# The plane contact problem for an initially stressed elastic strip reinforced by an infinite inhomogeneous stringer

 Dikhtyaruk, NN Dopov. Nac. akad. nauk Ukr. 2019, 12:27-32 https://doi.org/10.15407/dopovidi2019.12.027 Section: Mechanics Language: Ukrainian Abstract:  In the frame of linearized elasticity theory, the plane contact problem of load transmission from an infinite inhomogeneous stringer to an elastic strip which is jammed at one edge and undergoes the action of initial (residual) stresses is considered. The study is carried out in the general form within the theory of high initial strains, as well as within various versions of the theory of low initial strains, at any structure of the elastic potential. The effect of the presence of initial (residual) stresses in the strip on the law of distribution of stresses on the line of contact with the infinite inhomogeneous stringer is studied. If the stringer is simultaneously loaded by vertical and horizontal forces, it is bent in the vertical direction as an ordinary beam and is compressed or stretched as an ordinary rod with finite stiffness, being in the uniaxial stress-strain state. The problem is posed mathema tically as a system of integro-differential equations for the unknown contact stresses. Then the resolving system of recurrence systems of integro-differential equations is constructed and solved in the closed form with the use of the Fourier transformation. The contact stresses are given in the form of Fourier integrals. Keywords: elastic strap, initial (residual) stresses, initial deformations, linearized elasticity theory
References:

1. Arutyunyan, N. Kh. & Mhitaryan, S. M. (1968). Some contact problems for a half-plane with partially fastened elastic overlays. Izv. AS Arm. SSR. Mechanics, 32, No. 4, pp. 632-646. Doi: https://doi.org/10.1016/0021-8928(68)90096-8
2. Sarkisyan, V. S. (1983). Contact problems for the half-planes and strips with elastic straps. Yerevan: Yerevan Univ. Press (in Russian).
3. Guz, A. N., Babich, S. Y. & Rudnitskii, V. B. (1998). Contact problems for elastic bodies with initial stresses: Focus on Ukrainian research. Int. Appl. Mech. Rew., 51, No. 5, pp. 343-371. Doi: https://doi.org/10.1115/1.3099009
4. Rudnitskii, V. B. & Dihtyaruk, N. N. (2002). Elastic strip with initial stresses, reinforced by elastic linings. Prikl. Mekh. 38, No. 11, pp. 81-88 (in Russian).
5. Guz, A. N., Babich, S. Y. & Rudnitskii, V. B. (1995). Contact interaction of bodies with initial stresses. Kyiv: Vysha Schcola (in Ukrainian).
6. Guz, A. N. (1983). Mechanics of brittle fracture of materials with initial stresses. Kiev: Naukova Dumka. Doi: https://doi.org/10.1016/B978-1-4832-8440-8.50107-1
7. Shtaerman, I. Ya. (1949). Contact problems of the theory of elasticity. Moscow: GITTL (in Russian).