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  • Сalculation of circular cylindrical shell by bending theory taking into account creep

    The general equations of the moment theory of a circular cylindrical shell with creep are considered: static, geometric and physical. We solve the problem of determining the stress-strain state of a shell rigidly clamped in the base when an internal hydrostatic pressure acts on it. The problem has reduced to a linear nonhomogeneous differential equation of the fourth order with respect to deflection. The solution was performed numerically by the finite difference method in the Matlab software package. As a law of connection between creep strains and stresses, the generalized nonlinear Maxwell-Gurevich equation was used. To determine the creep strains, a linear approximation of the first time derivative was used. The shell was made from secondary PVC, and as a result, it was found that in the process of creep in the shell, the circumferential stresses increase by 15%.

    Keywords: cylindrical shell; creep; moment theory; polymers; finite difference method

  • Finite element modeling of creep of plates of arbitrary shape

    The article proposes the derivation of resolving equations for the bending of triangular finite element of plate with regard to creep. In deriving of the equations we use Lagrange variational principle. The problem is reduced to a system of linear algebraic equations. Creep contributes only to the right side of the system of equations. These equations allow to calculate the plates of arbitrary shape, taking into account the viscoelastic properties of the material. An example of the calculation for a rectangular plate of a secondary polymeric PVC, hinged along the contour and loaded uniformly distributed over the area load is presented. As a law establishing a link between stress and creep deformation we used nonlinear equation of Maxwell-Gurevich. Calculations were performed in Matlab software package. The graphs of change in time of deflection and stresses are presented. Stress during creep vary slightly, a difference between the stresses at the beginning and end of creep process does not exceed 6%. The result of numerical calculation of the maximum deflection value at the end of creep is different from the theoretical on 0.26%.

    Keywords: creep, finite element method, bending of plates, polymers, Maxwell-Gurevich equation, long cylindrical rigidity