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

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 cylind...

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Veröffentlicht in:International journal for numerical methods in engineering Jg. 123; H. 2; S. 411 - 443
Hauptverfasser: Konyukhov, Alexander, Shala, Shqipron
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Hoboken, USA John Wiley & Sons, Inc 30.01.2022
Wiley Subscription Services, Inc
Schlagworte:
"contact locking"
Algorithms
arbitrary surfaces
belt friction problem
Benchmarks
Convergence
Curve‐to‐Solid beam contact
Exact solutions
Finite element method
generalized Euler–Eytelwein problem
Locking
Rope
ropes/beams to surface contact
Verification
ISSN:0029-5981, 1097-0207
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Zusammenfassung: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 TT0, 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.
Bibliographie:ObjectType-Article-1
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6861