The Contact Problem is of great practical significance. The nature of contact and friction, however, is so complex that the science of contact interaction is not sufficiently advanced for assisting in real engineering problems. One of the difficulties with contact interaction is the nature of surface friction, another is the nonlinear character arising from the free boundary condition. The computation of the exact stress and deformation around the contact boundary region is vital for engineering analysis and design, but obtaining exact solutions based on the theory of elasticity has been a challenge for physicists and mathematicians since the end of nineteenth century. We have developed computing models to investigate static and quasi-static smooth and frictional contact between solid bodies with various two dimensional geometries. A variational inequality approach with penalty and multiplier optimization methods is used to study the contact problem. Friction is modelled according to the classical Coulomb friction law. To overcome the problem of the relative shift between particles on one surface and particles on the other surface, we have designed a scheme to solve each contact solid one by one iteratively. The solutions for the two elastic solid bodies in frictional contact are connected through the surface traction and surface deformation. This scheme has a good convergence rate. One new aspect of our approach to the frictional interaction problem is the application of cubic splines in approximating the contact surface. We also address the difference between Cauchy and Piola-Kirchoff stress, and show when it is significant. A numerical investigation of the stress dependence on the loading distribution and solid geometry is conducted. The stress distribution deviates from predictions of Hertz theory and subsequent research, and it is sensitive to the loading distribution and the geometrical shape of the contact solids. We therefore argue that an accurate analysis of the dry contact problem requires a more refined knowledge about loading conditions and the geometry of both solids.Dept. of Physics. Paper copy at Leddy Library: Theses u26 Major Papers - Basement, West Bldg. / Call Number: Thesis2002 .Y36. Source: Dissertation Abstracts International, Volume: 63-04, Section: B, page: 1917. Adviser: M. Schlesinger. Thesis (Ph.D.)--University of Windsor (Canada), 2002.
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