COMPARATIVE ANALYSIS OF SHORT AND LONG BEAMS ON ELASTIC FOUNDATIONS USING KRYLOV FUNCTIONS AND EXPONENTIALLY DECAYING BOUNDARY SOLUTIONS

This paper presents a comparative study of short and long beams resting on a Winkler elastic foundation. Two characteristic cases distinguished by the dimensionless length parameter λ are considered. This parameter defines the relationship between the beam length, flexural rigidity, and foundation stiffness. For the short beam, the analytical solution is obtained using Krylov functions, which enable accurate consideration of boundary-condition effects along the entire beam length. For the long beam, the solution is represented as the sum of a steady-state component and an exponentially decaying boundary effect. Deflections, rotations, bending moments, and shear forces are compared for both cases. The results demonstrate that an increase in the dimensionless length parameter leads to localization of boundary effects and the formation of a central zone with an almost uniform stress–strain state. The obtained results make it possible to determine the applicability limits of different analytical approaches for beams resting on elastic foundations.