@misc{Sadowski_Mirosław_Shape,
 author={Sadowski, Mirosław},
 howpublished={online},
 publisher={Zielona Góra: Uniwersytet Zielonogórski},
 language={eng},
 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.},
 abstract={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},
 title={Shape optimization of compressed rods considering material and geometric uncertainty: an analytical - stochastic approach},
 type={artykuł},
 keywords={stochastic analysis, Rayleigh quotient, material and geometric uncertainty, shape optimization, Gaussian profile, Reliability Index, Wolfram Mathematica, buckling},
}