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ANALYTICAL SOLUTION OF BEAM ON ELASTIC FOUNDATION BY SINGULARITY FUNCTIONS

The paper deals with a new manner of obtaining a closed-form analytical solution of the problem of bending of a beam on an elastic foundation. The basic equations are obtained by a variational formulation based on the minimum of the total potential energy functional. The basic methods for solving the governing equations are considered and their advantages and disadvantages are analyzed. The author proposes a felicitous approach for solving the equilibrium equation and applying the boundary conditions by transformation of the loading using singularity functions. This approach, combined with the resources of the modern computational algebra systems, allows a reliable and effective analysis of beams on an elastic foundation. The numerical examples show the applicability and efficiency of the approach for the solution of classical problems of soil-structure interaction.