基于物理中面与高阶剪切变形理论FGM圆板的后屈曲分析  

Post-Buckling Analysis of FGM Circular Plates Based on Physical Neutral Surface and Higher-Order Shear Deformation Theory

作　　者：张大光 ZHANG Daguang(School of Civil and Surveying Engineering,Jiangxi University of Science and Technology,Ganzhou 341000,Jiangxi,China)

机构地区：[1]江西理工大学土木与测绘工程学院,江西赣州341000

出　　处：《力学季刊》2020年第3期486-498,共13页Chinese Quarterly of Mechanics

基　　金：江西省教育厅科学技术研究一般项目(GJJ180458);江西理工大学博士科学研究启动基金(jxxjbs18022)。

摘　　要：本文假定FGM材料的主要参数是温度相关的,且沿板的厚度发生变化,基于物理中面与高阶剪切板理论,用多级数Ritz法分析了在径向压力作用下的FGM圆板后屈曲,以及在热场作用下FGM圆板热后屈曲力学行为.并且进一步详细地讨论了不同边界条件、热场、体积分数对后屈曲力学行为的影响.值得特别指出的是,具有可移动简支边界的FGM圆板受边界径向轴力作用在物理中面与几何中面下的后屈曲载荷-挠度曲线结果比较在文献中具有创新性,有助于澄清在文献中所存在的一类典型错误.此外,本文所采用的多级数Ritz法,可以计算屈曲前耦合挠度的影响,该方法具有一定的创新性与优越性,并且值得进一步推广.Mechanical and thermal post-buckling analysis is presented for FGM plates with variation of the temperature dependent properties along thickness direction,using the concept of physical neutral surface and high-order shear deformation theory.Approximate solutions of FGM plates are given using the multi-term Ritz method,and influences played by different boundary conditions,thermal environmental conditions and volume fraction index are discussed in details.Especially,comparisons of post-buckling for FGM plates with movable simply supported edge subjected to compression acting on the geometric middle surface and the physical neutral surface are innovative,and may be helpful to clarify typical mistakes in literature.In addition,the multi-term Ritz method is feasible to calculate the effect of the pre-buckling coupling deflection.This method is innovative,advantageous and worth further popularizing.

关 键 词：功能梯度材料 物理中面 高阶剪切变形理论 后屈曲 多级数Ritz法 

分 类 号：O343.9[理学—固体力学] O302[理学—力学]