stochastic analysis ; Rayleigh quotient ; material and geometric uncertainty ; shape optimization ; Gaussian profile ; Reliability Index ; Wolfram Mathematica ; buckling
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
Wydawca:Zielona Góra: Uniwersytet Zielonogórski
Data wydania: Typ zasobu: Format: DOI: Strony: Źródło:IJAME, volume 31, number 3 (2026)
Jezyk: Licencja: Licencja CC BY-NC-ND 4.0: Prawa do dysponowania publikacją: