弹性圆拱在考虑几何非线性和初始缺陷情况下的动力稳定性分析

The Dynamic Elastic Buckling Analysis of Circular Arch with Finite Displacement and Initial Imperfection

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。

The equilibrium equations of elastic circular arches are established using the principle of virtual work. The nonlinear partial differential equations of motion are solved using a finite difference method (Park's method for time difference). The dynamic stability of a hinged and a clamped elastic circular arch with a uniform step load is analyzed with finite deformation and initial imperfection. Results show that the buckling mode varies with the value of the arch half angle, θ0. The boundary condition and initial imperfection amplitude also have effects on the buckling mode. Both the direct and indirect buckling form are discussed. The effect of θ0 on the ratio Pd/Ps(Pdis the dynamic critical load and P,the static critical load. ) is shown for different initial imperfections and different boundary conditions.