Determination of the Equi-stress Hole Shape for a Stringer Plate Weakened by a Surface Crack

Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 23, no. 3, 2020 (September)
Pages 16-26
Cited by J. of Mech. Eng., 2020, vol. 23, no. 3, pp. 16-26



Minavar V. Mir-Salim-zade, Institute of Mathematics and Mechanics of the NAS of Azerbaijan (9, Vahabzade St., Baku, AZ1141, Azerbaijan), e-mail:, ORCID: 0000-0003-4237-0352



On the basis of the principle of equal stress, a solution is given to the inverse problem of determining the optimal shape of the hole contour for a plate weakened by a surface rectilinear crack. The plate is reinforced by a regular system of elastic stiffeners (stringers). The crack originates from the hole contour perpendicular to the riveted stringers. The plate is subjected to uniform tension at infinity along the stiffeners. The plate under consideration is assumed to be either elastic or elastic-plastic. The criterion that determines the optimal shape of the hole is the condition that there is no stress concentration on the hole surface and the requirement that the stress intensity factor in the vicinity of the crack tip be equal to zero. In the case of an elastic-plastic plate, the plastic region at the moment of nucleation should encompass the entire hole contour at once, without deep penetration. The problem posed is to determine the hole shape at which the tangential normal stress acting on the contour is constant, and the stress intensity factor in the vicinity of the crack tip is zero, as well as to determine the magnitudes of the concentrated forces that replace both the action of the stringers and the stress-strain state of the reinforced plate. The method of a small parameter, the theory of analytic functions, and the method for direct solution of singular integral equations were used. The problem posed is reduced to the problem of finding a conditional extremum. The method of Lagrange indefinite multipliers was used. The obtained solution to the inverse problem allows increasing the bearing capacity of the stringer plate.


Keywords: plate, stringers, equal strength hole, crack.


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Received 25 April 2020

Published 30 September 2020