On Λ-fractional buckling and post-buckling of beams

Abstract

Buckling of axially loaded beams is discussed in the context of Λ-fractional analysis and mechanics. An axially compressed cantilever beam is considered in the Λ-fractional space, and the critical load is defined. The variational buckling problem of the simply supported beam is considered in the Λ-fractional space. It is pointed out that the Euler–Lagrange equation corresponding to the minimization of the total energy function with the Weierstrass–Erdmann conditions is only acceptable. The Λ-fractional buckling elastic curve of a simply supported beam is presented. That elastic curve is transferred into the initial space. The post-critical buckling deformations are defined in the context of globally stable equilibrium deformations.