Analysis of beam on elastic foundation using the radial point interpolation method

The concept of beam on an elastic foundation has been extensively used by geotechnicalengineers for foundation design and analysis. however, most numerical solutions for beam on an elasticfoundation are obtained by mesh based methods, such as finite element or finite difference methods. meshbased methods suffer from some deficiencies, mostly related to mesh definition. in this paper, a mesh-freemethod, called the radial point interpolation method, is implemented for the analysis of a beam on twoparameter elastic foundation. the beam and the elastic foundation are modeled separately. the geometryof the beam is simulated by a set of nodes that are aligned on two or three parallel lines. the displacementfield along the beam is constructed by radial basis functions, and the discretized system of equations isderived by substitution of the displacement field into the weak form of the governing equation. the elasticfoundation is simulated by the concept of the linkage element and there is no need for nodes or elementsin the traditional sense. the stiffness of the foundation has been taken into account by defining normaland tangential stiffness coefficients along the foundation layer. the displacement of each point across thefoundation layer is tied to the displacement of the beam nodes. the final system of equations is derived bya combination of equations for both the beam and the elastic foundation in the global coordinate. basedon 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 elementanalysis.