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

作者: Gubaidullin D.A.¹, Krysko A.V.², Tebyakin А.D.³, Yakovleva T.V.³, Krysko V.A.³
隶属关系:
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
期: 卷 518, 编号 1 (2024)
页面: 43-50
栏目: МЕХАНИКА
URL: https://consilium.orscience.ru/2686-7400/article/view/677505
DOI: https://doi.org/10.31857/S2686740024050073
EDN: https://elibrary.ru/HXJWMW
ID: 677505

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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.

关键词

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

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作者简介

D. Gubaidullin

Саратовский государственный технический университет имени Ю.А. Гагарина

编辑信件的主要联系方式.
Email: gubaidullin@imm.knc.ru

Corresponding Member of the RAS

俄罗斯联邦, Саратов

A. Krysko

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

Email: kryskoav@sstu.ru
俄罗斯联邦, Kazan

А. Tebyakin

Yuri Gagarin State Technical University of Saratov

Email: gubaidullin@imm.knc.ru
俄罗斯联邦, Saratov

T. Yakovleva

Yuri Gagarin State Technical University of Saratov

Email: gubaidullin@imm.knc.ru
俄罗斯联邦, Saratov

V. Krysko

Yuri Gagarin State Technical University of Saratov

Email: tak@san.ru
俄罗斯联邦, Saratov

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1. JATS XML

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2. Fig. 1. Calculation scheme.

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

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

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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.

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

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

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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.