CALCULATION OF ROD ELEMENTS WITH CRACKS BASED ON A COMBINA-TION OF ROD THEORY AND ELASTICITY THEORY
Main Article Content
Abstract
Mathematical models for calculating the stress-strain state of rods with cracks under tension-compression and bending deformations are presented. A combination of the relations of the theory of elasticity and the theory of rods is used. The main provisions of the proposed modeling method are based on dividing the rod into fragments and finding deformations and stresses for each of the selected fragments according to the theory of rods or the theory of elasticity. Calculation algorithms are described, which are relatively simple to implement. Numerical data for solving problems are provided to illustrate the reliability and accuracy of calculations based on the models described in the article.
Keywords:
Article Details
References
2. Vatul`yan A.O., Soluyanov N.O. Identifikaciya polosti v uprugom sterzhne pri analize poperechny`x kolebanij // PMTF. 2008. T. 49, Vy`p. 6. S. 152–158
3. Shifrin E.I. Inverse spectral problem for a rod with multiple cracks // Mechanical Systems and Signal Processing. 2015. Vol. 56–57. P. 181–196. https://doi.org/10.1016/j.ymssp.2014.11.004
4. Shifrin E.I. Inverse spectral problem for a non-uniform rod with multiple cracks // Mechanical Systems and Signal Processing. 2017. Vol. 96. P. 348–365.
https://doi.org/10.1016/j.ymssp.2017.04.029
5. Lebedev I.M., Shifrin E.I. Reshenie obratnoj spektral`noj zadachi dlya sterzhnya, oslablennogo poperechny`mi treshhinami, s pomoshh`yu optimizacionnogo algoritma Levenberga–Markvardta // Izvestiya Rossijskoj akademii nauk. Mexanika tverdogo tela. 2019. T. 4. S. 8–26. https://doi.org/10.1134/ 80572329919040056
6. Lebedev I.M., Shifrin E.I. Identifikaciya poperechny`x treshhin v sterzhne po sobstvenny`m chastotam poperechny`x kolebanij // Izvestiya Rossijskoj akademii nauk. Mexanika tverdogo tela. 2020. T. 4. S. 50–70. https://doi.org/10.31857/s057232992004008x
7. Axtyamov A.M., Il`gamov M.A. Model` izgiba balki s nadrezom: pryamaya i obratnaya zadachi // Prikladnaya mexanika i texnicheskaya fizika. 2013. T. 54. № 1. S. 152–162 [Akhtyamov A.M., Ilgamov M.A. The model of bending a beam with an incision: direct and inverse problems // Applied mechanics and technical physics. 2013. Vol. 54. No. 1. P. 152–162.] // J. Appl. Mech. Tech. Phys. 2014. Vol. 54. No. 1. P. 132–141. https://doi.org/10.1134/S0021894413010161
8. Il`gamov M.A. Prodol`ny`e kolebaniya sterzhnya s zarozhdayushhimisya poperechny`mi treshhinami // MTT. 2017. № 1. S. 23–31. [Ilgamov M.A. Longitudinal vibrations of a rod with incipient transverse cracks // MTT. 2017. No. 1. P. 23–31.] URL: https://rucont.ru/efd/592439
9. Khiem N., Tran T., Ninh V. A closed-form solution to the problem of crack identification for a multistep beam on Rayleigh quotient // Int. J. Solid Struct. 2018. Vol. 150. P. 154–165. https://doi.org/10.1016/j.ijsolstr.2018.06.010
10. Akulenko L.D., Gavrikov A.A., Nesterov S.V. Identifikaciya defektov poperechnogo secheniya sterzhnya po sobstvenny`m chastotam i osobennostyam formy` prodol`ny`x kolebanij // Izvestiya Rossijskoj akademii nauk. Mexanika tverdogo tela. 2019. Vy`p. 6. S. 98–107. https://doi.org/10 . 1134/ S0572329919060023
11. Loya J., Lopez-Puente J., Zaera R., Fernandez-Saez J. Free transverse vibra-tions of cracked nanobeams using a nonlocal elasticity model // J. Appl. Phys. 2009. Vol. 105. 044309. https://doi.org/10.1063/1.3068370. Corpus ID: 121034133
12. Akbarzadeh Khorshidi M., Shariati M. Buckling and postbuckling of size-dependent cracked microbeams based on a modified couple stress theory // J. Appl. Mech. Tech. Phys. 2017. Vol. 58. No. 4. P. 717–724. https://doi.org/10.1134/S0021894417040174
13 Fu Ch., Yan S. Analiz izgiba balki Timoshenko s treshhinoj s ispol`zovaniem nelokal`noj gradientnoj teorii uprugosti // Prikladnaya mexanika i texnicheskaya fizika. 2019. T. 60. № 3. s. 196–206 [Fu Ch., Yan S. Analysis of the Timo-shenko beam bending with a crack using a non-local gradient theory of elasticity // Applied mechanics and technical physics. 2019. Vol. 60. No. 3 P. 196–206]. https://doi.org/10.15372/PMTF20190320
14. Xiao Y., Jin H., Yu O. Bending of Timoshenko beam with effect of crack gap based on equivalent spring model // Appl. Math. Mech. 2016. Vol. 37. P. 513–528. https://doi.org/10.1007/S10483-016-2042-9. Corpus ID: 124769412
15. Batihan A.Ç., Kadioğlu F.S. Vibration Analysis of a Cracked Beam on an Elastic Foundation // International Journal of Structural Stability and Dynamics. 2016. Vol. 16. № 5. 15500066. https://doi.org/10.1142/S0219455415500066
16. Mazaheri H., Rahami H., Kheyroddin A. Static and Dynamic Analysis of Cracked Concrete Beams Using Experimental Study and Finite Element Analysis // Pe-riodica Polytechnica Civil Engineering. 2018. Vol. 62. No. 2. P. 337–345. https://doi.org/10.3311/PPci.11450
17. Fu C., Wang Y. and Tong D. Chunyu F., Yuyang W., Duway T. Stiffness Estimation of Cracked Beams Based on Nonlinear Stress Distributions Near the Crack // Mathematical Problems in Engineering. 2018. 5987973. https://doi.org/10.1155/2018/5987973
18. Serazutdinov M.N. Modelirovanie treshhin i izmenenij v poperechny`x razmerax sterzhnya pri prodol`noj deformacii // Vestnik Texnologicheskogo universiteta. 2024. T.27. № 7. S. 144–150
19. Serazutdinov M.N. Opredelenie peremeshhenij balki s treshhinoj s ispol`zovaniem teorii sterzhnej // Izvestiya KGASU. 2024. № 2(68). S. 114–123. https://doi.org/10.48612/NewsKSUAE/68.10, EDN: JPGQMS
20. Serazutdinov M.N., Ubajdulloev M.N. Metod rascheta vozmozhny`x parametrov vizual`no nedostupny`x povrezhdenij sterzhnevy`x konstrukcij // Vestnik texnologicheskogo universiteta. 2025. T. 28. № 9. S. 112–115.
21. Serazutdinov M.N. Metod postroenie finitnoj funkcij klassa vy`sokoj stepeni approksimacii // Vestnik Texnologicheskogo universiteta. 2016. T. 19. № 11. S. 160–162

This work is licensed under a Creative Commons Attribution 4.0 International License.
Presenting an article for publication in the Russian Digital Libraries Journal (RDLJ), the authors automatically give consent to grant a limited license to use the materials of the Kazan (Volga) Federal University (KFU) (of course, only if the article is accepted for publication). This means that KFU has the right to publish an article in the next issue of the journal (on the website or in printed form), as well as to reprint this article in the archives of RDLJ CDs or to include in a particular information system or database, produced by KFU.
All copyrighted materials are placed in RDLJ with the consent of the authors. In the event that any of the authors have objected to its publication of materials on this site, the material can be removed, subject to notification to the Editor in writing.
Documents published in RDLJ are protected by copyright and all rights are reserved by the authors. Authors independently monitor compliance with their rights to reproduce or translate their papers published in the journal. If the material is published in RDLJ, reprinted with permission by another publisher or translated into another language, a reference to the original publication.
By submitting an article for publication in RDLJ, authors should take into account that the publication on the Internet, on the one hand, provide unique opportunities for access to their content, but on the other hand, are a new form of information exchange in the global information society where authors and publishers is not always provided with protection against unauthorized copying or other use of materials protected by copyright.
RDLJ is copyrighted. When using materials from the log must indicate the URL: index.phtml page = elbib / rus / journal?. Any change, addition or editing of the author's text are not allowed. Copying individual fragments of articles from the journal is allowed for distribute, remix, adapt, and build upon article, even commercially, as long as they credit that article for the original creation.
Request for the right to reproduce or use any of the materials published in RDLJ should be addressed to the Editor-in-Chief A.M. Elizarov at the following address: amelizarov@gmail.com.
The publishers of RDLJ is not responsible for the view, set out in the published opinion articles.
We suggest the authors of articles downloaded from this page, sign it and send it to the journal publisher's address by e-mail scan copyright agreements on the transfer of non-exclusive rights to use the work.