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.