【摘要】 本文通过变分原理建立圆拱的平衡方程。用有限差分法求解非线性微分方程组。在考虑有限变形和几何初始缺陷的情况下分析了两铰弹性圆拱在垂直于拱轴均布荷载作用下的静力稳定性,用双参数确定了Timoshenko公式以及扁拱理论的适用范围;提出了计算扁圆拱静力稳定临界值的公式;讨论了静力失稳模态;分析了初始缺陷对静力稳定临界值的影响;并发现当γ<0.7时扁圆拱不发生失稳。更多还原

【Abstract】 The equilibrium equations of elastic circular arch are established with the principle of variation. The nonlinear differential equations are solved using finite difference method. The static stability of a two-hinged elastic circular arch with finite deformation and initial imperfections under hydraustatic loading is analyzed. The effective ranges of the formulae for calculating the critical load from Timoshenko’s theory and shallow arch theory are given with two parameters. A new formula is provided in this paper to calculate the static critical load of shallow arches. The static buckling modes and the effects of initial inperfections on critical load are discussed. It is found that when γ<0.7, no buckling will happen.更多还原