圆形混凝土容器内点铆固圆环的热屈曲分析

Thermal buckling analysis of a point-anchored circular ring surrounded by a concrete cylinder

基于初始后屈曲理论的变分原理，导出了圆拱在均匀压力作用下弹性失稳的中性平衡方程，并计算了圆拱反对称屈曲的临界压力，得到了与经典解一致的结果。根据稳定的能量准则，研究了点铆固于圆形混凝土容器内壁上的圆环均匀受热的屈曲问题，给出了临界温度的解析表达式。算例表明，计算的临界温度与大挠度理论计算结果非常吻合，与实验结果符合也较好。给出的解析式同时适用于两铆栓间全域屈曲和局部屈曲的计算。

Based on the variational principle of initial post-buckling theory, the neutral equilibrium equation of the arch under uniform compression is derived. The critical load of the arch with the antisymmetric buckling mode is calculated and found to be identical with the classic solution. According to the energy criterion of stability, the thermal buckling problem of a point-anchored circular ring surrounded by a concrete cylinder is investigated. The analytical solution for the critical temperature is given. The numerical example shows that the critical temperature calculated by the formula in this paper is approximately the same as that calculated by the large deflection theory and is in good agreement with the experimental result. The analytical solution is suitable for calculating critical temperatures of both overall and local bucklings of the ring between two anchors.