Antiplane deformation of a body with a curved elastic sharp-ended inclusion

1982 ◽  
Vol 18 (3) ◽  
pp. 245-250 ◽  
Author(s):  
L. T. Berezhnitskii ◽  
P. S. Kachur ◽  
L. P. Mazurak ◽  
Ya. I. Khodan'
Keyword(s):  
Antiplane Deformation

Antiplane Deformation of Anisotropic Bodies with Periodic Systems of Thin Inhomogeneities

2014 ◽  
Vol 49 (5) ◽  
pp. 602-611
Author(s):  
I. M. Pasternak ◽  
H. T. Sulym ◽  
N. R. Oliyarnyk
Keyword(s):  
Periodic Systems ◽  
Antiplane Deformation ◽  
Anisotropic Bodies

Anti-Plane Deformation Uniformly Piecewise Homogeneous Space with a Periodic System of Semi-Infinite Internal Cracks

2020 ◽  
pp. 13-20
Author(s):  
V.N. Hakobyan ◽  
A.A. Grigoryan
Keyword(s):  
Integral Equation ◽  
Numerical Calculation ◽  
Homogeneous Space ◽  
Plane Deformation ◽  
Contact Stresses ◽  
Antiplane Deformation ◽  
Intensity Factors ◽  
Shear Moduli ◽  
Mechanical Quadrature ◽  
Equal Thickness

In this paper, we have constructed a solution for the problem of antiplane deformation of a uniformly piecewise homogeneous space of two alternately repeating heterogeneous layers of equal thickness from different materials, which are relaxed on their median planes by two semi-infinite, periodic parallel tunneling cracks. A system of defining equations of the problem is derived in the form of a system of two singular equations of the first kind, with respect to contact stresses acting in the contact zones on the median planes of heterogeneous layers, the solution of which, in the general case, is constructed by the method of mechanical quadrature. In the particular case when the cracks in the heterogeneous layers are the same, the solution of the problem is reduced to the solution of two independent equations and their closed solutions are constructed. The defining singular integral equation of the problem is also obtained in the case when there are no cracks in one of the heterogeneous layers. In the general case, a numerical calculation was carried out and patterns of changes in contact stresses and intensity factors of destructive stresses at the end points of cracks were determined depending on the physical and mechanical and geometric parameters of the problem, which are the ratios of the shear moduli of the layers and the ratio of the layer thickness and crack lengths.

On classical solutions of the Prandtl-Reuss equations of perfect elastoplasticity

1996 ◽  
Vol 126 (6) ◽  
pp. 1297-1308 ◽  
Author(s):  
Sergej B. Kuksin
Keyword(s):  
Simple Shear ◽  
Functional Equations ◽  
Classical Solutions ◽  
Antiplane Deformation ◽  
System Of Equations ◽  
Elastoplastic Medium ◽  
Shear Deformations ◽  
Nonlinear Functional

We study the elasticity domain for an antiplane deformation of a perfect elastoplastic medium, which is described by the Prandtl-Reuss equations. We prove that a boundary of this domain can be found by solving a system of nonlinear functional equations. In the simplest case of simple shear deformations, this system of equations is studied in detail.

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