About stresses in elastic stripe under normal forces on longitudinal borders

Abstract

The problem of stresses in the flat stripe S with constant wide 2c which borders loaded concentrated forces was analyzed. The analytical solution of this problem was founded in the terms of the function of complex variable. The stresses in arbitrary point of the strip determined by means of two regular functions Φ(z) and Ψ1(z). These functions are founded by the use of conform reflection of the region S on the lower half plane ζ. The problem of this half plane solved analytical (method Cauchy’s integrals). The exact mathematical expressions of the functions Φ(z) and Ψ1 (z) are obtained. The inversely conform reflection reduce to known quantity Φ(z) and Ψ1(z). The function Ψ1 (z) is coupled with Φ (z), and so stresses are defined by means of Φ(z) and its derivative Φ (z). The graphics of the normal and tangent stresses on the lines parallel strip’s borders are produced. The comparison of stresses on the axis of strip and Filon’s data were investigated. The solutions satisfy differential equations of equilibrium, border’s conditions and the equation of continuous.