液化场地中Timoshenko桩自由振动与屈曲的精确数值解

基于单桩的Timoshenko梁模型和桩-土相互作用的Winkler模型，建立考虑轴力效应的具有分布参数的Timoshenko梁模型微分控制方程，确定对应的齐次方程的通解，并以此作为有限单元的基函数。推导得精确形函数矩阵，建立分布参数Timoshenko梁的精确有限单元，根据拉格朗日方程得到有限元离散方程和单元刚度矩阵、几何刚度矩阵和一致质量矩阵。应用建立的精确Timoshenko梁单元于分层液化土中单桩-土-结构系统的自由振动与屈曲模态分析，通过与对应解析解以及常规有限元解的对比，表明精确Timoshenko桩基础单元的可靠性与较常规有限元法的优势。

EXACT NUMERICAL SOLUTIONS FOR VIBRATION AND BUCKLING OF A TIMOSHENKO PILE IN LIQUEFIED DEPOSIT

Differential equations governing an axial force-loaded Timoshenko beam with distributing parameters are derived, based on Timoshenko beam theory and a Winkler model that describes the interaction between a pile and soil. And the corresponding solutions for the homogeneous equations, served as the basis functions of the exact finite element, are obtained. Thus, matrices of shape functions are formulated, and an exact finite element for a Timoshenko beam with distributing parameters is constructed. According to Lagrange#x02019;s equations, the discrete finite element equations, element stiffness matrix, geometric stiffness matrix and consistent mass matrix are formulated. Applying the derived exact Timoshenko FEM (Finite Element Method), conventional FEM and corresponding analytical method respectively, to solve the free vibration and buckling problems of a single pile in a deposit of layered liquefiable soils. Comparison shows the reliability and superiority of the exact Timoshenko pile finite element.