ANALYTICAL SOLUTION OF BEAM ON ELASTIC （在弹性梁的解析解）.pdf

Engineering MECHANICS, Vol. 19, 2012, No. 6, p. 381–392 381 ANALYTICAL SOLUTION OF BEAM ON ELASTIC FOUNDATION BY SINGULARITY FUNCTIONS Dobromir Dinev* 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 con- sidered 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 ap- proach, combined with the resources of the modern computational algebra systems, allows a reliable and effective analysis of beams on an elastic foundation. The nume- rical examples show the applicability and efficiency of the approach for the solution of classical problems of soil-structure interaction. Keywords : beam on elastic foundation, soil-structure interaction, singularity func- tions 1. Introduction The computational model of a beam or a plate on an elastic foundation is often used to describe a lot of engineering problems and has application in geotechnics, road, railroad and marine engineering and bio-mechanics. The key issue in the analysis is modelling the contact between the structural elements- the beam and the soil bed. In most cases the contact is presented by replacing the elastic foundation with simple models, usually spring elements, because the main task is conside