BEM analysis of elastic foundation beams on multilayered isotropic soils

Abstract

This paper presents a boundary element method to analyze the elastic foundation finite beams on 2D plane-strain and 3D multilayered isotropic soils. Starting with the basic equations of elasticity and based on the Fourier transform, the transfer matrix of a single soil layer is derived. According to the boundary conditions and continuity conditions between two adjacent soil layers, the solution of multilayered elastic soils is obtained to be a kernel function of BEM analysis. The elastic foundation beam is modeled as a Bernoulli-Euler beam using the finite difference method. With the displacement and stress condition of coordination between beam and soil, the solution is acquired for beams resting on multilayered soils. Comparing the solution with the published data shows that the solution is in good agreement, and some numerical examples show that the beam behavior is affected vitally by soil-beam stiffness ratio and the stratification of soils.

Finite-Element Analysis of Beam Resting on Footing

“…Beam responses with an accuracy comparable to those obtained from an equivalent two-dimensional (2D) finite-element analysis were obtained within seconds. A boundary element method has been developed [7] to analyse elastic foundation finite beams on 2D plane-strain and 3D multilayer isotropic soils. The authors analysed the solution of multilayer elastic soils, which was a kernel function of a BEM analysis.…”

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

“…Considering soils are naturally layered, Ai et al [20] studied the static behavior of an Euler-Bernoulli beam on two/three-dimensional layered soils by the coupling of finite difference method and the BEM, and later Ai and Cai [21] analyzed the response of a Timoshenko beam on layered soils based on the combination of analytical layer element method and the FEM, where the length of the beam is assumed to be integral multiple of the beam width, which would be restricted.…”

Practical Soil-Shallow Foundation Model for Nonlinear Structural Analysis

“…Incorporation of SSI requires explicit modelling of soilfoundation system adequately. For instance, several models have been proposed depending on the foundation type, its embedment, and its rigidity ( [13][14][15], among others). The Federal Emergency Management Agency [16] required that the foundation stiffness should be determined with one of the following three methods: (i) uncoupled spring model comprising three spring elements, for shallow foundations that are stiffer than the supporting soil; (ii) a finite element formulation of linear (or nonlinear) foundation behavior using Winkler models, for shallow foundations that are less stiff than the supporting soil; (iii) decoupled Winkler model, for shallow foundations that are flexible with respect to the supporting soil.…”