Modelling of plates made from bimodular material taking into account elastic-plastic deformations

D. A. Gubaidullin; Губайдуллин Д. А.; A. V. Krysko; Крысько А. B.; А. D. Tebyakin; Тебякин А. Д.; T. V. Yakovleva; Яковлева Т. В.; V. A. Krysko; Крысько B. А.

doi:10.31857/S2686740024050073

Modelling of plates made from bimodular material taking into account elastic-plastic deformations

Authors: Gubaidullin D.A.¹, Krysko A.V.², Tebyakin А.D.³, Yakovleva T.V.³, Krysko V.A.³
Affiliations:
1. Саратовский государственный технический университет имени Ю.А. Гагарина
2. Institute of Mechanics and Engineering, FRC “Kazan Scientific Center, Russian Academy of Sciences”
3. Yuri Gagarin State Technical University of Saratov
Issue: Vol 518, No 1 (2024)
Pages: 43-50
Section: МЕХАНИКА
URL: https://ter-arkhiv.ru/2686-7400/article/view/677505
DOI: https://doi.org/10.31857/S2686740024050073
EDN: https://elibrary.ru/HXJWMW
ID: 677505

Cite item

Full Text

Open Access
Restricted Access

Access granted
Restricted Access

Subscription Access

Abstract
Full Text
About the authors
References
Supplementary files
Statistics

Abstract

A mathematical model of the stress-strain state of plates made of bimodular material with elastic-plastic deformations according to the deformation theory of plasticity is constructed. The stress-strain state of plates is studied by the variational iterations method or the extended Kantorovich method. The solutions obtained are close to exact. For rectangular plates subjected to a uniformly distributed load, the neutral plane is found to be the interface between the compression and tension zones.

Keywords

bimodular material, variational iteration method, Birger’s variable parameter method, neutral surface, exact solutions

Full Text

About the authors

D. A. Gubaidullin

Саратовский государственный технический университет имени Ю.А. Гагарина

Author for correspondence.
Email: gubaidullin@imm.knc.ru

Corresponding Member of the RAS

Russian Federation, Саратов

A. V. Krysko

Institute of Mechanics and Engineering, FRC “Kazan Scientific Center, Russian Academy of Sciences”

Email: kryskoav@sstu.ru
Russian Federation, Kazan

А. D. Tebyakin

Yuri Gagarin State Technical University of Saratov

Email: gubaidullin@imm.knc.ru
Russian Federation, Saratov

T. V. Yakovleva

Yuri Gagarin State Technical University of Saratov

Email: gubaidullin@imm.knc.ru
Russian Federation, Saratov

V. A. Krysko

Yuri Gagarin State Technical University of Saratov

Email: tak@san.ru
Russian Federation, Saratov

References

Supplementary files

Supplementary Files

Action

1. JATS XML

Download

2. Fig. 1. Calculation scheme.

Download (93KB)

Indexing metadata

3. Fig. 2. Dependence q[w(0.5, 0.5)] for a plate, obtained by the MWI and MBG methods in various approximations.

Download (106KB)

Indexing metadata

4. Fig. 3. Dependence for gray iron for approximation of models 1 and 2.

Download (120KB)

Indexing metadata

5. Fig. 4. Dependence q[w(0.5, 0.5)] for a plate made of monomodular and bimodular materials and the displacement of the neutral surface.

Download (148KB)

Indexing metadata

6. Fig. 5. Distribution of ei in a plate of single-module material at q = 120 for approximating models 1 and 2.

Download (265KB)

Indexing metadata

7. Fig. 6. Distribution of ei in a plate made of bimodular material at q = 120 for approximating models 1 and 2.

Download (228KB)

Indexing metadata

8. Fig. 7. Distribution of ei in the plate at q = 120 taking into account bimodularity and neutral surface displacement for approximating models 1 and 2.