Mixed Eulerian–Lagrangian description in the statics of a flexible belt with tension and bending hanging on two pulleys

Studying the mechanics of thin, axially moving strings, beams or plates (e.g.: belt drives, cable cars, …) at mixed Eulerian–Lagrangian description, which features the transformation of material coordinates to spatial ones, is more appropriate than the classical material (Lagrangian) one, see [1, 2]. Aiming at testing a newly proposed non‐material finite element formulation we study the statics of a looped belt as a rod hanging in contact with two pulleys. Numerical experiments demonstrate rapid mesh convergence as well as correspondence to semi‐analytical results and conventional Lagrangian finite element solutions.