热环境下圆弧拱的面内非线性屈曲

Nonlinear In-plane Instability of Circular Arch in Thermal Environment

为了避免拱在热环境下的失稳,以热环境下固接圆弧拱为研究对象,分析了其在拱顶径向集中力下的面内非线性屈曲行为,基于能量变分原理,建立了非线性平衡微分方程,跟踪了屈曲平衡路径,得到了拱的极值点屈曲和分岔屈曲荷载的理论解析解。并采用有限元数值结果验证了理论解的准确性,揭示了在热环境和集中力作用下拱的非线性极值点屈曲与分岔屈曲行为的区别与联系。研究结果表明:集中力作用下温度显著影响圆弧拱的非线性屈曲行为,极值点屈曲和分岔屈曲荷载随着温度的升高而增大;拱的上下极值点荷载随修正长细比的增大而增大;分岔屈曲最大温差随着修正长细比的增大而急速减小。

In order to avoid the instability of arch in thermal environment,the nonlinear in-plane instability of a fixed circular arch under a central radial concentrated load in thermal environment was studied.The nonlinear equilibrium equations and buckling equilibrium equations were derived by the minimum potential principle.The theoretical solutions of the limit buckling and bifurcation buckling loads were then obtained and verified by the ANSYS software finite element results.The nonlinear limit point instability and the bifurcation instability behavior of the arch was investigated.The results show that the temperatures have a significant effect on the nonlinear instability behavior of an arch.The limit instability loads and bifurcation instability loads increase with the rise of the temperature.The upper and lower limit point instability loads decrease with a decrease of the modified slenderness.It is also found that the maximum temperature difference for bifurcation bucking decreases rapidly with the increase of the slenderness.