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1
Content available A circular inclusion and two radial coaxial cracks with contacting faces in a piecewise homogeneous isotropic plate under bending
Sulym Heorhiy, Opanasovych Viktor, Zvizlo Ivan, Seliverstov Roman, Bilash Oksana
Acta Mechanica et Automatica
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2020
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Vol. 14, no. 1
16--21
EN
The bending problem of an infinite, piecewise homogeneous, isotropic plate with circular interfacial zone and two coaxial radial cracks is solved on the assumption of crack closure along a line on the plate surface. Using the theory of functions of a complex variable, complex potentials and a superposition of plane problem of the elasticity theory and plate bending problem, the solution is obtained in the form of a system of singular integral equations, which is numerically solved after reducing to a system of linear algebraic equations by the mechanical quadrature method. Numerical results are presented for the forces and moments intensity factors, contact forces between crack faces and critical load for various geometrical and mechanical task parameters.
2
Content available remote A multi-layered ring under parabolic pressure
Markides Ch. F., Pasiou E. D., Kourkoulis S. K.
Engineering Transactions
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2016
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Vol. 64, iss. 4
433--440
EN
The stress- and displacement-fields developed in a circular ring consisting of a finite number of linearly elastic homogeneous and isotropic concentric layers are determined. The composite ring is subjected to a distribution of radial stresses (acting along two finite arcs of its periphery) varying according to a parabolic law. The problem is solved analytically adopting Savin’s approach for an infinite plate with a hole strengthened by rings. Taking advantage of the analytic solution, a numerical model is properly calibrated and validated by considering the case of a three-layered ring. It is concluded that the constructed model simulates reality in an excellent manner and therefore it can be safely used for a thorough parametric analysis of the numerous factors influencing the stress- and displacement-fields.
3
Content available remote Stresses and Displacements in an Elliptically Perforated Circular Disc Under Radial Pressure
Markides Ch. F., Kourkoulis S. K.
Engineering Transactions
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2014
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Vol. 62, iss. 2
131--169
EN
The complex potentials governing the elastic equilibrium of a finite circular disc, elliptically perforated at its center, are obtained using Muskhelishvili’s formulation. The disc is subjected to non-uniform distribution of pressure along two symmetric finite arcs of its periphery. Given the complex potentials, the stress- and displacement-fields can be determined everywhere on the disc by introducing a novel flexible interpretation of the conformal mapping, suitably adjusted to the computational process. The results of this procedure are given for various strategic loci and are critically discussed. The length of the loaded arc is considered similar to that obtained from the solution of the intact disc-circular jaw elastic contact problem assuming that the disc is compressed between the steel jaws of the device suggested by the International Society for Rock Mechanics for the implementation of the Brazilian-disc test. Concerning the distribution of the externally induced pressure along the loaded arcs, it is proven that for the general asymmetric configuration (i.e. the axes of the elliptical hole are neither parallel nor normal to the loading axis) the induced asymmetric displacement field does not permit maintenance of equilibrium of the disc as a whole in case the disc is considered exclusively under a distribution of radial pressure: Additional tractions must be exerted along the loaded arcs, obviously in the form of frictional stresses. Besides, providing full-field, analytic expressions for stresses and displacements, the main advantage of the present solution is that, by properly choosing the ratio of the ellipse’s semi-axes, the solution of three additional configurations, of major importance in engineering praxis, are obtained: These of the intact disc, the circular ring and the cracked disc.
4
Content available remote Revisiting the Reflected Caustics Method : the Accurate Shape of the “Initial Curve”
Markides Ch. F., Kourkoulis S. K.
Engineering Transactions
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2013
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Vol. 61, iss. 4
265–-287
EN
The shape of the “initial curve”, i.e. the locus of material points, which if properly illuminated provide (under specific conditions) the “caustic curve”, is explored. Adopting the method of complex potentials improved formulae for the shape of the “initial curve” are obtained. Application of these formulae for two typical problems, i.e. the mode-I crack and the infinite plate with a finite circular hole under uniaxial tension, indicates that the “initial curve” is in fact not a circular locus. It is either an open curve or a closed contour, respectively, the actual shape of which depends also on the in-plane displacement field.
5
Content available remote Smooth elastic contact of cylinders by caustics: the contact length in the Brazilian disc test
Kourkoulis S. K., Markides Ch. F., Bakalis G.
Archives of Mechanics
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2013
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Vol. 65, nr 4
313--338
EN
The smooth contact of two elastic cylinders compressed against each other along a common generatrix is studied analytically and experimentally. The main objective is the quantification of the length of the contact arc. For the analytic study, the complex potentials method is employed while experimentally the contact arc’s length is determined by extending the reflected caustics technique. A series of experiments are then carried out using the device suggested by the International Society for Rock Mechanics for the standardized implementation of the Brazilian test and the typical set-up of the reflected caustics method. The experimental results are compared to the analytically determined ones. The agreement is satisfactory especially for low load levels, ensuring validity of the linear elasticity assumption.
6
Content available Interaction between a stratified elastic half-space and an irregular base allowing for the intercontact gas
Machyshyn I., Nagórko W.
Journal of Theoretical and Applied Mechanics
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2003
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Vol. 41 nr 2
271-288
EN
The paper is devoted to the investigation of contact interaction of a laminated half-space and a rigid body with a smooth cylindrical depression under conditions of plane deformation allowing for an intercontact ideal gas. To describe the homogenized model of the laminated body with microlocal parameters and to describe the behavior of the gas - equations of ideal gas state are used. Applying the method of comlex potentials the problem is reduced to the singular integral equation for the height of intercontact gap and its solution is obtained in a closed form. To find the lenght of the gap, its volume and the gas pressure a system of three equations is derived. With the aid of this system the dependence of the external loading and amount of the gas in the gap on the contact pressure and geometrical parameters of the gap is analyzed.
PL
W pracy analizuje się oddziaływanie sprężystej półprzestrzeni warstwowo-niejednorodnej na ciało sztywne z walcową szczeliną wypełnioną gazem. Półprzestrzeń sprężystą poddaje się homogenizacji mikrolokalnej, a do rozwiązania otrzymanych równań modelowych stosuje się metodę potencjałów zespolonych. Analizowany problem sprowadza się do poszukiwania rozwiązania równania całkowego. W pracy uzyskuje się rozwiązania w postaci zamkniętej oraz przeprowadza analizę numeryczną zależności rozwartości szczeliny oraz jej objętości od obciążenia zewnętrznego.
7
Content available remote Contact problem for rough rigid disk and plate with thin coating on the cylindric hole
Kravchuk A. S.
International Journal of Applied Mechanics and Engineering
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2001
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Vol. 6, no 2
489-497
EN
The model of elastic interior contact between a rough rigid disk and an isotropic plate with thin coating on a smooth cylindrical hole was developed. These investigations allowed us to take into account plastic deformations of a layer of the hole and probability characteristics of surface roughness of a disk. The method of complex potentials (the potentials of Kolosov-Muskhelishvily) and the dependence of plastic deformations of the layer obtained by Alecseev for plain joints were used. The problem was reduced to an integral-differential equation with respect to normal contact stress.
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