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

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, th...

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Veröffentlicht in:Applied sciences Jg. 11; H. 6; S. 2859
Hauptverfasser: Delyavskyy, Mykhaylo, Opanasovych, Viktor, Seliverstov, Roman, Bilash, Oksana
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.03.2021
Schlagworte:
bending
Boundary conditions
complex potential
crack
Crack propagation
Integral equations
layered plate
Mathematical functions
moment intensity factor
Stress state
Symmetry
ISSN:2076-3417, 2076-3417
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Zusammenfassung: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.
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ISSN:2076-3417
2076-3417
DOI:10.3390/app11062859