Contact problems in elasticity and the solution for a thick layer on a Winkler type foundation



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This study is written to present many aspects of contact problems and to present the solution to the problem of an arbitrarily loaded thick layer resting on an elastic (Winkler type) foundation. When working stress problems, the forces are usually transmitted by a contact between two bodies. If the method of contact influences the stress, the problem is called a contact problem. Here, such problems are discussed, considering the simplest first and the more difficult later. The first type of contact problem considered is the non-linear bending of beams. The solution to the two-dimensional, and, later, three-dimensional problems are presented. Finally, the stress in a layer that is resting on a rigid foundation is determined. The problem of a thick layer resting on an elastic foundation is then solved in order to determine the effect of plate thickness on the stress distribution. The solution is given in terms of infinite integrals which are virtually impossible to integrate by hand. In order to plot the solution, the integrals are numerically integrated on a computer. Numerous plots are given for a particular surface loading consisting of a pressure uniformly distributed over a circle.