Transfer of loading from endless stringer to one and to two prestressed stripe

M. Dikhtyaruk, N. Yaretska
2019 Scientific journal of the Ternopil national technical university  
The article is devoted to the research of problems of contact interaction of infinite elastic stringer with one and two identical clamped along one edge of pre-stressed strips. In general, the research was carried out for the theory of great initial and different variants of the theory of small initial deformations within the framework of linearized theory of elasticity with the elastic potential having arbitrary structure. The integral integer-differential equations are obtained using the
more » ... ral Fourier transform. Their solution is represented in the form of quasiregular infinite systems of algebraic equations. In the article alsaw was investigated the influence of the initial (residual) stresses in strips on the law of distribution of contact stresses along the line of contact with an infinite stringer. Statement of the problem. Investigation of the problems of contact interaction of thinwalled elements in the form of overlays (stringers) and coatings of various geometric forms with massive deformed bodies is very important problem both in the theoretical and in the applied aspect. When creating structures and machines mechanisms for improving the strength characteristics and properties of parts, as well as the possibility of their use under high temperatures conditions, or in aggressive media presence, various coatings and reinforcements are widely used. Since such parts are often the structures responsible elements, which fracture can result in catastrophic effects, then their regular diagnosis is required. In theory, this problem can be reduced to the consideration of contact problems concerning the interaction of overlays and inclusions with elastic bodies of various forms. One of the important factors that significantly affect the reliability and durability of engineering structures and machine parts is the presence of their initial (residual) stresses. Analysis of the available investigation results. Despite the fact that investigations concerning the impact of initial stresses have been actively carried out in our country and abroad only at the end of the XX century, it is possible to list many names, researches and publications related to this problem [1, 2]. In strict formulation of contact problems for elastic bodies with initial stresses [1, 2], it is necessary to involve the apparatus of nonlinear elasticity theory, which considerably complicates the analytic solutions construction of. But in case of large (finite) stresses (deformations) we can restrict ourselves to the consideration of linearized elasticity theory [1]. Historically, the investigation of contact problems in the framework of the linearized elasticity theory consisted of two directions. The first one is connected with the investigation of contact interaction of bodies with definite form of elastic potential [3]. In the second one, the problem is set up in general form for compressible (incompressible) bodies with the arbitrary structure potential based on the linearized elasticity theory [1, 2, 4−13]. The solutions of the contact problems concerning contact interaction of infinite stringer with one and two pre-stressed stripes using the linearized elasticity theory relations [1, 2] are Load transmission from the endless stringer to one and two pre-stressed stripes
doi:10.33108/visnyk_tntu2019.01.137 fatcat:7fassj5pojhaldcljyqhg526la