elastic stability ; variable bending stiffness ; special functions ; Euler-Lagrange equation ; Sturm-Li-ouville equation
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. ; 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.
Description:tytuł dodatkowy: Prace z Inżynierii Lądowej i Środowiska
Publisher:Zielona Góra: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
Date: Resource Type: Format: DOI: Pages: Source:Civil and Environmental Engineering Reports (CEER), no 36, vol. 2
Language: License: License CC BY 4.0: Rights: