Mathematical modeling of the stress-strain state of flexible threads with regard to plastic deformations

Abstract

The object of the study is the main power elements of mechanical systems made of flexible threads working on the perception of transverse loads. The paper focuses on the calculating the stress-strain state of a flexible thread with nonlinear elasticity by means of MathCAD program based upon geometric and physical nonlinearity of flexible threads. The proposed method is based on mathematical modeling theory including differential and integral calculation of one and several variables functions, as well as on the points of materials strength. We propose a method for nonlinear calculation of the stress-strain state of flexible threads taking into account the real properties which may be introduced to study the work of structures outside the elastic work of the material. Comparison of the parameters of the stress-strain state of a flexible thread obtained with the help of a digital experiment in a computer program, also with the results obtained by the finite element method, confirmed the adequacy of the proposed method and the method of mathematical modeling. Divergences in the values of the calculated parameters were no more than 5%.