初应力位形上的附加变形和拱的弹性屈曲

Additional Deformation on Pre-stressed Configuration and Elastic Buckling of an Arch

从初应力位形上的附加变形场论出发 ,导出了弹性屈曲问题的控制方程和变分原理的普遍形式 ,并在该理论框架下 ,对于平面拱的弹性屈曲问题 ,通过降维处理 ,得到了求临界载荷条件的变分方程、控制方程及相应的线性齐次微分方程的特征值 (平面拱面内、侧向屈曲临界值 ) .分析结果表明 ,对于临界载荷问题 ,面内屈曲与侧向屈曲彼此独立 ;与建立控制方程的几何分析方法相比 ,该方法具有理性化的优点 .在曲线形构件等几何复杂情况下 ,按该方法导出的变分方程或控制方程条理清晰 。

According to the field theory of additional deformation on pre-stressed configuration, in the paper, the ordinary expression of the governing equation and variational equation of elastic buckling are mentioned; under the theory system, through lowering dimensions, the governing equation and variational equation for the critical condition solution of elastic buckling of a flat arch are deduced, and the eigenvalues problem (the critical load of flat arch’s plane buckling and lateral buckling) of the linear homogeneous differential equations, corresponding to the equations, are concluded. It shows plane buckling is independent of lateral buckling for critical load problem; compared with the method geometric analysis through building up governing equation,this method the arctic uses is rational.When the investigated objects are complicated structures such as curving structure, the governing equation and variational equation what obtained with this method are less wrong and distinct in logic, and improves the method geometric analysis.