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 |
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| 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 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. |
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| AbstractList | 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. 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 , 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 ‐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. |
| Author | Shala, Shqipron Konyukhov, Alexander |
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| Cites_doi | 10.1002/nme.5743 10.1016/j.cma.2011.03.013 10.1002/nme.5701 10.1007/s00466-015-1169-7 10.1017/CBO9781139171731 10.1016/j.ijsolstr.2017.07.020 10.1016/0021-9797(75)90018-1 10.1002/nme.6356 10.1016/j.cma.2010.04.012 10.1002/zamm.201300129 10.1002/nme.5253 10.1002/1097-0207(20001120)49:8<977::AID-NME986>3.0.CO;2-C 10.1007/978-3-642-31531-2 10.1007/978-94-015-7889-9 10.1098/rspa.1971.0141 10.1007/978-94-017-0169-3 |
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| References_xml | – year: 1985 – volume: 95 start-page: 406 issue: 4 year: 2015 end-page: 423 article-title: Contact of ropes and orthotropic rough surfaces publication-title: ZAMM ‐ J Appl Math Mech / Zeitschrift für Angewandte Mathematik und Mechanik – year: 2005 – volume: 154 start-page: 124 year: 2018 end-page: 146 article-title: Geometrically exact beam elements and smooth contact schemes for the modeling of fiber‐based materials and structures publication-title: Int J Solids Struct – volume: 108 start-page: 1290 issue: 11 year: 2016 end-page: 1306 article-title: General descriptions of follower forces derived via a geometrically exact inverse contact algorithm publication-title: Int J Numer Meth Eng – year: 2003 – volume: 324 start-page: 301 issue: 1558 year: 1971 end-page: 313 article-title: Surface energy and the contact of elastic solids publication-title: Proc Royal Soc Lond Math Phys Sci – volume: 1 year: 2020 article-title: Contact between shear‐deformable beams with elliptical cross sections publication-title: Acta Mech – volume: 114 start-page: 255 issue: 3 year: 2018 end-page: 291 article-title: A mortar finite element approach for point, line, and surface contact publication-title: Int J Numer Methods Eng – volume: 199 start-page: 2510 issue: 37 year: 2010 end-page: 2531 article-title: Geometrically exact covariant approach for contact between curves publication-title: Comput Methods Appl Mech Eng – volume: 49 start-page: 977 issue: 8 year: 2000 end-page: 1006 article-title: Contact with friction between beams in 3‐D space publication-title: Int J Numer Methods Eng – year: 2018 – year: 1990 – volume: 113 start-page: 1108 issue: 7 year: 2018 end-page: 1144 article-title: Consistent development of a beam‐to‐beam contact algorithm via the curve‐to‐solid beam contact: analysis for the nonfrictional case publication-title: Int J Numer Methods Eng – volume: 53 start-page: 314 year: 1975 end-page: 326 article-title: Effect of contact deformations on the adhesion of particles publication-title: J Colloid Interf Sci – year: 2014 – volume: 56 start-page: 243 year: 2015 end-page: 264 article-title: Frictional beam‐to‐beam multiple‐point contact finite element publication-title: Comput Mech – year: 2012 – volume: 205‐208 start-page: 130 year: 2012 end-page: 138 article-title: Geometrically exact theory for contact interactions of 1D manifolds. algorithmic implementation with various finite element models publication-title: Comput Methods Appl Mech Eng – volume: 5 year: 2020 article-title: Non‐localised contact between beams with circular and elliptical cross‐sections publication-title: Comput Mech – volume: 121 start-page: 3249 issue: 15 year: 2020 end-page: 3273 article-title: A tribological model for geometrically structured anisotropic surfaces in a covariant form publication-title: Int J Numer Meth Eng – volume: 18 start-page: 265 year: 1769 end-page: 278 – year: 1808 – year: 2015 – year: 2013 – volume-title: Exact Solutions of Axisymmetric Contact Problems year: 2018 ident: e_1_2_7_4_1 – start-page: 265 volume-title: Remarques sur l'effet du frottement dans l'équilibre year: 1769 ident: e_1_2_7_8_1 – ident: e_1_2_7_15_1 doi: 10.1002/nme.5743 – volume-title: Introduction to Differential Geometry year: 2018 ident: e_1_2_7_16_1 – ident: e_1_2_7_20_1 doi: 10.1016/j.cma.2011.03.013 – ident: e_1_2_7_18_1 doi: 10.1002/nme.5701 – ident: e_1_2_7_13_1 doi: 10.1007/s00466-015-1169-7 – ident: e_1_2_7_2_1 doi: 10.1017/CBO9781139171731 – ident: e_1_2_7_14_1 doi: 10.1016/j.ijsolstr.2017.07.020 – ident: e_1_2_7_6_1 doi: 10.1016/0021-9797(75)90018-1 – ident: e_1_2_7_23_1 doi: 10.1002/nme.6356 – ident: e_1_2_7_27_1 doi: 10.1016/j.cma.2010.04.012 – ident: e_1_2_7_11_1 doi: 10.1002/zamm.201300129 – ident: e_1_2_7_24_1 doi: 10.1002/nme.5253 – volume-title: Theory of Wire Rope year: 2012 ident: e_1_2_7_10_1 – ident: e_1_2_7_12_1 doi: 10.1002/1097-0207(20001120)49:8<977::AID-NME986>3.0.CO;2-C – volume-title: Conference Proceedings, WCCM XI, ECCM V, ECFD VI, WCCM XI year: 2014 ident: e_1_2_7_19_1 – volume-title: Computer Graphics and Geometric Modeling year: 2005 ident: e_1_2_7_21_1 – volume-title: Handbuch der Statik fester Körper. 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| SubjectTerms | "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 |
| Title | New benchmark problems for verification of the curve‐to‐surface contact algorithm based on the generalized Euler–Eytelwein problem |
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