复杂荷载及边界条件下基桩有限杆单元方法研究

Study on applying finite pole element method to analysis of piles under complex loads with different boundary restraints

基于传统有限杆单元法并假定桩身位移为三次幂函数,结合倾斜偏心荷载下单桩受力微分方程确定的桩身弯矩、剪力与桩身水平位移关系,导得了具有简洁统一形式、计入P-Δ效应的杆单元刚度矩阵,由此得出成层地基中倾斜偏心荷载、桩自重、水平分布荷载、竖向分布荷载和竖向分散集中荷载综合作用下考虑桩身倾斜影响基桩内力位移分析的改进有限杆单元法。利用本文改进有限杆单元Matlab分析程序,结合某具体实例,对不同边界条件下基桩内力及位移进行了计算分析。结果表明:改进有限杆单元方法用于复杂荷载及各种边界条件下基桩计算分析是有效的,且桩顶边界条件对桩身内力位移影响显著,而桩端边界条件对桩身内力位移影响较小。

Assumed that horizontal displacement of piles was a longitudinally cubic power function, improved pole element equation with consideration of P-Δ effect was derived from the traditional finite element method incorporating the moment/ horizontal-displacement relationship and shear/horizontal-displacement relationship inferred from differential equation of piles under inclined and eccentric loads. And then the improved pole element method was presented to calculate displacement and stress of piles under inclined and eccentric loads, moments, weight of piles, horizontal and vertical distributed loads, scattering vertical forces and soil-pile friction considering the effect generated by slight inclination of piles. Case study was done for displacement and stress calculation of piles under different boundary restraints with the Matlab process edited with the improved finite pole element method. Finally conclusions were drawn as follows： （i） the improved finite pole element method was proved to be an effective method for pile analysis under complex loads with different boundary restraints; （ii） there would be great difference between the calculated results of displacement and stress of piles with different pile head restraints, while there would be little difference between the calculated results of displacement and stress of piles with different pile tip restraints.