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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2016, Volume 20, Number 3, Pages 508–523 (Mi vsgtu1467)  

Mechanics of Solids

Limit analysis and optimal support of reinforced three-layer circular plates of different resistant materials under non-uniform loading

T. P. Romanova

Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation

Abstract: Within the model of an ideal rigid-plastic body the limit behavior of the hybrid composite circular plates is considered. The exact solution of the problem of bending is built for three-layer reinforced circular plates having different angular structure reinforcement at the top and bottom layer. The material of the middle layer and the binder in the upper and lower layers has a yield stress in compression much greater than in tension. In this case the condition of plasticity for the main moments that are based on the structural model of the reinforced layer with one-dimensional states of stress in the fibers has the form of a rectangle of type Johansen condition. The plates are hinge supported along the internal annular contour and have the rigid circular insert in the central part. The plates are under load non-uniformly distributed over the surface of the plate. It is shown that there are a few schemes of limit deformation of the plate, depending on the location of the internal support and on distribution of load. The conditions of implementation are defined for all schemes. The main moments and the velocities of the deflections of the plate are defined at different locations of the internal support. The simple analytic expressions are obtained for the limit load. The optimal location of support is determined. The optimal support is such support, at which the plate has a maximum limit load. It is shown that the optimal position of the support corresponds to the formation of plastic hinge on it. It is obtained that with increase in the applied distributed load in several times, the limit loads will be reduced in the same times and the optimal location of the support will not change. Numerical examples are given. The solution can be useful in engineering practice to evaluate the bearing capacity of three-layer reinforced concrete plates.

Keywords: rigid-plastic model, hybrid reinforcement, different-resistant materials, corner reinforcement, three-layer plate, non-uniform loading, internal support, limit load, optimal support

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00102-а
This work was supported by the Russian Foundation for Basic Research (project no. 14–01–00102-a).


DOI: https://doi.org/10.14498/vsgtu1467

Full text: PDF file (752 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 539.37:539.411.5
MSC: 74P99, 74K20, 74C99
Original article submitted 12/I/2016
revision submitted – 25/VI/2016

Citation: T. P. Romanova, “Limit analysis and optimal support of reinforced three-layer circular plates of different resistant materials under non-uniform loading”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:3 (2016), 508–523

Citation in format AMSBIB
\Bibitem{Rom16}
\by T.~P.~Romanova
\paper Limit analysis and optimal support of reinforced three-layer
circular plates of~different resistant materials under non-uniform loading
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2016
\vol 20
\issue 3
\pages 508--523
\mathnet{http://mi.mathnet.ru/vsgtu1467}
\crossref{https://doi.org/10.14498/vsgtu1467}
\zmath{https://zbmath.org/?q=an:06964523}
\elib{https://elibrary.ru/item.asp?id=28282246}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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