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 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. (c) 2012 Sharif University of Technology. Production and hosting by Elsevier B.V. All rights reserved.