Abstract :
The concept of beam on an elastic foundation has been extensively used by geotechnical
engineers for foundation design and analysis. However, most numerical solutions for beam on an elastic
foundation are obtained by mesh based methods, such as finite element or finite difference methods. Mesh
based methods suffer from some deficiencies, mostly related to mesh definition. In this paper, a mesh-free
method, called the radial point interpolation method, is implemented for the analysis of a beam on two
parameter elastic foundation. The beam and the elastic foundation are modeled separately. The geometry
of the beam is simulated by a set of nodes that are aligned on two or three parallel lines. The displacement
field along the beam is constructed by radial basis functions, and the discretized system of equations is
derived by substitution of the displacement field into the weak form of the governing equation. The elastic
foundation is simulated by the concept of the linkage element and there is no need for nodes or elements
in the traditional sense. The stiffness of the foundation has been taken into account by defining normal
and tangential stiffness coefficients along the foundation layer. The displacement of each point across the
foundation layer is tied to the displacement of the beam nodes. The final system of equations is derived by
a combination of equations for both the beam and the elastic foundation in the global coordinate. Based
on the derived equations, a computer code has been developed and the results of analysis with the mesh-
free method are compared with the results of the exact solution and results obtained from finite element
analysis.
