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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Axisymmetric bending of a round elastic plate in case of creep

Vestnik MGSU 5/2014
  • 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 .
  • Yazyev Batyr Meretovich - Rostov State University of Civil Engineering (RSUCE) Doctor of Technical Sciences, Professor, Chair, Depart- ment of Strength of Materials; +7 (863) 201-91-09, Rostov State University of Civil Engineering (RSUCE), 162 Sotsialisticheskaya St., Rostov-on-Don, 344022, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Chepurnenko Anton Sergeevich - Don State Technical University (DGTU) Candidate of Engineering Science, teaching assistant of the strength of materials department, Don State Technical University (DGTU), 162 Sotsialisticheskaya str., Rostov-on-Don, 344022; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 16-24

In the article the problem of bending of circular axially loaded flexible plate during creep was solved. The solution is reduced to a system of two nonlinear differential equations. These equations are suitable for arbitrary dependencies between tensions and creep deformations. The system was solved by the method of successive approximations in conjunction with the finite difference method. Calculations were performed with the help of software package Matlab. We considered round rigidly clamped along the contour plate, which was loaded by the load uniformly distributed over the area. Polymer EDB-10 was taken as a material, which obeys the Maxwell-Gurevich physical law. Creep strains at each point of time were found using linear approximation. In order to verify the correctness of the program, we compared the elastic solution with the result of Professor A. Volmir. He solved this problem by the method of Bubnov-Galerkin only taking into account the geometric nonlinearity. Our results are in good agreement with the solution of. A. Volmir.It is revealed that the calculation excluding geometric nonlinearity gives high values of deflections. The analysis of the equations for t→∞ showed that in linear geometric theory stresses across the thickness of the plate at the end of the creep change linearly. Also the formula for long cylindrical rigidity was obtained. This formula allows us to find the deflection at the end of the creep process, if we know the elastic solution. It is shown that long cylindrical rigidity depends not only on the long elastic modulus v , but also on short elastic modulus v and Poisson's ratio v . It was also found out that in case of high loads stress distribution across the thickness is nonlinear.

DOI: 10.22227/1997-0935.2014.5.16-24

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