Contact problem for a stamp with narrow rectangular base

A rigid rectangular footing on an elastic layer

“…The values given by Fabrikant (1986) are based on formulae applicable to general polygons. The values given by Borodachev & Galin (1974) and Panek & Kalker (1977) are valid for narrow rectangles. The values given by Noble (1960), Fraser & Wardle (1976), and Brothers et al (1977) were obtained by using a variational method, the finite element method, and a singularity method, respectively.…”

“…The solutions for a rigid rectangular footing on an elastic half-space (a layer of infinite depth) can be found in papers by Noble (1960), Gorbunov-Passadov & Serebrjanyi (1961), Borodachev & Galin (1974), Borodachev (1976), Brothers, Sinclair & Segedin (1977), Panek & Kalker (1977), Mullan, Sinclair & Brothers (1980), Fabrikant (1986), and Li & Dempsey (1988b). The solutions for a rigid strip (a footing with an infinite aspect ratio) on an elastic layer can be found in papers by Smith (1962), Aleksandrov (1968), and Li & Dempsey (1988a).…”

Application of a contact model due to L. A. galin to problems of contact interaction between stringers and massive deformable bodies

“…The adjacent problems of indentation of a punch with a narrow rectangular base into an elastic half-space were considered earlier in [12,13]. We also mention the paper [14], where the solutions of the plane and axisymmetric problems of contact interaction between an elastic strip (stringer) and an elastic half-space were constructed.…”

A solution for the narrow rectangular punch

“…It is desired to know the stress developed at the face of the punch, as well as the depth of penetration into the half-space. Borodachev and Galin [1] present one approximate solution to this problem. Starting from the Lam6 equilibrium equation, and assuming a square root singular stress distribution across the width of the punch, they are able to formulate the problem as a pair of dual integral equations.…”