Investigation into a knitted loop structure as buckled-twisted elastic rod using finite element method

Abstract

The finite element modeling with nonlinear geometry and static Riks analysis for an elastic rod was employed to estimate the 2D and 3D Elastica shapes under post-buckling condition. The studied case is in ill-condition and the Riks method is useful for unstable cases and can speed up convergence in ill-conditioned problems that do not exhibit instability. Therefore, this method is used in this study. Then, a twisted shape of Elastica was investigated by applying a pair of equal unbalancing twisted torques to the ends of a 2D Elastica shape using finite element analysis (static analysis). Static method that is implicit, accurate and limited to simple issues without complex contacts is used in this study. Problem analysis with the FEM software is easier and faster than the analytical solution and simplified assumption can be reduced for achieving more perfect models in future research. An experimental method was designed to calculate aspect ratios of base and twisted Elastica forms. Low density polyethylene (LDPE) due to availability and uniformity of the produced rod has been used in experiments and therefore LPDE properties are used in the modeling software. At the end, being compared together, the experimental and theoretical aspect ratios were in good agreement.

Keywords

Finite Element Method, Knitted Loop, Twist and Buckling, 3D Elastica, Loop Geometry