载荷作用下的网格加筋筒壳结构进行了细致的承载稳定性特性分析。该方法将Koiter初始后屈曲理论与Newton弧长法相结合,通过多次使用Koiter摄动展开来跟踪结构非线性平衡路径。计算比较了特征值屈曲载荷和计及几何非线性效应的非线性屈曲载荷值;采用侧向小扰动载荷模拟结构初始几何形状缺陷,分析了缺陷幅度对临界屈曲载荷的影响规律,在验证了非线性有限元降阶方法分析精度的同时,细致考核了该方法在结构非线性屈曲分析以及缺陷敏感性分析中的计算效率优势。

Buckling Load-carrying Capability Analysis of Grid-stiffened Cylinders Using a Nonlinear Finite Element Reduced-order Method

The nonlinear finite element(FE) method is a traditional method to evaluate the buckling performance of thin-wall structures. However, this method needs a fine FE grid and repeated iterative solutions. Therefore, reducing the scale of nonlinear structural calculation is one of the key issues. In this paper, a novel nonlinear finite element reduced-order method is used to analyze the structural stability of a grid-stiffened cylinder under a uniform axial load. The method combines Koiter''s initial post-buckling theory with Newton''s arc-length method and uses Koiter''s perturbation expansion several times to track the nonlinear equilibrium path of the structure. In this paper, the buckling loads from structural linear eigenvalue analysis and from the nonlinear structural analysis with geometric nonlinear effects are calculated and compared. Then, the initial geometric shape imperfections are simulated with lateral small perturbation load, and effects of the imperfection amplitude on the critical buckling load are analyzed. The numerical accuracy of the proposed method has been validated and its advantages in computational efficiency for nonlinear buckling and imperfection sensitivity analysis have also been carefully tested.