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对竖向均布荷载作用下固接抛物线浅拱进行了平面内稳定性分析.利用虚功原理对浅拱建立了非线性平衡条件和非线性屈曲方程,得到了均布荷载作用抛物线浅拱的反对称分岔失稳以及对称跃越失稳模式下的解析解以及区分不同失稳模式的拱的修正长细比临界值.为了简化求解临界荷载的过程,利用最小二乘原理得到了对称跃越失稳临界荷载的近似解.通过有限元分析与理论解的对比验证了理论解的正确性.最后给出了一种提高拱面内性能的索拱结构形式,分析结果表明:随着拱修正长细比的提高,索对拱结构面内稳定性能提高的作用越明显.
The in-plane stability analysis of shallow parabolas attached to a uniformly distributed vertical load is carried out.The nonlinear equilibrium conditions and nonlinear buckling equations are established for the shallow arch using the principle of virtual work, and the parabolic shallow arch with uniform load is obtained The antisymmetric bifurcation instability and the symmetric jump instability model and the modified slenderness ratio critical value of the arch to distinguish different instability modes.In order to simplify the process of solving the critical load, The approximate solution of the more unstable critical load is obtained.The comparison between the finite element analysis and the theoretical solution verifies the correctness of the theoretical solution.Finally, an arch structure is proposed to improve the performance of the arch surface. The analysis results show that with the arch The improvement of the slenderness ratio, the more obvious the effect of the cable on the improvement of the in-plane stability of the arch structure.