弹性圆底扁球壳在边缘均布力矩作用下的非线性稳定问题

叶开沅; 刘人怀; 张传智; 徐一帆

弹性圆底扁球壳在边缘均布力矩作用下的非线性稳定问题

甘肃兰州大学

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出版历程
- 收稿日期: 1978-11-01
- 刊出日期: 1980-02-15

Nonlinear Stability of Thin Elastic Circular Shallow Spherical Shell under the Action of Uniform Edge Moment

Lanchow University

摘要

摘要: 本文对边缘简单支承在边缘均布力矩作用下的弹性圆底扁薄球壳的非线性问题进行了研究.用我们提出的修正迭代法求出决定上下临界载荷的二次和三次近似方程.结果画成曲线以供工程应用.并将此结果和胡海昌的结果进行了比较,我们还研究了临界点,即上下临界载荷相重点附近的情况,并指出二次近似的适用范围.文末还附带得出本问题的特殊情况:相同边缘支承和载荷下的圆平板大挠度问题的刚度设计公式及p=0.3的相应曲线,并与黄择言用摄动法得到的结果进行了比较.

Abstract: In 1939. the importance of the nonlinear feature in the shell buckling problem was first pointed out in a most spectacular manner by von Karman and Tsien,but the mathematical difficulty is so great that progress has been slow after the first attempts.According to our experience, we should face the difficult barrier of solving nonlinear differential equations and an effective, simple, accurate method is required.On the other hand, modern rapid developements in technics, such as aeronautical, naval, structure, precise instrument manufacturing and automatic control engineerings require keenly these problems to have accurate, reliable theory results for direct design use, With such background, we suggest the modified iteration method and have worked out four cases for the purpose of certaining it, This is the one, in which nonlinear stability of thin elastic circular shallow spherical shell under the action of uniform edge moment are considered.As a special case, w e also investigate large deflection of circular plate under the same load.

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参考文献(16)

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