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