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

Area of Science:

• Structural Engineering
• Solid Mechanics
• Geotechnical Engineering

Background:

• Axially compressed columns are critical structural elements.
• Winkler foundations are commonly used to model soil-structure interaction.
• Non-homogeneous foundations introduce complex stability challenges.

Purpose of the Study:

• To analyze the stability of axially compressed columns on Winkler foundations with stepwise stiffness variations.
• To develop a theoretical model for predicting buckling behavior and deformation localization.
• To validate the model against numerical simulations.

Main Methods:

• Energy approach utilizing the Rayleigh quotient.
• Development of an original buckling mode function to capture deformation localization.
• Numerical verification using finite element analysis software (COSMOS/M, ABAQUS).

Main Results:

• The theoretical model accurately predicts critical load values, with discrepancies under 1.7% compared to numerical simulations.
• Increasing stiffness contrast between foundation segments enhances buckling localization in the weaker segment.
• The proposed buckling mode function effectively captures localized deformations at foundation discontinuities.

Conclusions:

• The developed energy-based model provides a reliable method for analyzing column stability on non-homogeneous Winkler foundations.
• Buckling localization is a significant phenomenon influenced by foundation stiffness variations.
• The model is suitable for preliminary assessments of load-carrying capacity in structural elements with distributed, non-uniform foundations.