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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 ,改善了微小变形几何分析方法的不足之处
Based on the theory of additional deformation field on the initial stress form, the governing equations of elastic buckling problems and the general form of variational principle are deduced. Under the framework of this theory, the elastic buckling problem of plane arch is obtained through the dimension reduction processing For the critical load condition, the governing equations and the eigenvalues of the corresponding linear homogeneous differential equations (the critical values of the plane buckling and the lateral buckling) are obtained. The analysis results show that for the critical load problem, Compared with the geometric analysis method of establishing control equations, this method has the advantages of rationalization.In the case of geometric complexity such as curved members, the variational equations or governing equations derived by this method are well-defined and improved Shortcomings of the method of geometric analysis of small deformation