Finite element modeling of creep bending of polymer plates

Thin rigid plates are considered in the article and the derivation of the equations of bending of a quadrangular finite element of a plate is given that takes creep into account creep. The equations are derived using the Lagrange variational principle. The relationships between the integral characteristics of stresses (linear bending and torque moments) and the curvatures of the middle surface are taken as physical relationships. Given as an example, the problem of analyzing a rectangular polymer plate made of secondary PVC, hinged along the contour and loaded with a load uniformly distributed over the area, is reduced to a system of linear algebraic equations. Maxwell-Gurevich equation was choosen as the equation of state between stresses and creep strains. Graphs of stress and deflection changes over time are presented. The stresses in the creep process change insignificantly, the difference between the stresses at the beginning and at the end of the creep process is less than 5%.

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