Stability of a Compressed Bar Resting on an Elastic Substrate with Stepwise Changes in Parameters

The study presents a stability analysis of an axially compressed column resting on a Winkler foundation with a stepwise variation in stiffness. The solution is based on an energy approach using the Rayleigh quotient, and the original buckling mode function is proposed to capture the localization of deformations in the region of foundation discontinuity. The theoretical model was verified numerically for rectangular-section columns by comparing the results with simulations performed in COSMOS/M and ABAQUS systems. The differences in critical load values did not exceed 1.7%. The investigation showed that increasing the stiffness contrast leads to stronger buckling localization within the weaker foundation segment. The developed model can be used for preliminary assessment of the load-carrying capacity of structural elements interacting with a non-homogeneous distributed foundation.