非线性弹性土中桩基的屈曲和后屈曲分析

Analysis of Buckling and Post-Buckling for Piles in Non-Linear Elastic Soils

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。

A single pile was regarded as an elastic beam-column structure embedded in a nonlinear elastic foundation,and the buckling and post-buckling for a pile subjected to the distributed loads and an end axial force was studied. Firstly,a nonlinear mathematical model for analyzing the mechanical behaviors of elas-tic piles was presented under the case of a moderate finite deformation. Secondly, the nonlinear stability of a pile with the three different boundary conditions was studied,and the stability problems were respective- ly transformed into the corresponding bifurcation problems of finite dimensional equations by using the shooting method. Finally, based on the singularity theory and the numerical calculation method of bifurca-tion problems,a new numerical method was presented to calculate the bifurcation solutions for the corre-sponding bifurcation problems, and the corresponding pre-buckling states（trivial solutions）, critical loads （bifurcation points） and post-buckling states（bifurcation solutions）as well as the post-buckling equilibrium paths were all obtained successfully and compared.