{"id":4703,"date":"2021-03-12T14:19:10","date_gmt":"2021-03-12T12:19:10","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=4703"},"modified":"2021-03-17T11:34:45","modified_gmt":"2021-03-17T09:34:45","slug":"%d0%bf%d0%bb%d0%be%d1%81%d0%ba%d0%b0-%d0%ba%d1%80%d0%b0%d0%b9%d0%be%d0%b2%d0%b0-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b0-%d0%b4%d0%b8%d1%81%d0%ba%d1%80%d0%b5%d1%82%d0%bd%d0%be%d0%b3%d0%be-%d1%81%d0%b5","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=4703","title":{"rendered":"\u041f\u043b\u043e\u0441\u043a\u0430 \u043a\u0440\u0430\u0439\u043e\u0432\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u043e\u0433\u043e \u0441\u0435\u0440\u0435\u0434\u043e\u0432\u0438\u0449\u0430"},"content":{"rendered":"

<\/p>\n

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FLAT BOUNDARY VALUE PROBLEM OF A DISCRETE MEDIUM<\/p>\n

\"\"<\/a> \u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 160-171. \u041d\u043e\u043c\u0435\u0440: \u21165, 2020 (289)<\/strong>
\n\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong>
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\n\u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442
\nO.DOROFEYEV, O.BAHRII, V.\u00a0KOVTUN
\nKhmelnytskyi National University
\nDOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2020-289-5-160-171<\/a>
\n\u0420\u0435\u0446\u0435\u043d\u0437\u0456\u044f\/Peer review :<\/strong> 05.11.2020 \u0440.
\n\u041d\u0430\u0434\u0440\u0443\u043a\u043e\u0432\u0430\u043d\u0430\/Printed :<\/strong> 27.11.2020 \u0440.<\/p>\n

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\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u043f\u043b\u043e\u0441\u043a\u0430 \u043a\u0440\u0430\u0439\u043e\u0432\u0430 \u0437\u0430\u0434\u0430\u0447\u0430; \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u0435 \u0441\u0435\u0440\u0435\u0434\u043e\u0432\u0438\u0449\u0435; \u0432\u043d\u0443\u0442\u0440\u0456\u0448\u043d\u0454 \u043a\u0443\u043b\u043e\u043d\u043e\u0432\u0435 \u0442\u0435\u0440\u0442\u044f; \u0434\u0438\u043b\u0430\u0442\u0430\u043d\u0441\u0456\u044f.<\/p>\n

\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

The article deals with the defining relations of the plane boundary value problem of a discrete medium and specific methods of its solution. A boundary value problem is considered to assess the state of a discrete medium. Its physical ratios should reflect the fundamental features of the deformation of the discrete medium: the influence of internal Coulomb friction on the deformation process at all stages of loading; occurrence of volume deformations during shear (dilatancy); significant influence of the type of stress-strain state on the nature of the laws of discrete materials deformation. The problem is formulated as a boundary value problem of a flat physically nonlinear inhomogeneous area filled with a discrete material that does not perceive tensile stresses and counteracts external perturbations only due to internal dry pendant friction. The material is considered to be quasi-continuous, which is deformed under conditions of plane deformation according to the experimentally established nonlinear laws of Coulomb’s rheological model. The hypothesis of small deformations is introduced, which allows using linear differential Cauchy dependences to fulfil the condition of deformation continuity. It is assumed that the stress-strain state of the calculation area is estimated only by the stresses and strains that occur in the plane of deformation perpendicular to the axis with zero deformation. Mathematical and finite-element formulation of the problem is given. Iterative procedures for solving a plane boundary value problem of the mechanics of a discrete medium by the finite element method are described.
\nKeywords:<\/strong> flat boundary value problem, discrete environment, internal Coulomb’s friction, dilatation.<\/p>\n

References<\/strong><\/p>\n

    \n
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