Date of Degree

2009

Document Type

PhD diss.

Degree Name

PhD (Doctor of Philosophy)

Department

Mathematics

First Advisor

David E. Stewart

Abstract

This thesis consists of two parts. In the first part, a simulation of contact between a two dimensional elastic object in motion in contact with a rigid obstacle under Coulumb friction is developed. Once this simulation is developed, the simulation attempts to find out what initial numerical conditions cause the object to go unstable. All results found in this first part are numerical. Based on the numerical results of this thesis it appears that the friction coefficient is the main source of instabilities occuring, but the initial velocity does impact whether or not an instability occurs to some degree as well. The second part of this thesis investigates whether or not energy is conserved during the simulations conducted in the first part of the thesis. In the first part we discover that whether or not energy is conserved has little impact on whether an instabilty occurs, but it is still desireable for energy to be conserved in a mathematical model. We show that with a slight modification to the friction condition that energy will be conserved. This is desireable as energy dissipation is usually needed to prove convergence of solutions. Unfortunately as of yet convergence of solutions cannot be proven as existance of solutions has yet to be established.

Pages

x, 109

Bibliography

107-109

Copyright

Copyright 2009 Brian Douglas Gillispie

InstabilityNotes.xls (81 kB)
InstabilityNotes.xls

fivenodecases.zip (8712 kB)
fivenodecases.zip

Additional Files

InstabilityNotes.xls (81 kB)
InstabilityNotes.xls

fivenodecases.zip (8712 kB)
fivenodecases.zip

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Mathematics Commons

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