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Mathematically modelling the deformation of frictional elastic half-spaces in contact with a rolling rigid cylinder
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Bharth, Hanson (2022) Mathematically modelling the deformation of frictional elastic half-spaces in contact with a rolling rigid cylinder. PhD thesis, University of Warwick.
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WRAP_Theses_Bharth_2022.pdf - Submitted Version - Requires a PDF viewer. Download (3304Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3821823
Abstract
In this thesis we derive an analytical model of the deformation of an elastic half-space caused by a cylindrical roller. The roller is considered rigid, and is forced into the half-space and rolls across its surface, with contact modelled by Coulomb friction. In general, portions of the surface of the roller in contact with the half-space may slip across the surface of the half-space, or may stick to it. In this thesis, we consider the contact surface to have a central sticking region as well as a simplifying regime where the entire contact surface is fully slipping. This results in two mixed boundary value problem, which are formulated into a 4_4 matrix Wiener{Hopf problem for the stick-slip regime and a 2_2 matrix Wiener{Hopf problem for the full-slip regime. The exponential factors in the Wiener{Hopf matrix allows a solution by following the iterative method of Priddin, Kisil, and Ayton (Phil. Trans. Roy. Soc. A 378, p. 20190241, 2020) which is implemented numerically by computing Cauchy transforms using a spectral method following Slevinsky and Olver (J. Comput. Phys. 332, pp. 290{315, 2017). The limits of the contact region and stick-slip transitions are located a posteriori by applying an free-boundary method based on the secant method. The solution is illustrated with several examples, and the frictional regimes are analysed.
| Item Type: | Thesis (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics T Technology > TA Engineering (General). Civil engineering (General) |
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| Library of Congress Subject Headings (LCSH): | Contact mechanics, Rolling contact, Elasticity, Deformations (Mechanics) -- Mathematical models | ||||
| Official Date: | 13 June 2022 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute ; Warwick Manufacturing Group | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Brambley, Edward James | ||||
| Format of File: | |||||
| Extent: | xiii, 155 leaves : illustrations | ||||
| Language: | eng |
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