扁球壳在热-机械荷载作用下的稳定性分析

Thermomechanical Stability Analysis of Shallow Spherical Shells

基于扁壳几何非线性理论,应用虚功原理和变分法推导了均匀变温场中圆底扁薄球壳在均布外侧压力作用下的位移型几何非线性控制方程.考虑周边不可移简支边界条件,运用打靶法计算获得了不同几何参数的扁球壳轴对称弯曲变形的数值结果.定义了壳体临界几何参数.考察了壳体几何参数对平衡路径和临界荷载的影响.当壳体几何参数大于壳体临界几何参数时,上临界荷载随几何参数的增加单调增加,下临界荷载在很小范围内随几何参数的增加而增加,之后随几何参数的增加而减小.给定几何参数时,考察了不同均匀温度变化对壳体临界几何参数、临界荷载和平衡构型的影响.均匀升温使上临界荷载显著增加,使下临界荷载和临界几何参数显著减小.

Based on the geometric nonlinear theory for shallow shells,with the virtual work principle and the variational method,the displacement-type geometric nonlinear governing equations for shallow spherical shells in uniform temperature field under uniform external pressure were derived. With the shooting method,the numerical results of axisymmetric bending deformation of the shallow spherical shell in the immovable simply supported boundary condition were obtained. The critical geometric parameters were defined.The effects of various shell geometric parameters on the equilibrium paths and the critical loads were investigated. It is found that the upper critical load increases but the lower critical load first increases in a small range and then decreases with the geometric parameter in the range beyond its critical value. The effects of different values of the uniform temperature on the shell critical geometric parameter,the critical load and the equilibrium configurations were investigated under a given geometric parameter. Rise of the uniform temperature brings obvious increase of the upper critical load and obvious decrease of the lower critical load and the critical geometric parameter.