MINIMIZATION OF THE STRESSED STATE OF A STRINGER PLATE WITH A HOLE AND RECTILINEAR CRACKS

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DOI https://doi.org/10.15407/pmach2019.02.059
Journal Journal of Mechanical Engineering
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 22, no. 2, 2019 (June)
Pages 59-69
Cited by J. of Mech. Eng., 2019, vol. 22, no. 2, pp. 59-69

 

Author

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

 

Abstract

As is known, thin plates with holes are one of the most common structural ele-ments. To increase their reliability and service life, it is of interest to find such a hole contour that ensures the minimum circumferential stress thereon, and also prevents the growth of possible cracks in the plate. This article deals with the problem of minimizing the stress state on the contour of a hole in an un-bounded isotropic stringer plate weakened by two rectilinear cracks. Crack faces are considered to be free of stress. Determined is the optimal hole con-tour, at which   no crack growth occurs, and the maximum circumferential stress thereon is minimal. The minimax criterion is used. The parameter char-acterizing the stress state in the vicinity of crack tips, according to the Irwin-Oroan theory of quasi-brittle fracture, is the stress intensity factor. The plate undergoes uniform stretching at infinity along the stringers. It is believed that the plate and the stringers are made of various elastic materials. The action of the stringers is replaced by the unknown equivalent concentrated forces ap-plied at the points of their attachment to the plate. To determine these forces, Hooke’s law is used. Applying the small parameter method, the theory of ana-lytic functions and the method of direct solution to singular equations, we con-structed a closed system of algebraic equations. This system depends on the mechanical and geometrical parameters of the plate and stringers, ensures the on-hole contour stress state minimization and equality of stress intensity fac-tors to zero in the vicinity of crack tips. The minimization problem is reduced to a linear programming problem. The simplex method is applied.

 

Keywords: stringer plate, stress minimization, cracks, optimal hole contour, minimax criterion.

 

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Received 12 May 2019