Smooth indentation of finite layer

The plane problem of a layer of finite length under the action of a frictionless indenter is studied. The solution obtained accounts for both the local contact behavior near the indenter and the overall beam behavior as well. The analysis superposes an infinite layer solution derived through the use of integral transforms with a pure bending beam theory solution. The problem is reduced to a Fredholm integral equation of the second kind, which is solved numerically. Clamped and simply supported end conditions are studied; overall compliances and local indenter stresses are computed and plotted for various ratios of contact length to layer thickness. The results are compared to beam theory compliances and Hertz theory contact stresses.