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

## TL;DR

This paper analyzes the stability of a compressed bar on a foundation with varying stiffness, showing how stiffness changes affect buckling behavior.

## Contribution

A new buckling mode function is proposed to capture deformation localization at foundation discontinuities.

## Key findings

- The theoretical model was verified with numerical simulations, showing less than 1.7% difference in critical load values.
- Higher stiffness contrast leads to stronger buckling localization in the weaker foundation segment.
- The model can be used for preliminary assessments of load-carrying capacity in non-homogeneous foundations.

## Abstract

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.