The exact determination of strain on the load application area, regards to changing material or shape is one of the main problems of the mini structure constructions, which it does not interfere with the classical methods of linear elasticity. The main purpose of this article is to demonstrate accomplishments in the knowledge of linear elasticity with different mathematical methods, in order to penetrate into the area or into the contact lining, taking into consideration the friction between the bodies in contact. The methods and hypotheses are related to the analysis of different classical half-plane problems in loads of different types of linear elasticity. This material shows a clear original solution of the strained state in the contact area including the surface lining; it serves as a solution to the various contact plan problems. The details and the elements of the vehicles are part of a broad field, which should be optimized considering different analytical solutions and using various computer programs. These solutions can be installed in their structure. Classical methods in the details apply only when the hypotheses on studied subjects are being met, such as Material Resistance studying the Rod. A detail with a length of ten times greater than the transverse dimension. That’s the reason why extreme problems or problems out of the different hypotheses are solved and proven in practice with the most creative and sophisticated methods. The solution given in this article is an important contribution to constructive calculations, which is also associated with other works carried out by me on the friction coefficient on the flip-flop slippery contact.
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