Perturbation analysis of internally constrained beams subjected to large longitudinal force

In this paper, the development and application of a perturbation technique is carried out to analyze the behavior of unshearable and inextensible planar beams, with specific attention to the buckling phenomenon and to the application of prescribed shortening, under different boundary conditions. The mechanical model is driven from the literature and revisited in order to specifically address the case of large longitudinal force, which naturally arises in the considered applications. The problem is tackled by deriving an analytical solution, accounting for a proper scaling and expansion of the variables, depending on the considered case (namely, free or prescribed shortening). The mechanical response is then systematically compared to a numerical solution derived via a finite difference approach, showing an excellent agreement within the considered ranges.