Finite element modeling of creep of plates of arbitrary shape
Abstract
Finite element modeling of creep of plates of arbitrary shape
Incoming article date: 14.02.2017The 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