基于模态重分析的GFEM模型突风响应计算  

Calculation of gust response of GFEM model based on modal reanalysis

作　　者：肖宇 刘景光[1] 邬旭辉 常亮 XIAO Yu;LIU Jingguang;WU Xuhui;CHANG Liang(Load Department,Shanghai Aircraft Design and Research Institute,Shanghai 201210,China;State Key Lab of Strength and Structural Integrity,Xi’an 710065,China)

机构地区：[1]上海飞机设计研究院载荷部,上海201210 [2]强度与结构完整性全国重点实验室,西安710065

出　　处：《振动与冲击》2024年第13期333-340,共8页Journal of Vibration and Shock

摘　　要：基于模态重分析技术,提出一种适合全局有限元模型(global finite element model, GFEM)的突风动响应高效计算方法。针对模型局部结构质量或刚度的细微变化,进行增量建模,充分利用现有构型结果,避免了传统分析中重复计算的步骤。对于质量阵的变化,以已有构型模态向量为初始向量,通过迭代分析进行特征值求解,针对刚度阵的微小变化,特别引入Sherman-Morrison-Woodbury公式,实现刚度逆矩阵的增量分析,从而克服了大规模GFEM模型的特征值求解效率低的问题,最终建立了一套适合于工程应用的GFEM突风高效动响应分析方法。采用GTA模型进行了突风分析算法的验证,在此基础上,基于某模型机翼,对模态重分析算法在突风动响应分析中的应用进行了研究。结果表明,通过LU分解可避免保存稠密形式的刚度逆矩阵,通过合理的松弛因子和收敛阈值,可有效提升计算效率。Here,based on modal reanalysis technology,an efficient calculation method for gust dynamic response suitable for global finite element model(GFEM)was proposed.Aiming at subtle changes in mass or stiffness of local structure of the model,incremental modeling was performed to fully utilize existing configuration results and avoid repetitive calculation steps in traditional analysis.For changes in mass matrix,the existing configuration modal vector was taken as the initial vector,and eigenvalues were solved with iterative analysis.For small changes in stiffness matrix,Sherman-Morrison-Woodbury formula was specially introduced to realize incremental analysis of stiffness inverse matrix,and overcome low efficiency problem of eigenvalue-solving for large-scale GFEM model.Finally,a set of efficient GFEM gust dynamic response analysis methods suitable for engineering application was established.GTA model was used to verify the gust analysis algorithm.Furthermore,based on a certain model wing,the application of modal reanalysis algorithm in gust dynamic response analysis was studied.The results showed that by adopting LU decomposition being able to avoid saving stiffness inverse matrix with dense form,reasonable relaxation factor and convergence threshold,computational efficiency can be effectively lifted.

关 键 词：模态重分析 全局有限元模型 突风 动响应 Sherman-Morrison-Woodbury公式 

分 类 号：V215.3[航空宇航科学与技术—航空宇航推进理论与工程]