Abstract
Minimax criterion is used to carry out the theoretical analysis of normal displacement of points at the boundary of a circular disk weakened by arbitrarily placed rectilinear cracks. This paper presents a criterion and method for solving the problem of fracture of the circular disk with mixed conditions on its boundary. A closed system of algebraic equations is constructed, which allows for minimization of stress intensity factors. The normal displacement of points at the boundary of the circular disk, for which the bearing capacity of the disk increases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. P. Savruk, Mechanics of Fracture and Strength of Materials, Vol. 2: Stress Intensity Coefficients in Bodies with Cracks (Naukova Dumka, Kiev, 1988) [in Russian].
M. P. Savruk, P. N. Osiv, and I. V. Prokopchuk, Numerical Analysis in the Plane Problems of the Fracture Theory (Naukova Dumka, Kiev, 1989) [in Russian].
N. M. Kalantarly, “Fracture of a Nonuniformly Heated Circular Disk,” Probl. Mashinostr. 17 (3), 19–25 (2014).
N. M. Kalantarly, “Limit-Equilibrium State of a Nonuniformly Heated Circular Disk Weakened by an Arbitrary System of Cohesive Cracks,” Vestn. Chuvash. Gos. Ped. Univ., Ser. Mekh. Predel. Sost., No. 3, 37–47 (2014).
V. M. Mirsalimov and N. M. Kalantarly, “Simulation of Crack Nucleation in an Circular Disk Loaded by Concentrated Forces,” Izv. Sarat. Univ., Ser. Mat. Mekh. Inform. 15 (1), 90–97 (2015).
V. M. Mirsalimov and N. M. Kalantarly, “Crack Nucleation in Circular Disk Under Mixed Boundary Conditions,” Arch. Mech. 67 (2), 115–136 (2015).
V. M. Mirsalimov and N. M. Kalantarly, “Cracking in a Circular Disk Under Mixed Boundary Conditions,” Acta Mech. 226 (6), 1897–1907 (2015).
V. M. Mirsalimov and N. M. Kalantarly, “Interaction of Bridged Cracks in a Circular Disk with Mixed Boundary Conditions,” Mechanika 21 (5), 361–366 (2015).
V. M. Mirsalimov and N. M. Kalantarly, “Fracture of a Circular Disk with Mixed Conditions on the Boundary,” Period. Polytech. Civil Eng. 59 (3), 423–432 (2015).
V. N. Shlyannikov and B. V. Il’chenko, “Calculating Stress Intensity in a Gas Turbine Disk in a Three- Dimensional Elastic Formulation. Pt. 2,” Strength Mat. 25 (2), 128–133 (1993).
V. Shlyannikov, A. Zakharov, and R. Yarullin, “A Plastic Stress Intensity Factor Approach to Turbine Disk Structural Integrity Assessment,” Frattura Integrit`a Strutturale 37, 193–199 (2016).
N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity (Nauka, Moscow, 1966; Springer Netherlands, 1977).
V. V. Panasyuk, M. P. Savruk, and A. P. Datsyshin, Stress Distribution near Cracks in Plates and Shells (Naukova Dumka, Kiev, 1976) [in Russian].
V. M. Mirsalimov, Non-One-Dimensional Elastoplastic Problems (Nauka, Moscow, 1987) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.M. Mirsalimov.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 2, pp. 218–226,March–April, 2018.
Rights and permissions
About this article
Cite this article
Mirsalimov, V.M. Fracture Parameter Minimization of a Circular Disk with Mixed Conditions on Its Boundary. J Appl Mech Tech Phy 59, 376–384 (2018). https://doi.org/10.1134/S0021894418020220
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894418020220