Various methods for solving the partial contact of surfaces with regularly periodic profiles-- which might arise in analyses of asperity level contact, serrated surfaces or even curved structures--have previously been employed for elastic materials. A new approach based upon the summation of evenly spaced Flamant's solution is presented here to analyze periodic contact problems in plane elasticity. The advantage is that solutions are derived in a simple and straightforward manner without extensive experience with advanced mathematical theory, which, as it will be shown, allows for the evaluation of new and more complicated problems. Much like the contact of a single indenter, the formulation produces coupled Cauchy singular integral equations of the second kind upon transforming variables. The integral equations of contact along with both the boundary and equilibrium conditions provide the necessary tools for calculating the surface tractions, often found in closed-form. Various loading conditions are considered, such as frictionless contact, sliding contact, complete stick and partial slip. Solutions for both elastically similar and dissimilar materials of the mating surfaces are evaluated assuming Coulomb friction. An alternative method for solving partial slip problems with the superposition of a complete stick problem and periodic external cracks with localized loading is developed. Further applications of the contact mechanics solutions to such failure mechanisms as fretting fatigue and crack propagation are briefly discussed for periodic profiles. Finally, partial contact problems in polar coordinates are solved with a modified Fourier-Michell potential function. The mixed boundary conditions result in dual series equations, which are simplified to a Fredholm integral equation of the second kind for a curved beam and a coated cylinder pressed by a flat surface. Limiting cases for the curved structures are plotted to demonstrate dependence on material parameters and layer thickness.

Last modified

• 08/27/2018

Creator

• Joseph M Block

DOI

• https://doi.org/10.21985/N2B42R

Subject

• Mechanical Engineering

Keyword

• Periodic Problems
• Contact Mechanics
• Plane Elasticity

Date created

• 2007-11-18

Resource type

• Dissertation

Rights statement

• In Copyright