A solution for the narrow rectangular punch

Abstract

This paper considers the problem of a rectangular flat ended punch acting on an elastic half-space. An approximate solution is generated through application of the elastic line integral equations. The results produced by this method are then compared with another approximate solution already available. ZUSAMMENFASSUNGDieser Aufsatz behandelt das Problem eines starren, flachen Stempels mit rechteckigen Grundriss, der in einen elastischen Halbraum gepresst wird. Eine Ngherungsl6sung wird erzeugt mittels der Integralgleichung des elastischen Linienkontakts. Die auf dieser Weise gewonnene Ergebnisse werden mit einer schon bekannten N~iherungsl6sung verglichen. RESUMEDans ce rapport, on consid~re le probl~me d'un cachet rigide h base plane rectangulaire qui est pouss6e dans une semi-espace 61astique. Une solution approximative est g6n6r6e par application de l'6quation integrale du contact 61astique de ligne. Les r6~ultats produits par cette m6thode sont compar6s ~t une solution approximative d6j~ connue.

A rigid rectangular footing on an elastic layer

“…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).…”

Three-dimensional Contact of a Rigid Roller Traversing a Viscoelastic Half Space

“…The actual three-dimensional analysis is done in an approximate manner by employing the elastic line contact theory (Kalker, 1972(Kalker, , 1977Panek & Kalker, 1977). Pertinent line contact equations which were not included in the original publications are developed in the body of this paper.…”

Contact Problem for a Rectangular Punch on the Porous Elastic Half-Space

“…It should be noted that for a classical linear elastic foundation an interesting asymptotic approach has been proposed in the 70s by Sivashinsky [6], Panek and Kalker [7], so we have a good opportunity to compare the method proposed at the present work with their results, on example of our problem.…”

“…Some comparison of the S-P-K solution with results of exact and asymptotic methods, for a porous medium, are shown in Figures 3 and 4. It should be noted, when doing the comparison, that the authors of [7] calculate the value of the ratio w 0 /π P , unlike our quantity P /w 0 , so we have re-calculated their results for our appropriate treatment.…”

“…which is a porous-medium generalization of an integral equation developed by Sivashinsky [6] and, independently, by Panek and Kalker [7] for a narrow punch in the case of classical elastic solids. Let us note that in their case N = 0, so L(s 2 ) ≡ const = 1, b 0 = 0 (see (4.8f)), hence equation (7.6) reduces to that obtained by those authors with the use of an absolutely different method.…”