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Contact Problems

S. K. Roy Chowdhury, Prasanta Sahoo · 2025

Solid Mechanics, as compared to Mechanics of Materials or Strength of Materials, is generally considered to be a higher-level course. It is usually taught in higher semesters to senior undergraduate students. However, there is no suitable textbook on this subject. The book is primarily aimed at this group of students and the text is an attempt to bridge the gap between complex formulations in the theory of elasticity and elementary strength of materials in a simplified manner. The book is intended to present the basics of Solid Mechanics in a simple and concise manner to the initial learners. A large number of solved problems on each topic have been included to illustrate the text materials. Because of the simpler approach adopted in solving difficult problems, the book will be useful for all student groups who wish to learn the basic solid mechanics without much difficulty.

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Contact Problems

Marko V. Lubarda, Vlado A. Lubarda · Cambridge University Press eBooks · 2019

A brief coverage of the mechanics of contact problems is presented. The governing equations for three-dimensional axisymmetric elasticity problems in cylindrical coordinates are first formulated, which is followed by the solutions to classical problems of a concentrated force within an infinite medium (Kelvin problem), and a concentrated force at the boundary of a half-space (Boussinesq problem). The stress fields in a half-space loaded by an elliptical and a uniform pressure distribution over a circular portion of its boundary are presented. Indentation by a spherical ball and by a cylindrical circular indenter are analyzed. The second part of the chapter is devoted to Hertzian contact problems. The nonlinear force–displacement relation is derived for elastic contact of two spherical bodies pressed against each other by two opposite forces. The elastic contact of two circular cylinders is also considered. The contact pressure and the maximum shear stress are determined. The approach of the centers of the cylinders requires the consideration of the local contact stresses, as well as the stresses within the bulk of each cylinder.

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