Approximation of deflections of plates lying on winkler base
https://doi.org/10.33979/2073-7416-2024-111-1-30-37
Abstract
The purpose of this research is to develop the method of shape factor interpolation for calculating the maximum deflection of thin plates on an elastic Winkler base, which are widely used in modeling the operation of elements of building constructions of buildings and structures. The above calculation method allows to obtain solutions based on direct analytical dependences, the argument of which is an integral characteristic of a flat convex one-connected area - the shape factor. This characteristic has applications in a number of problems of mathematical physics and is known from the works of scientists G. Polia and G. Szegö. The shape factor was first applied to the calculation of plates by Professor V.I. Korobko. The method of interpolation by shape factor was developed by Professor A.V. Korobko. When determining the maximum deflection of thin plates on an elastic base, some parameters of the problem are considered as functions of the shape factor of the plate in consideration and are determined by the type of boundary conditions on its contour. The present study is devoted to the construction of approximating functions for continuous sets of plates of characteristic outlines and boundary conditions. The paper presents functions for calculating the maximum deflection of elastic plates in the form of isosceles triangles, rhombuses and rectangles. The plates with various combinations of hinged support and rigid pinch along their individual sides, loaded with a continuous uniformly distributed load, are considered. The established functional dependences are intended for direct use in the calculation of plates of the specified outlines, as well as for obtaining reference solutions during interpolation of the values of maximum deflections of plates of more complex outlines.
About the Authors
A. V. Korobko
Orel State University named after I.S. Turgenev
Russian Federation
Russian Federation
Korobko Andrey V., Doctor of Technical Sciences, Professor, Professor of the Department of mechatronics, mechanics and robotics,
Orel.
M. Yu. Prokurov
Bryansk State Technological University of Engineering
Russian Federation
Russian Federation
Prokurov Maxim Yu., Candidate of Technical Science, Assoc. Prof., Associated Professor of the Department of Building Structures,
Bryansk.
References
1. Sahoo S., Veerendar C., Thammishetti N., Prakash S.S. Experimental and numerical study on behaviour of fibre reinforced lightweight hollow core slabs under different flexure to shear ratios. Structures. 2023. Volume 50. Pp. 1264-1284. https://doi.org/10.1016/j.istruc.2023.02.099
2. Zheng B., Zheng W., Cao B., Zhang Y. Nonlinear finite element analysis of non-symmetrical punching shear of rectangular flat slabs supported on square columns. Engineering Structures. 2023. Volume 277. 115451. https://doi.org/10.1016/j.engstruct.2022.115451
3. Wang R., Fang Z., Lezgy-Nazargah M. Khosravi H. Nonlinear analysis of reinforced concrete slabs using a quasi-3D mixed finite element formulation. Engineering Structures. 2023. Volume 294. 116781. https://doi.org/10.1016/j.engstruct.2023.116781
4. Sahoo S., Veerendar C., Prakash S.S. Experimental and numerical studies on flexural behaviour of lightweight and sustainable precast fibre reinforced hollow core slabs. Construction and Building Materials. 2023. Volume 377. 131072. https://doi.org/10.1016/j.conbuildmat.2023.131072
5. Plans A., Grau D., Soltanalipour M., Ferrer-Ballester M., Marimon F., Andreu A. Three-dimensional finite element modeling for bending and pull-out tests of composite slabs. Engineering Structures. 2023. Volume 295. 116785. https://doi.org/10.1016/j.engstruct.2023.116785
6. Korobko A.V. Geometricheskoe modelirovanie formy oblasti v dvumernykh zadachakh teorii uprugosti [Geometric modeling of the shape of the region in two-dimensional problems of elasticity theory]. Moskva: Izdatel'stvo ASV, 1999. 320 p. (rus)
7. Polia G., Szegö G. Izoperimetricheskie neravenstva v matematicheskoy fizike [Isoperimetric inequalities in mathematical physics]. Moskva: Izdatel'stvo KomKniga, 2006. 336 p. (rus)
8. Korobko V.I. Izoperimetricheskiy metod v stroitel'noy mekhanike: Teoreticheskie osnovy izoperimetricheskogo metoda [Isoperimetric method in structural mechanics: Theoretical foundations isoperimetric method]. Moskva: Izdatel'stvo ASV, 1997. 390 p. (rus)
9. Korobko V.I., Korobko A.V., Morozov S.A., Prokurov M.Yu. Raschyot plastinok metodom predel'nogo ravnovesiya [Calculation of plates using the limit equilibrium method]. Oryol: Tipografiya «Trud», 2012. 360 p. (rus)
10. Korobko A.V., Prokurov M.Yu., Chernyaev A.A. Razvitie tekhnicheskoy teorii rascheta plastinchatykh konstruktsiy na osnove metodov geometricheskogo modelirovaniya ikh formy [Development of the technical theory of calculation of plate structures on the basis of methods of geometric modeling of their shape]. Stroitel'stvo i rekonstruktsiya. 2015. Vol. 57. No. 1. Pp. 17-21. (rus)
11. Prokurov M.Yu. Novyy interpolyatsionnyy metod opredeleniya maksimal'nykh znacheniy progibov tonkikh uprugikh plastinok s proizvol'nym vypuklym konturom [A new interpolational method of estimating maximum deflection values for thin elastic plates with arbitrary convex contour]. Stroitel'stvo i rekonstruktsiya. 2016. Vol. 64. No. 2. Pp. 39-46. (rus)
12. Fetisova M.A., Volodin S.S. Koeffitsient formy kak geometricheskaya kharakteristika [Shape factor as a geometric characteristic]. Molodoy uchyonyy. 2011. Vol. 28. No 5. Pp. 105-107. (rus)
13. Fetisova M.A., Volodin S.S. Primenenie metoda interpolyatsii po koeffitsientu formy dlya resheniya zadach stroitel'noy mekhaniki [Application of the method of interpolation by the factor of shape for solving problems of structural mechanics]. Molodoy uchyonyy. 2013. Vol. 50. No 3. Pp. 114-116. (rus)
14. Aktuganov A.A. Primenenie metoda interpolyatsii po koeffitsientu formy k raschetu plastinok na uprugom osnovanii, nagruzhennykh sosredotochennoy siloy [Application of the method of interpolation by the factor of shape to the calculation of plates foundated on an elastic base and loaded with concentrated force]. Stroitel'stvo i rekonstruktsiya. 2013. Vol. 46. No 2. Pp. 3-11. (rus)
15. Korobko V.I., Aktuganov A.A. Primenenie metoda interpolyatsii po koeffitsientu formy k raschyotu plastinok na uprugom osnovanii [Application of the method of interpolation by the factor of shape to the calculation of plates on an elastic base]. Stroitel'naya mekhanika i raschyot sooruzheniy. 2014. Vol. 252. No 1. Pp. 18-24. (rus)
16. Prokurov M.Yu. Programma rascheta maksimal'nogo progiba tonkikh plastinok na uprugom osnovanii metodom interpolyatsii po koeffitsientu formy [Calculation programme for maximum deflection of thin elastic plates on elastic foundation using interpolation method based on shape factor]. Stroitel'naya mekhanika i raschyot sooruzheniy. 2019. Vol. 285. No 4. Pp. 37-46. (rus)
17. Chernyaev A.A. Opredelenie maksimal'nogo progiba treugol'nykh plastinok s kombinirovannymi granichnymi usloviyami s ispol'zovaniem otnosheniya konformnykh radiusov [Determination of the maximum deflection of triangular plates with combined boundary conditions using the ratio of conformal radii]. Stroitel'naya mekhanika i raschyot sooruzheniy. 2011. Vol. 239. No 6. Pp. 23-29. (rus)
Review
For citations:
Korobko A.V., Prokurov M.Yu. Approximation of deflections of plates lying on winkler base. Building and Reconstruction. 2024;(1):30-37. (In Russ.) https://doi.org/10.33979/2073-7416-2024-111-1-30-37
Views:
121
Email this article 