微分求积方法对于桩基大变形分析的应用

Application of Differential Quadrature Method for Large Deformation Analysis of Piles

本文基于大变形的理论,采用弧坐标首先建立了具有初始位移的桩基的非线性数学模型,一组强非线性的微分-积分方程,其中,地基的抗力采用了Winkeler模型;其次,引入变数变换将微分-积分方程转化为一组非线性微分方程,并用微分求积方法离散了方程组,得到一组离散化的非线性代数方程;最后用Newton-Raphson迭代方法对离散化方程进行了求解,得到了桩基变形前后的构形、弯矩和剪力。计算中选取了两种不同类型的初始位移,并考察了它们对桩基大变形力学行为的影响。

Following the theory of large deformations, a mathematical model for nonlinear analysis of piles with an initial displacement on an elastic foundation was first presented by arc coordinate. This is a system of strong nonlinear differential-integral-equations, in which, the Winkeler model was used to simulate the counterforce of foundation. Then, the differential-integral-equations were transformed into a system of nonlinear differential equations by introducing variable transform. The differential quadrature method was applied to discretize the system of differential equations and the set of discretization algebraic equations were educed. Finally, the Newton-Raphson iterative method was used to solve the set of discretization algebraic equations and to obtain the configuration, bending moment and shear force of deformed piles. In the calculation, two initial displacements were considered and the effects of parameters on the mechanical behaviors of pile were considered.