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.