Interaction Between a Finite Stringer and Two Identical Prestressed Strips: Contact Problem
The plane contact problem of the transfer of a horizontal concentrated load from a finite stringer to two identical prestressed strips clamped at one edge is solved using the linearized theory of elasticity. The research is carried out in general form for the theory of large initial deformations and various variants of the theory of small initial deformations for an arbitrary elastic potential. The problem for tangential contact stresses is reduced to a singular integro-differential equation, whose solution is defined as a series of Jacobi polynomials. Subsequently, after a series of transformations, a completely quasiregular infinite system of linear algebraic equations is obtained. Its solution can be found with wellknown numerical methods. The initial stresses in elastic strips have a strong effect on the distribution of contact stresses, namely: under compression (tension), the contact stresses substantially decrease (increase), while the displacements substantially increase (decreases). In highly elastic materials, the initial stresses have a stronger (quantitative) effect than stiffer materials do, the qualitative effect being the same.
Keywordscontact problem linearized theory of elasticity strip initial compression (tension) initial deformation
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- 1.A. N. Guz, S. Yu. Babich, and V. B. Rudnitskii, Contact Interaction of Prestressed Bodies [in Ukrainian], Vyshcha Shkola, Kyiv (1995).Google Scholar
- 2.A. N. Guz, S. Yu. Babich, and Yu. P. Glukhov, Mixed Problems for Elastic Base with Initial Stresses, Lambert Academic Publishing, Saarbrücken (2015).Google Scholar
- 3.M. M. Dikhtyaruk, “Determining the influence function for an elastic strip with initial (residual) stresses”, in: Proc. 4th Int. Symp. on Tribo-Fatigue (September 23–27, 2002, Ternopil) [in Ukrainian], Ternop. Derzh. Tekhn. Univ. im. Ivana Pulyuya, Ternopil (2002), pp. 426–431.Google Scholar
- 5.V. S. Sarkisyan, Contact Problems for Half-Planes and Strips with Elastic Pads [in Russian], Izd. Yerevan. Univ., Yerevan (1983).Google Scholar