The effect of friction on the stamp’s flat sole coming off the sole base
DOI:
https://doi.org/10.15587/1729-4061.2015.47782Keywords:
elastic two-layer base, flat-solestamp, the Coulomb friction, coming offAbstract
The study provides an algorithm for precise determining of the contact pressure under a flat-solestamp that is pressed into an elastic laminated multilayer base with any finite number of layers. We have taken into account the friction between the stamp and the base whose contact was one-sided. The algorithm can solve fundamentally new contact problems of elastic multilayer media. As an example, we have solved the problem of a cylindrical flat-sole stampindented in a two-layer base for two cases. In the first case, in contrast to the second, friction was not taken into account. A distinctive feature of the two-layer base is its top layer that is much stiffer than the lower one. We have found that in the first case the two-layer base partially comes off the stamp, while in the second caseit does not. Ultimately, the suggested algorithm can reduce the safety factors for strength and rigidity in calculations of real multilayer structures.Consequently, it can reduce consumption of materials and cost of the structures.
References
- Kravchuk, A. S. (2009). Variacionnyj metod v kontaktnyh zadachah. Sostojanie problemy, napravlenija razvitija. Prikl. matemat. i mehanika, 73 (3), 492–502.
- Reina, S., Dini, D., Hills, D. A., Iida, Y. (2011). A quadratic programming formulation for the solution of layered elastic contact problems: Example applications and experimental validation. European Journal of Mechanics – A/Solids, 30 (3), 236–247. doi: 10.1016/j.euromechsol.2010.12.003
- Aleksandrov, A. I. (2012). Reshenie zadach o kontakte uprugih tel s ispol'zovaniem nelinejnyh integral'nyh uravnenij. Dop. Nacіonal'noi akademіi nauk Ukraini, 11, 47–52.
- Aleksandrov, V. M., Kalker, J. J., Pozharskij, D. A. (1999). Prostranstvennaja kontaktnaja zadacha dlja dvuhslojnogo uprugogo osnovanija s zaranee neizvestnoj oblast'ju kontakta. Izv. RAN. MTT, 4, 51–55.
- Chebakov, M. I. (2002). Trjohmernaja kontaktnaja zadacha dlja sloja s uchjotom sil trenija v oblasti kontakta. Izv. RAN. Mehanika tvjordogo tela, 6, 29–42.
- Sundaram, N., Farris, T. N. (2010). Mechanics of advancing pin-loaded contacts with friction. Journal of the Mechanics and Physics of Solids, 58 (11), 1819–1833. doi: 10.1016/j.jmps.2010.08.004
- Ostrik, V. I. (2004). Kontaktnoe vzaimodejstvie shtampa s uprugoj poluploskost'ju pri nalichii trenija i sceplenija. Teor. i prikl. mehanika, 39, 94–101.
- Ostrik, V. I. (2011). Vdavlivanie shtampa v upruguju polosu pri nalichii trenija i sceplenija. Izv. RAN. Mehanika tvjordogo tela, 5, 119–129.
- Kolosova, E. M., Chebakov, M. I. (2012). Kontaktnye zadachi dlja trjohslojnoj polosy pri nalichki sil trenija. Prikl. matemat. i mehanika, 76 (5), 795–802.
- Stoljarchuk, I. A. (2006). Periodychna kontaktna zadacha ploskoi' teorii' pruzhnosti dlja bagatosharovyh osnov. Dynamika naukovyh doslidzhen' – 2006. Dnipropetrovs'k, 7, 11–15.
- Matuzko, Ju. O. (2004). Prostorovi kontaktni zadachi dlja pruzhnoi' bagatosharovoi' osnovy z gladkoju mezheju. Donec'k, 22.
- Privarnikov, A. K., Lamzjuk, V. D. (1985). Uprugie mnogoslojnye osnovanija. Dep. v VINITI 23.12.8, 8789 –V, 162.
- Aleksandrov I. O. (2015). Prostorova kontaktna zadacha pro diju shtampa z ploskoju pidoshvoju na pruzhnu bagatosharovu osnovu z urahuvannjam tertja mizh shtampom i osnovoju. Visnyk ZNU. Fizyko-matematychni nauky, 3, 54–64.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Іван Олександрович Александров, Аркадій Константинович Приварников
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.
