Readdressing the classic falling U-chain problem by a modular nonlinear FEM approach

Abstract

This paper uses a classical one-dimensional single-DOF model of the falling U-chain as an analytical paradigm for the assessment of a recursive modular modeling methodology, in which constraints can be enforced a posteriori. A two-dimensional nonlinear FEM model for the falling of an inextensible folded string is derived, and a numerical simulation is compared with the adopted paradigm. The proposed model not only reproduces with great accuracy the results obtained from the analytical paradigm, but also shows interesting features of this strongly nonlinear problem that might not be revealed by classical single-DOF models.