Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Kalutsky L. A., Krysko A. V., Yakovleva T. V., Krysko V. A. Variational iteration method for investigating flexible porous functionally graded size-dependent oblique plates. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2025, vol. 25, iss. 4, pp. 524-533. DOI: 10.18500/1816-9791-2025-25-4-524-533, EDN: MVMKLN

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
28.11.2025
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Language: 
Russian
Heading: 
Mechanics
Article type: 
Article
UDC: 
519.6
DOI: 
10.18500/1816-9791-2025-25-4-524-533
EDN: 
MVMKLN

Variational iteration method for investigating flexible porous functionally graded size-dependent oblique plates

Autors: 
Kalutsky Leonid A., Lavrentiev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences
Krysko Anton V., Lavrentiev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences
Yakovleva Tatiana V., Lavrentiev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences
Krysko Vadim A., Lavrentiev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences
Abstract: 

A model of flexible oblique Kirchhoff plates made of porous functional-gradient materials is derived. Nonlinearity is accounted for by the theory of T. von Karman. The nonlinear partial derivative equations are solved using the method of variational iterations. The validity of the results obtained by the method of variational iterations is ensured by comparative analysis with known solutions. The stress-strain state (STS) of oblique-angled plates is investigated. The influence of plate inclination angle, dimensional effects, porosity and functional gradient of the material is analyzed. The stress concentration near voids can be neglected due to their small size, and a smooth, continuous stress variation along the plate thickness is assumed. It is revealed that the increase in the volume fraction of ceramics in functionally graded materials allows to significantly increase the bearing capacity of oblique plates. The oblique plates with increased pore concentration from the upper and lower surfaces to the center have the highest bearing capacity compared to the uniform porosity distribution and reduced concentration. The magnitude of the inclination angle and size-dependent parameter significantly affects the bearing capacity of porous functional-gradient oblique-angled plates.

Key words: 
flexible oblique plates
plates of complex geometry
porosity distribution
Yang’s theory
Acknowledgments: 
This work was supported by the Russian Science Foundation (project No. 22-11-00160-P).
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Received: 
05.06.2025
Accepted: 
20.07.2025
Published: 
28.11.2025
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