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把桩基视为一种嵌入于非线性弹性土中的梁-柱结构,研究了受轴力和分布力作用的桩基的屈曲和后屈曲。首先,在中等程度的有限变形条件下,建立了分析弹性梁-柱结构力学行为的一般的3维非线性数学模型。其次,作为模型的应用,分析了3种不同端部条件下桩基的非线性稳定性。借助于打靶法,这些稳定性问题被转化为相应的有限维分支方程的分叉问题。最后,根据奇点理论和分支问题的数值计算方法,提出了一种计算相应分叉问题分支解的新的数值计算方法,并成功计算了3种不同端部条件下桩基的前屈曲状态,前3个临界载荷,后屈曲状态,以及相应的后屈曲平衡路径,并进行了比较。
The pile foundation is regarded as a kind of beam-column structure embedded in nonlinear elastic soil, and the buckling and post-buckling of pile foundation subjected to axial force and distributed force are studied. First, a general 3-D nonlinear mathematical model for analyzing the mechanical behavior of the elastic beam-column structure was established under the moderate finite deformation conditions. Secondly, as the application of the model, the nonlinear stability of pile foundation under three different end conditions is analyzed. With the help of the shooting method, these stability problems are transformed into bifurcation problems of the corresponding finite dimensional branch equations. Finally, based on the singularity theory and the numerical calculation method of bifurcation problem, a new numerical method to calculate the bifurcation problem is proposed and the pre-buckling state of the pile foundation under three different end conditions is successfully calculated. The first three critical loads, the post-buckling state, and the corresponding post-buckling equilibrium pathways were compared.