# Dikhtyaruk N.N., Poplavska O.A. Analog of melan problems for elastic mixture with initial influences with diagnostic lubrication.

### Abstract

The article is devoted problems of contact interaction of infinite elastic stringer and clamped along one of pre-stressed strip. The study was performed in the framework of linearized of elasticity theory in a General form for the theory of large (finite) initial deformations and two variants of the theory of small initial deformations with arbitrary structure of elastic potential. The study is carried out in the coordinates of the initial strain associated with Lagrangian coordinates (the natural state). In addition, it is assumed that the interaction with the stringer occurs after the bands appeared, the initial tension and the external load caused in the bands small perturbation of the basic stress strain state.

Based on the assumption that the stringers are loaded at the same time horizontal forces, a fair model of the bending beam in combination with horizontal tension rod, the problem is formulated mathematically as a system of integral-differential equations relative to the unknown contact stresses. Using Fourier transforms, the system is solved in closed from. Expressions of the stresses are represented by Fourier integrals rather simple structure. The influence of initial stresses on the distribution of the contact stresses and the identified effects of concentrated loads

### References

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3. Dihtyaruk N.N., Rudnitskiy V.B. Uprugaya polosa s nachalnyimi napryazheniyami, usilennaya uprugimi nakladkami. N.N. Dihtyaruk , V.B. Rudnitskiy. Prikladnaya mehanika. 2002. № 11. S. 81 – 88.

4. Melan E., Ein Beitrag zur Theorie geschweiss der Verbindungen. Ingenieur Archiv, 1932, Bd.3, Negt 2. s 126-128.

*Problems of Tribology*,

*87*(1), 37-42. Retrieved from http://tribology.khnu.km.ua/index.php/ProbTrib/article/view/650