弹性桩m法计算的有限单元法

Finite Element Analysis of Elastic Piles by m Method

基于经典梁理论和文克尔地基的基本假定,构造了适用于弹性桩m法计算的两节点桩基单元,并基于虚功原理推导了单元刚度矩阵的表达式。该单元在任意位置处的横向挠曲变形由Hermite插值函数得到,在单元交界面处满足C1连续性。通过引入沿桩基轴向分布的横向约束刚度,土体对桩基的作用力与单元线位移和角位移自由度均相关,使单元可更准确地模拟土对桩基的约束作用。算例表明,桩基单元相对传统有限元法在系统自由度不变的情况下可获得更高的求解精度和计算效率,具有更好的工程实用性。

This paper presents a numerical method of calculating the response of elastic pile subjected to the lateral and axial compressive loadings.A new C1 continuous two node pile element formulation,which is based on a displacement formulation,is developed by using the assumptions of conventional beam theory and Winkler elastic foundation.Based on the incremental form of the virtual work,the element stiffness matrix can be derived.The interaction between the pile and the surrounding soil is modeled as a Euler-Bernoulli beam with the distributed lateral springs.The proposed method simulates the laterally loaded pile response more accurately than that of the conventional discrete element model using element-end springs to represent the surrounding soils.A good agreement is obtained between the numerical results of the current element and the reference solutions.The proposed analytical methodology gives an exact solution at the nodes even for a coarse mesh.