Static interaction analysis between a Timoshenko beam and layered soils by analytical layer element/boundary element method coupling

Abstract

This paper presents the analytical layer element/boundary element method coupling theory for the static interaction analysis between a Timoshenko beam and layered soils. The boundary integral equations for a Timoshenko beam are established by taking the fundamental solutions of a static infinite Timoshenko beam as the kernel functions. The Timoshenko beam and the foundation reaction area are properly divided, and the distribution of the foundation reaction for each part of the reaction area is assumed to be uniform. With the application of the boundary integral equations of the Timoshenko beam to each beam node, the BEM matrices of the beam are obtained. The flexibility matrix of the subgrade is obtained with Gaussian quadrature of the fundamental solution of the stratified soils by analytical layer element. Combining the above BEM matrices for the beam and the flexibility matrix of the soils, the global boundary integral equations for the soils-Timoshenko beam system are established with the compatible condition of the settlement at the interface. A program is compiled according to the proposed theory and a comparison of the results between this theory and existing reference or the ABAQUS FEM modeling is carried out, which shows the accuracy and efficiency of the theory. Some numerical examples show that the static behavior of soil–beam system is significantly influenced by the beam–soil stiffness ratio, the thickness of the first soil layer and the layered characteristics of soils.