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该文使用一种新的数值跟踪策略对无平面外支撑和有顶点平面外支撑的弹塑性圆管拱的平面外二次分岔屈曲的荷载-位移曲线的全过程进行跟踪分析,得到了跨中集中荷载和全跨均布荷载作用下,相同截面不同矢跨比的拱的平面外弹塑性二次分岔屈曲荷载,将其与平面内二次分岔屈曲荷载比较。计算结果表明:对于具有相同截面的无平面外支撑弹塑性圆管拱,在跨中集中荷载作用下,平面内二次分岔屈曲荷载小于平面外二次分岔屈曲荷载,平面内二次分岔屈曲会先于平面外屈曲发生,矢跨比0.2时平面外二次分岔屈曲荷载最大。全跨均布荷载作用下的拱平面外二次分岔屈曲会先于平面内二次分岔屈曲发生;矢跨比0.3时平面外二次分岔屈曲荷载最大。矢跨比为0.1时,拱的平面内与平面外屈曲荷载相差最大。对于有顶点平面外支撑拱,在集中荷载作用下,支撑对分岔屈曲荷载作用不明显,只是改变了屈曲形式。全跨均布荷载作用下,支撑可以大幅提高全跨均布荷载作用下拱的平面外屈曲荷载,尤其是对矢跨比小的拱的影响更大一些,平面外二次分岔屈曲会先于平面屈曲发生。
In this paper, a new numerical tracking strategy is used to track the whole process of load-displacement curve of out-of-plane second-order bifurcation buckling of out-of-plane support and elasto-plastic pipe arch with apex out-plane support. In the case of concentrated load and full span uniform load, the out-of-plane elastic-plastic bifurcated buckling load of arch with different span-wise ratios of the same section is compared with the buckling load of second order bifurcation in plane. The calculation results show that for the elastic-plastic circular pipe arch without outside plane support with the same cross section, the buckling load of the second bifurcation in the plane under the mid-span concentrated load is smaller than the buckling load of the out-of-plane second bifurcation, Bifurcated flexion occurs before out-of-plane flexion, and the buckling load out-of-plane secondary bifurcation is the largest when the sagittal span is 0.2. The out-of-plane second bifurcation buckling under full-span uniform load will precede the in-plane secondary bifurcation buckling, and the out-of-plane second-order bifurcation buckling load is the largest when the sag ratio is 0.3. When the sag ratio is 0.1, the difference between in-plane and out-of-plane buckling loads is the largest. For the arch with out-of-plane support arch, under the action of concentrated load, the support has no obvious effect on bifurcation buckling load, but only changed the buckling mode. Under the condition of full-span uniform load, the support can significantly increase the out-of-plane buckling load of the arch under full-span uniform load, especially for arch with smaller aspect ratio. The out-of-plane secondary bifurcation buckling Occur in plane buckling.