One Discrete Element vs. Two Finite Elements and the Arbelos of Archimedes

Abstract

In this article, a visual proof is given that for a certain simple, yet analytically challenging mechanical system a unique solution exists, which can be found by simple fixed-point iteration as easily to be performed by the reader. As turns out, this system is mostly intractable by means of the finite element method, yet being easily manageable by means of the distinct/discrete element method. Thus, this article gives evidence to the assumption that systems exist which may yield almost arbitrarily wrong results when treated with the finite element method, while giving arbitrarily accurate results when handled by means of the discrete element or similar method.

Full Paper