Open AccessStability of compressed rods when their stiffness changes according to the law of the fourth power
Author(s) -
Kaiping Yu,
Mykola Surianinov,
Oleksii Shyliaiev
Publication year - 2021
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1164/1/012041
Subject(s) - stability (learning theory) , polynomial , rod , stiffness , work (physics) , power law , function (biology) , mathematics , mathematical analysis , bending stiffness , power (physics) , law , physics , thermodynamics , computer science , statistics , medicine , alternative medicine , pathology , machine learning , evolutionary biology , biology , political science
Based on the previously obtained representations for the state parameters of a rod with arbitrary continuous bending stiffness, the stability problem for a family of rods whose stiffness varies according to the law of the fourth power is solved. The spectrum of critical forces is determined and formulas for curved forms of equilibrium are derived. We propose to consider the stability coefficient as a function of the variable α , and having a set of values of this function corresponding to the values of the independent variable 0 < α ≤ 1, approximate the function K by a polynomial. The result is the expression K 2 = 0.0001 α + 80.7626 α 2 + 0.0002 α 3 . The power of the polynomial was chosen from the condition that the coefficient of determination should not be less than 0.9999. The directions for further research are presented: introduction of the results of this work into the practice of calculations for stability of real objects; application of general formulas for state parameters to the study of stability of rods with other laws of change in transverse stiffness encountered in practice.