具有初始缺陷弹性板的稳定性分析  

Analysis of Stability on Elastic Plates with lnitial lmperfections

作　　者：徐凯宇[1] 

机构地区：[1]上海大学,上海市应用数学和力学研究所

出　　处：《应用数学和力学》1995年第10期887-894,共8页Applied Mathematics and Mechanics

摘　　要：本文以Ｍａｒｇｕｅｒｒｅ方程为基础，用奇异性理论研究了初始挠度缺陷以及横向载荷对弹性板屈曲后分叉解的影响。借助于普适开折的原理，在单特征值局部邻域内将该问题的失稳分析转化为三次代数方程的讨论，从而确定出分叉解的性态。同时绘出了在不同参数下的分叉解文，讨论了几何缺陷和横向载荷对特征值的影响。On the basis of Marguerre equations, the influence on a bifurcation diagram of an elastic plate affected by initial deflection imperfection and transverse loading is studied with the help of the singularity theory. This paper applies universal unfolding principles:it is put forward that the unstable analysis of this problem can transform into the study of a triple algebraic equation in theneighborhood of a simple eigenvalue. Thus the bifurcated states are decided,and the bifurcation diagrams are drawn up following distinct parameters.Then the quantitative series of interfering with eigenvalues are discussed.

关 键 词：缺陷 特征值 弹性板 稳定性 板 挠度 

分 类 号：O343.9[理学—固体力学]