中文摘要：

对拱结构的极值点届曲及分支点屈曲进行了详细阐述。利用有限元分析程序ANSYS对拱进行非线性分析，考虑结构屈曲前变形对临界力的影响。选取线性届曲前几阶模态作为扰动位移，对拱的整个受载过程进行跟踪分析，得到拱的屈曲临界力。将矢跨比、跨径及矢高与截面回转半径的比值作为影响参数，分析竖向均布力及径向均布力作用下，无铰拱和两铰拱的届曲性能。分析表明，屈曲前变形降低了坦拱的屈曲临界力，考虑。：阶效应后拱的屈曲临界力与线性届曲临界力的比值，随矢跨比的减小而减小，随跨径的增大而增大；对于矢跨比较小的坦拱，矢高与截面回转半径的比值将决定拱的屈曲形式。

英文摘要：

Snap-through buckling and bifurcation buckling of elastic arches are introduced. Nonlinear Finite Element analysis of arches was performed using FE software ANSYS. Using the first-order bucking modes as displacement perturbations, the effects of pre-buckling displacement on buckling were considered. After tracing the complete load-deflection path of arches, secondary buckling load was obtained. Rise-span ratio, span and the ratio of rise to gyration radius were used as variables to investigate the buckling behavior of end-pinned and fixed arches with uniform distributed radial or vertical loads. The results show that the secondary buckling load of shallow arches was much lower than their linear buckling load. With the decrease of rise-span ratio or span of arches, the ratio of secondary buckling load to linear buckling load decreased. Secondary buckling mode of shallow arches depended on the ratio of rise to gyration radius.