求解具有弹性接头桩基动力学大变形的微分-代数方法

Differential-algebraic Approach for Solving Dynamic Large Deformation of Piles with Elastic Joints

本文采用弧坐标首先建立了求解具有弹性接头的桩基大变形分析的非线性动力学微分方程,其中,广义Winkler模型用来模拟土对桩基的抗力。其次,在空间域内应用微分求积单元法来离散非线性微分方程组,并给出了处理弹性接头处连接条件的微分求积单元公式,得到了时间域内的一组微分-代数方程,采用二阶向后差分来代替二阶时间导数离散微分-代数方程组,得到一组离散化的非线性代数方程,应用Newton-Raphson方法求解了该非线性代数方程组。最后给出了数值算例,得到了桩基在顶部处受到组合动载荷作用时的响应,考察了弹性接头的刚度、位置对桩基动力学行为的影响。

A set of dynamic differential equations of were first formulized by arc-coordinates, in which, soil resistance. The differential quadrature element large deformation analysis of piles with elastic joints a generalized Winkler model was used to simulate the method was applied to discretize the nonlinear differential equations in the spatial domain, and the differential quadrature element formulas were presented to deal with the discontinuity conditions at elastic joints. A set of nonlinear differential-algebra equations were obtained in the temporal domain. The second order backward differentiation scheme was applied to discretize the set of equations and a system of nonlinear algebraic equations were yielded. Newton-Raphson method was used to solve the set of discretization algebraic equations at each time step. Finally, the numerical examples were pressented and the dynamical responses of piles were analyzed under dynamic loads. The effects of rigidity and the position of elastic joints on the dynamical mechanical characteristics of piles were considered.