扁拱静力失稳的突变特性及临界荷载分析

The analysis of static bucking catastrophe characteristics and critical load of shallow arches

考虑扁拱的轴向变形,采用能量原理建立了扁拱的平衡方程,将其简化为尖点突变模型的标准形式,得出了扁拱突跳的临界荷载表达式及其稳定的参数范围。以一H型钢截面扁拱为例分析了其在竖向均布荷载作用下平面内的跳跃特性,得到了对应的临界荷载。采用有限元软件对理论分析结果进行了比较,两者具有很好的一致性,并进一步分析了支座条件、材料非线性和拱轴类型对扁拱突跳的影响。分析表明,上突扁拱的临界荷载应取其上极限,拱轴形状对临界荷载的影响不明显,固支约束能够显著提高扁拱的稳定性,数值分析时应考虑材料及几何非线性的影响。

Considering the axial deformation of shallow arch,the equilibrium equation is established based on the energy principle,and is simplified into standard form of cusp catastrophic model.The expression of critical load and the stable range of parameters are further obtained.Taking a shallow arch with H-section steel for example,the jump characteristic in plane is analyzed under vertical uniform load,and the corresponding critical load is acquired.Theoretical analytical results are compared with finite element results and both have good consistency.The influence of the bearing condition,material nonlinearity and arch axis type on shallow jumping is further considered by numerical analysis.The analysis shows that the critical load of shallow arch should be taken its upper limit.The influence of the arch axis shape on the critical load is not obvious.Clamped constraints can significantly improve the stability of the shallow arch.The influence of material and geometric nonlinearity on shallow arch should be considered.