基于均匀化转换方法的FGM圆柱壳静水压力下临界压力预测研究  

Research on free critical pressure prediction of the FGM cylindrical shells under hydrostatic pressure based on the homogenization transformation method

作　　者：杨萌[1] 李戎[1] 梁斌[1] YANG Meng;LI Rong;LIANG Bin(School of Civil Engineering and Architecture,Henan University of Science and Technology,471023 Luoyang,China)

机构地区：[1]河南科技大学土木建筑学院,洛阳471023

出　　处：《应用力学学报》2023年第4期956-964,共9页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目(No.U1604135;11402077);河南省科技攻关资助项目(No.202102210039)。

摘　　要：依据经典Flügge壳体理论,利用功能梯度材料(FGM)和均匀材料物理性质和力学行为相似性的均匀化转换计算方法,研究了静水压力下FGM圆柱壳临界压力的预测方法。针对水下FGM圆柱壳耦合系统的振动问题,考虑流体影响,采用波动法推导出相应的振动方程,使用了牛顿迭代法,以确定在静水压力下FGM圆柱壳的固有频率。根据临界载荷与固有频率为零的载荷水平线性相关性,运用拟合曲线法和均匀化转换后的公式法对静水压力下FGM圆柱壳临界压力进行了预测分析,并讨论了FGM圆柱壳各项参数对静水压力下FGM圆柱壳临界压力的影响。结果表明,FGM圆柱壳的材料弹性模量E合值、几何尺寸h/R和L/R,以及不同边界条件改变对临界压力影响较大。通过对多组算例的对比分析,证明了本研究方法的正确性和有效性。使用该方法进行预测的精度高,计算量小,能够为非均匀结构力学行为的分析提供新的研究途径。According to the classic Flügge shell theory,the calculation method of the homogenization conversion of the physical properties and mechanical behavior similarity of functionally graded materials(FGM)and homogeneous materials is used to study the prediction method of the critical pressure of FGM cylindrical shells under hydrostatic pressure.Considering the influence of the fluid,the wave method is used to derive the vibration equation of the underwater FGM cylindrical shell coupled system,and the Newton iteration method is used to find the natural frequency of the FGM cylindrical shell under hydrostatic pressure;According to the linear correlation between the critical load and the load level when the natural frequency is zero,the critical pressure of the FGM cylindrical shell under hydrostatic pressure is predicted and analyzed by the fitting curve method and the formula method after homogenization conversion,and the influence of various parameters of FGM cylindrical shell on the critical pressure of FGM cylindrical shell under hydrostatic pressure is discussed.The results show that the total value of the material elastic modulus E of the FGM cylindrical shell,geometric dimensions h/R and L/R of the FGM cylindrical shell,and changes in different boundary conditions have a greater impact on the critical pressure.Through the comparative analysis of multiple sets of calculation examples,the correctness and effectiveness of the method in this paper are verified,and the prediction accuracy is high and the calculation amount is small,which can provide a new exploration approach for the analysis of the mechanical behavior of non-uniform structures.

关 键 词：FGM圆柱壳 静水压力 Flügge薄壳理论 波动法 临界压力预测 均匀化转换 

分 类 号：TB535.1[理学—物理]