Open AccessMODELING OF DEFORMATION OF OBJECTS OPERATING UNDER CONDITIONS OF TEMPERATURE INFLUENCES
Author(s) -
G. V. Grygorchuk
Publication year - 2019
Publication title -
prikarpatsʹkij vìsnik ntš. čislo
Language(s) - English
Resource type - Journals
ISSN - 2304-7399
DOI - 10.31471/2304-7399-2019-1(53)-38-44
Subject(s) - conical surface , cauchy stress tensor , mathematics , deformation (meteorology) , tensor (intrinsic definition) , stress (linguistics) , representation (politics) , elasticity (physics) , basis (linear algebra) , mathematical analysis , geometry , physics , linguistics , philosophy , politics , meteorology , political science , law , thermodynamics
A mathematical model of the deformation and stress state process for long rotating objects complex geometric configuration is proposed. The model of the process of deformation of plots, which are combinations of sections of rectilinear, spherical and conical forms, is proposed, parametric representation of the law of motion of the specified plots in the initial and control moments of time is constructed, on the basis of which the components of vectors of local bases and components of the metric tensor for the specified types of plots are determined. What are the components of the stress tensor. The theory of systems of systems of linear algebraic equations was used to determine the geometric characteristics of a deformed spherical section, as well as the apparatus of the Hermite interpolation polynomials for modeling the axis deformation process. Within the framework of linear elasticity theory, the components of the stress tensor arising from non-isothermal processes characteristic of sugar industry technological objects operation have been calculated. The components of the stress tensor, which allows to take into account the features of the deformed object at different ambient temperatures, have been refined. The model of the stress state of objects is offered, the test calculations for the model sites are carried out, the directions of further researches are revealed.