Axisymmetric bending of a round elastic plate in case of creep
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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