A meshfree method for beams on elastic foundation

This article presents meshfree analysis for beams on elastic foundation. The elastic supports can be found in a variety of engineering problems, for example in the case of actual foundations or in the case of railroad track. Any constitutive model may be used for simulating the action of the soil media. Currently, the finite element method (FEM) is being used to model the beams on elastic foundations by representing continuity of the soil medium. In this paper, an attempt has been made to provide a simple but sufficiently accurate model for beams on elastic foundation using a meshfree technique, called the element free Galerkin method (EFGM) that does not rely on mesh. The formulation for the beams on elastic foundation is given for the governing equation, which treats the soil in the form of rows of closely spaced independent elastic springs. Generalized moving least square (GMLS) approximants are used in the EFGM to approximate the state variables. Numerical examples are provided to study the convergence with various loading and boundary conditions. The results of the proposed method are compared with the analytical solutions.