On the properties of integral equations arising in contact problems for porous elastic strip

The paper is concerned with a Fredholm integral equation of the first kind arising in contact problems for elastic foundations with voids. In the structure of its kernel there are two principal parameters. The first one is of a relative thickness of the strip foundation. The second one is coupled with the porosity of the material. We study uniqueness and solvability of the main integral equation, and then give explicit analytical asymptotics for the leading asymptotic term of the strip compliance, in the two limiting cases of thick and thin strip. Finally, analytical results are compared with results obtained by direct numerical treatment.