@misc{Sadowski_Mirosław_Analytical,
 author={Sadowski, Mirosław},
 howpublished={online},
 publisher={Zielona Góra: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego},
 language={eng},
 abstract={The paper presents an analytical framework for the classification of buckling problems of compressed rods with variable bending stiffness. The governing Euler?Bernoulli stability equation with spatially varying coeffi-cients is transformed into a Sturm?Liouville form and further reduced to a Schrödinger-type equation using the Liouville transformation. This formulation establishes a direct correspondence between the bending stiffness distribution and the associated spectral problem, allowing a systematic mapping of stiffness profiles to classes of differential equations.},
 abstract={Depending on the resulting Liouville potential, the eigenvalue problems can be ex-pressed in terms of classical special functions such as Airy, Bessel, Hermite, or error-function-based solutions. The proposed approach provides a unified classification of variable-stiffness buckling problems within a single operator framework and organizes known analytical results as special cases of a general spectral formulation. The study focuses on analytical structure and classification rather than on optimization procedures, and it does not assume or solve a shape optimization problem.},
 title={Analytical Classification of Buckling Problems of Compressed Rods With Variable Bending Stiffness Using Special Functions},
 type={artykuł},
 keywords={elastic stability, variable bending stiffness, special functions, Euler-Lagrange equation, Sturm-Li-ouville equation},
}