Email this article Solution of the Föppl – von Kármán equations for square plates
- Authors: Digilov A.V.1, Lychev S.A.1
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Affiliations:
- Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences
- Issue: Vol 30, No 4 (2024)
- Pages: 26-45
- Section: Mechanics
- URL: https://journals.rcsi.science/2541-7525/article/view/310461
- DOI: https://doi.org/10.18287/2541-7525-2024-30-5-26-45
- ID: 310461
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Abstract
The present paper develops an approach to obtaining solutions of the Föppl – von Kármán equations for square plates, which are based on direct algebraisation of the boundary-value problem. The solution is obtained in term of expansion into basis of the space of square-integrable function. The system of eigenfunction of a linear self-adjoined operator is used as the basis. The expansion coefficients are defined by the reduction method from an infinite-dimensional system of cubic equations. It allows one to consider the proposed solution as non-linear generalisation of classic Galerkin method.
About the authors
Alexander V. Digilov
Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences
Email: digilov@ipmnet.ru
ORCID iD: 0000-0001-6892-7740
Junior researcher of Laboratory of Modelling in Solid Mechanics
Russian Federation, MoscowSergey A. Lychev
Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences
Author for correspondence.
Email: lychevsa@mail.ru
ORCID iD: 0000-0001-7590-1389
leading researcher of Laboratory of Mechanics of Technological Processes
Russian Federation, MoscowReferences
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