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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Calculation of plates with variable rigidity on elastic basis by finite difference method

Vestnik MGSU 12/2014
  • Andreev Vladimir Igorevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences, Professor, corresponding member of Russian Academy of Architecture and Construction Sciences, chair, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Barmenkova Elena Vyacheslavovna - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Science, Associate Professor, Department of the Strength of materials, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Matveeva Alena Vladimirovna - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of the Strength of materials, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 31-39

The article describes the calculation of plates on the elastic basis, both two-layer and single-layer. The calculation is based on the solution of the differential equation of bending plate by finite difference method. The calculation results are compared with the numerical solution in the program complex. The percentage of differences of values depending on the method of division or method of solving is shown. We considered a problem when a foundation plate and a construction are plates, which are deformed together, that, in fact, corresponds to the problem of bending a two-layer plate on elastic basis. In case of a two-layer plate in order to find the solution of the problem we need to solve the equation of bending of plates that are structurally similar to the traditional, but still give different results. In solving finite difference operators derivatives are substituted into differential equation which must be in accordance with each grid point, as well as at the border. If we consider the problem in the conventional formulation, only the lower layer is bended in the plate; the analysis of the plate, which takes into account the weight of its own layers, both layers are deformed together. Also when considering a two-layer plate, the neutral layer is deposed away from the upper layer, consequently, the whole foundation plate may be in the condition of stretching. When comparing the results of analytical and numerical calculations of the values obtained in general there are little discrepancies. Thus, there is the possibility of holding combined calculation of the “structure-foundation-base system” by finite difference method using a two-layer model of a plate on elastic basis.

DOI: 10.22227/1997-0935.2014.12.31-39

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