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A Symmetric Three-Layer Plate with Two Coaxial Cracks under Pure Bending

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Department of Mechanics Construction and Buildings Materials, Faculty of Civil, Architecture and Environmental Engineering, UTP University of Science and Technology, Al. Prof. S. Kaliskiego 7, 85-796 Bydgoszcz, Poland
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Department of Mechanics, Faculty of Mechanics and Mathematics, Ivan Franko National University of L’viv, Universytetska St. 1, 79000 Lviv, Ukraine
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Department of Programming, Faculty of Applied Mathematics and Informatics, Ivan Franko National University of L’viv, Universytetska St. 1, 79000 Lviv, Ukraine
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Department of Engineering Mechanics (Weapons and Equipment of Military Engineering Forces), Faculty Training Specialists Battle (Operational) Software, Hetman Petro Sahaidachnyi National Army Academy, Heroes of Maidan Street, 32, 79026 Lviv, Ukraine
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Author to whom correspondence should be addressed.
Academic Editor: José A. F. O. Correia
Appl. Sci. 2021, 11(6), 2859; https://doi.org/10.3390/app11062859
Received: 21 February 2021 / Revised: 10 March 2021 / Accepted: 15 March 2021 / Published: 23 March 2021
(This article belongs to the Section Mechanical Engineering)
The purpose of this research was to investigate the effect of mechanical features and geometrical parameters on the stress–strain state of a cracked layered plate under pure bending (bending moments are uniformly distributed at infinity). The sixth-order bending problem of an infinite, symmetric, three-layer plate with two coaxial through cracks is considered under the assumption of no crack closure. By using complex potentials and methods of the theory of functions of a complex variable, the solution to the problem was obtained in the form of a singular integral equation. It is reduced to the system of linear algebraic equations and solved in a numerical manner by the mechanical quadrature method. The distributions of stresses and bending moments near the crack tips are shown. Numerical results are presented as graphical dependences of the reduced moment intensity factor on various problem parameters. In this particular case, the optimum ratio of layer thicknesses is determined. View Full-Text
Keywords: bending; layered plate; crack; complex potential; moment intensity factor bending; layered plate; crack; complex potential; moment intensity factor
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MDPI and ACS Style

Delyavskyy, M.; Opanasovych, V.; Seliverstov, R.; Bilash, O. A Symmetric Three-Layer Plate with Two Coaxial Cracks under Pure Bending. Appl. Sci. 2021, 11, 2859. https://doi.org/10.3390/app11062859

AMA Style

Delyavskyy M, Opanasovych V, Seliverstov R, Bilash O. A Symmetric Three-Layer Plate with Two Coaxial Cracks under Pure Bending. Applied Sciences. 2021; 11(6):2859. https://doi.org/10.3390/app11062859

Chicago/Turabian Style

Delyavskyy, Mykhaylo, Viktor Opanasovych, Roman Seliverstov, and Oksana Bilash. 2021. "A Symmetric Three-Layer Plate with Two Coaxial Cracks under Pure Bending" Applied Sciences 11, no. 6: 2859. https://doi.org/10.3390/app11062859

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