CLOSED PROBLEM OF PLASTICITY THEORY
Chigirinsky V. Naizabekov A. Lezhnev S.
2021University of Chemical Technology and Metallurgy
Journal of Chemical Technology and Metallurgy
2021#56Issue 4867 - 876 pp.
A plane closed problem of theory of plasticity has been formulated and solved. Generalizing factors of the problem solution are the argument functions for which differential dependencies are obtained in a form of Cauchy-Riemann and Laplaces equations. It is shown that differential equations with different purposes and with different physical quantities have the same solution formats, which allows using them to establish the connection between the mechanical characteristics of the process. Closed solution allows determining this connection. A multicomponent model of a plastic medium, depending on integral characteristics of a deformed state of the medium and its temperature, i.e. on thermomechanical processing parameters, is presented in the analytical form. Stress state calculations have been carried out for various methods of metal forming with pressure. Their comparability with a real distribution of contact stresses under symmetrical and asymmetric loading, determined by technological factors of production is shown.
argument functions , basic functions , boundary conditions , Cauchy-Riemann conditions , closed problem , complex variables , environment model , Laplaces equations , plasticity theory
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Rudny Industrial Institute, 50 let Oktyabrya str. 38, Rudny, 111500, Kazakhstan
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