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本文由虚功原理建立弹性圆拱的平衡方程,用有限差分法对非线性偏微分方程组进行求解(Park法对时间进行差分)。在考虑几何非线性和初始几何缺陷情况下对铰支、固支圆拱在均布突加阶跃荷载作用下的动力稳定性进行分析。结果表明:圆拱中心角的大小、边界条件及初始缺陷幅值都对圆拱失稳模态有影响。文中分析了直接、间接两种失稳形式。并给出了不同初始缺陷及边界条件下圆拱中心角对比值Pd/Pa(Pd为动力稳定临界值,Ps为静力稳定临界值)的影响。
In this paper, the equilibrium equations of the elastic circular arch are established by the principle of virtual work, and the nonlinear partial differential equations are solved by the finite difference method (the Park method differentiates the time). The dynamic stability of hinged and fixed-arched circular arches under the action of uniform step load is analyzed under geometric nonlinearity and initial geometrical defects. The results show that the size of the central angle of the circular arch, the boundary conditions and the initial flaw amplitude all have an effect on the instability mode of the circular arch. This article analyzes two direct and indirect forms of instability. The influences of Pd/Pa (Pd is the dynamic stability critical value and Ps is the static stability critical value) of the central angle of the arch under different initial defects and boundary conditions are given.