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研究了跨中在集中荷载作用下的两端采用不同径向、轴向弹性约束的圆弧拱的面内稳定性。利用拱结构的变形几何关系和能量变分原理推导了圆弧拱考虑外部集中力、弹性约束边界时的非线性平衡方程,建立了外荷载、结构内力、径向位移三者之间的对应关系,通过定义拱的深浅参数和约束刚度参数对屈曲过程中的荷载-内力、荷载-位移曲线进行了分析,通过屈曲分析进而得到圆弧拱发生失稳时的临界荷载。结果表明:本文方法所得屈曲路径、屈曲荷载与有限元法所得结论吻合良好;另一方面,对集中荷载作用下圆弧拱采用不同径向、轴向弹性约束刚度和结构的深浅程度等结构参数时的屈曲路径、临界荷载进行了分析,结果表明约束刚度和深浅参数对面内稳定性影响显著。
The in-plane stability of arc arch with different radial and axial elastic constraints at both ends under concentrated load is studied. Based on the deformation geometry and the principle of energy variation of the arch structure, the nonlinear equilibrium equation of the circular arch considering the external concentrated force and the elastic constrained boundary is deduced, and the corresponding relationship among the external load, the internal force of the structure and the radial displacement is established The load - internal force and load - displacement curve during buckling are analyzed by defining the parameters of the depth and the restraining stiffness of the arch, and then the critical loads of the circular arc arch are obtained by buckling analysis. The results show that the buckling paths and buckling loads obtained by this method are in good agreement with the conclusions obtained by the finite element method. On the other hand, the structural parameters such as different radial and axial elastic restraint stiffness, When the buckling path, the critical load is analyzed, the results show that the constraint stiffness and depth parameters have a significant impact on the in-plane stability.