DOI: https://doi.org/10.20535/2305-9001.2012.66.38947

SOLUTION OF THE PLASTICITY THEORY FLAT TASK AT THE TENSION

В. В. Чигиринский, А. Н. Бень, А. Н. Бень

Abstract


Purpose. The analytical solution of the plasticity theory flat task with using the built-in difficult double-link harmonic function. The analysis of a task solution for the simple being strengthened environment is carrying out.

Methodology. At the basis of the flat task closed solution the general approaches of the analytical tasks solution with using harmonic functions are developed. Decisions with using the plastic current theory are shown. Possibility of implementation of the decision with using the enclosed harmonious coordinate functions shows that there is an area of admissible values in limits in which the real result of distribution of tension is received.

Results. The solution of a flat task of the plasticity theory at tension at the general view, at the expense of using the enclosed harmonious functions is received. It is remarkable that fields of tension are described by one analytical expression without splitting into separate sites of all deformation centers. Expressions for definition of tensor tension components with using the enclosed harmonic functions are received.

Originality. The method of the plasticity theory tasks solution with using a plastic metal forms change mathematical model with the enclosed harmonious functions is developed


Keywords


Tensions; Harmonic Functions; Scope Terms; Form’s Factor; Friction’s Factor

References


1. Chigirinskij V.V., Kachan A.Ja., Ben' A.N. Vestnik nacional'nogo tehnicheskogo universiteta Ukrainy. Politehnicheskij institut – Herald of National Technical University of Ukraine. Polytechnical institute, 2008, pp. 141-148.

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GOST Style Citations


1.            Чигиринский В.В. Обобщенная теория пластичности. Модель сложной пластической среды / В.В. Чигиринский, А.Я. Качан, А.Н. Бень // Вестник национального технического университета Украины. Политехнический институт. – 2008. – С. 141-148.

 

2.            Чигиринский В.В. Некоторые особенности обобщенной теории пластичности для упрочняющейся среды / В.В. Чигиринский, А.Н. Бень // Вестник двигателестроения. – 2008. –  № 2. – С. 8-12.

 

3.            Chygyrynskyy V.V.AGeneralisedTheoryofPlasticity [Text] / V.V. Chygyryns’kyy, A.Ya. Kachan, I. Mamuzić, A.N. Ben’ // Materials and Technology. Institute of Metals and Technology – Liubljana, Slovenija. – 2010. – POB 431. – P. 141-145.

 

4.            Смирнов В.С. Теория обработки металлов давлением / В.С. Смирнов. – М.: Металлургия,1973. – 496 с. – (уч. для студ. вузов, обучающихся по спец. “ОМД”).

 

5.            Малинин, Н.Н. Прикладная теория пластичности и ползучести / Н.Н. Малинин. - М.: Машиностроение, 1975. – 399 с. – (уч. для студ. машиностр. спец. вузов).

 

6.            Cторожев М.В. Теория обработки металлов давлением / М.В. Сторожев, Е.А. Попов. - М.: Машиностроение, 1977. - 424 с. – (уч. для маиностр. и политехн. вузов).





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