title: Statistical criteria for the limits of application of Hooke’s law
metadata.name: dc.contributor.author
metadata.value: Orekhov, Andrey V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-01-19T13:11:18Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-01-19T13:11:18Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Orekhov A. V. Statistical criteria for the limits of application of Hooke’s law. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2020, vol. 16, iss. 4, pp. 391–401.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2020.404
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/22454
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Modern methods for studying the stress-strain state of solids use graphical methods based on
  a stress-strain curve to determine the transition from elastic deformation to plastic
  deformation. However, this approach is not formal and it is intended only for when stress
  is a function of strain in the one-dimensional case. Cases, when strain is a function of the
  stress, are also of practical importance. The purpose of the study is to develop formal rules
  for determining the limits of applicability of Hooke’s law. The proposed analytical methods
  for determining the transition from elastic deformation to plastic deformation are based on
  consistent statistical sequential. In this article, quadratic forms are derived for calculating
  the point at which the type of an increasing monotonous numerical sequence changes
  from linear to non-linear type. With the help of these quadratic forms, statistical criteria
  (approximation-estimation tests) are constructed to determine the limits of applicability
  for Hooke’s law. These boundaries are defined as Markov moments. The novelty of the
  results shows that it is possible to determine the yield point without visualizing the
  experimental data. The numerical example of the application of a parabolic approximationestimation
  test is provided. From the results of this experiment, it can be concluded that the
  analytical determination of the limits of applicability of Hooke’s law coincides with a visual
  assessment. Approximation-estimation tests provide an opportunity to determine the limits
  of applicability of Hooke’s law analytically.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 16; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: Hooke’s law
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stress
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: strain
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: approximation-estimation test
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: least squares method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Markov moments
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Statistical criteria for the limits of application of Hooke’s law
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 391-401.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/22454/1/391-401.pdf
resources.format: Adobe PDF
resources.size: 263,74 kB