New benchmark problems for verification of the curve‐to‐surface contact algorithm based on the generalized Euler–Eytelwein problem

Abstract

Development of the numerical contact algorithms for finite element method usually concerns convergence, mesh dependency, etc. Verification of the numerical contact algorithm usually includes only a few cases due to a limited number of available analytic solutions (e.g., the Hertz solution for cylindrical surfaces). The solution of the generalized Euler-Eytelwein, or the belt friction problem is a stand alone task, recently formulated for a rope laying in sliding equilibrium on an arbitrary surface, opens up to a new set of benchmark problems for the verification of rope/beam to surface/solid contact algorithms. Not only a pulling forces ratio T T 0 , but also the position of a curve on a arbitrary rigid surface withstanding the motion in dragging direction should be verified. Particular situations possessing a closed form solution for ropes and rigid surfaces are analyzed. The verification study is performed employing the specially developed Solid-Beam finite element with both linear and C1-continuous approximations together with the Curve-to-Solid Beam (CTSB) contact algorithm and exemplary employing commercial finite element software. A crucial problem of "contact locking" in contact elements showing stiff behavior despite the good convergence is identified. This problem is resolved within the developed CTSB contact element.

Laboratory Machine Verification of Force Transmission Provided by Friction Acting on the Drive Drum of a Conveyor Belt

“…The Euler-Eytelwein formula, written by Leonhard Euler (1707-1783) and Johann Alber Eytelwein (1764-1848), describes the friction of a flat belt surrounding a cylindrical drum [2]. Konyukhov et al state in [3] that the solution of the generalized Euler-Eytelwein, or the belt friction issue, is a stand-alone task recently formulated for a rope placed in a sliding equilibrium on an arbitrary surface. It brings a new set of benchmark issues for the verification of a rope/beam placed on a surface/solid contact and its algorithms.…”

A beam contact benchmark with analytic solution

“…Moreover, numerical schemes have to be validated by comparing them to a reference. Such validations may rely on analytic solutions to carefully designed, but simple test problems [5]. Therefore, the goal of this paper is to present a benchmark for simulation codes involving beam contact with a closed form analytic solution.…”