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ORIGINAL PAPER
Shape optimization of compressed rods considering material and geometric uncertainty: an analytical – stochastic approach
1
Chair of Building Constructions, Institute od Civil Engineering, University of Zielona Góra, Poland
Submission date: 2025-12-18
Final revision date: 2026-01-19
Acceptance date: 2026-03-26
Online publication date: 2026-07-06
Publication date: 2026-07-06
Corresponding author
Mirosław Sadowski
Chair of Building Constructions, Institute od Civil Engineering, University of Zielona Góra, Poland
Chair of Building Constructions, Institute od Civil Engineering, University of Zielona Góra, Poland
KEYWORDS
shape optimizationreliability indexstochastic analysismaterial and geometric uncertaintyGaussian profile
TOPICS
ABSTRACT
The article presents a stochastic approach to the shape optimization of compressed rods, taking into account random deviations of Young’s modulus and the second moment of area. The parameters are described as stationary random fields with a specified correlation length, and their influence on the critical buckling load is determined using a first-order perturbation expansion. The obtained expressions for the expected value and variance of the critical load made it possible to assess the sensitivity of the structure to local stiffness disturbances. Subsequently, a probabilistic optimization problem was formulated within a family of Gaussian-type profiles, with the aim of minimizing mass while maintaining the required level of reliability. Numerical analysis shows that accounting for uncertainties makes it possible to obtain a rod approximately 12 % lighter than the reference rod, without reducing load-carrying capacity. The presented approach demonstrates that modeling
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