Equilibria determination of elastic articulated duoskelion beams in 2D via a Riks-type algorithm

Abstract

The overall behavior of an articulated beam structure constituted by elements arranged according to a specific chirality is studied. The structure as a whole, due to its slenderness and geometry, is called duoskelion beam. The name duoskelion is a neologism which is inspired by the Greek word δύοσκέλιον (two-legged). A discrete model for shearable beams, formulated recently, is exploited to investigate its mechanics. A purposely designed numerical scheme, adapting the Riks rationale, is used to calculate large displacement and deformation equilibria of duoskelion beams. Aimed at computing the current step correction, the Riks arc-length method is modified and made more efficient by applying a specific orthogonality condition, defined via the stiffness matrix, to an adapted extrapolation step. The robustness of the resulting scheme and its capability to follow equilibrium branches allows, in principle, for the exploration of the whole set of local energy minima in the introduced space of configurations, by using suitably modulated perturbative external loads. The developed numerical tool can be used to understand the mechanics of duoskelion beams. It is proved that there exists a stable principal equilibrium branch in which only compression is observed for any compression load. Additional stable equilibrium branches are found in compression such that the clamped–clamped compressed beam assumes a characteristic S shape which, upon reaching a critical load, is significantly amplified. A mechanically relevant stable equilibrium is also found in extension, being observed the S-shaped configuration experimentally found in Misra et al. (2020).