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New benchmark problems for verification of the curve‐to‐surface contact algorithm based on the generalized Euler–Eytelwein problem
Author(s) -
Konyukhov Alexander,
Shala Shqipron
Publication year - 2021
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6861
Subject(s) - finite element method , algorithm , surface (topology) , convergence (economics) , rope , benchmark (surveying) , beam (structure) , mathematics , computer science , mathematical analysis , geometry , structural engineering , engineering , geodesy , geography , economics , economic growth
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 ratioTT 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 C 1 ‐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.