SOLUTION OF THE CONTACT PROBLEM ON THE TRANSMISSION OF A CONCENTRATED LOAD

Abstract

The paper considers the solution of the plane contact problem based on the linearized theory of elasticity about the load transfer using an infinite non-uniform stringer to two elastic strips clamped by one face in the presence of initial (or residual) stresses. The authors performed a general study for very large initial deformations and considered some variants of the theory of small initial deformations under the condition of an arbitrary structure of the elastic potential. Using the integral Fourier transform, it was possible to obtain the solution of the main integro-differential equations and present it in the form of quasi-regular infinite systems. In addition, the influence of existing initial (residual) stresses for elastic strips on the distribution law of actual contact stresses along a line with an infinite non-homogeneous stringer was investigated.
The initial stresses present in such strip systems lead to a qualitative change in the law of distribution of contact stresses, namely, during compression, the contact stresses significantly decrease (and for stretching, they increase), thus, displacements during compression significantly increase, and during stretching, they decrease. The quantitative nature of the influence of the initial stresses in highly elastic materials when compared with stiffer materials has a similar nature to the qualitative one.