Analytical Classification of Buckling Problems of Compressed Rods With Variable Bending Stiffness Using Special Functions
issued: 2026
type: artykuł
creator: Sadowski, Mirosław
rights: CC 4.0
date: 2026
subject: variable bending stiffness
description: 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.
format: application/pdf
language: eng
description: tytuł dodatkowy: Prace z Inżynierii Lądowej i Środowiska
subject: elastic stability
subject: Euler-Lagrange equation
rights: Biblioteka Uniwersytetu Zielonogórskiego
subject: special functions
subject: Sturm-Li-ouville equation
contributor: Kuczyński, Tadeusz - red.
publisher: Zielona Góra: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
source: Civil and Environmental Engineering Reports (CEER), no 36, vol. 2
description: 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.