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УДК 539.374.001.8


Chygyryns’kyy V., Ben’ A.
Zaporizhzhya National Technical University, Zaporizhzhya, Ukraine



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


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