中文摘要：

考虑任意载荷作用下变截面柔性构件的变截面特征及变形的非线性问题，建立了任意载荷作用下变截面柔性构件变形求解的二阶非线性微分方程。采用离散化的数值计算方法，利用泰勒级数展开式对微分方程进行求解，给出了求解的一般过程。采用上述方法对承受不同载荷的变截面柔性构件的变形进行了分析，并采用有限元法进行了仿真分析，通过对比所得结果验证了该分析方法与微分方程的正确性。

英文摘要：

The deflection of a variable cross sectional flexible component under arbitrary loads was analysed. The variable cross section and the nonlinear were considered,a second order nonlinear differ- ential equation about deflection of the variable cross sectional compliant component under arbitrary loads was established. The discrete numerical calculation method and Taylor＇s expansions were used to solve the nonlinear differential equation. The variable cross sectional flexible components under dif- ferent loads were analysed with the analysis method obtained from this paper and the finite element method simultaneously,the two results were obtained and contrasted,so the correctness of the analy- sis method and the differential equation were proved.