Numerical and analytical modeling of plate creep under bending

Objective. This paper considers the stress-strain state of a rigid plate subject to bending under creep conditions, with various boundary conditions. A resolving linear inhomogeneous differential equation of the fourth order with respect to deflection is obtained. The solution is numerically solved using a Maurice-Lévy-type analytical method in the MATLAB software package using unary trigonometric series. The nonlinear Maxwell-Gurevich equation is used as the equation of state between creep strains and stresses.

Method. A linear approximation of the first time derivative, the Euler method, was used to determine creep strains. To verify the solution, a mesh calculation was performed on a recycled PVC plate [1]. The method was validated by comparing the solution with calculations by other renowned researchers.

Result. A program was developed for calculations in the MATLAB package with the ability to vary the initial data and plot a graph of displacements and stresses versus time. Using a recycled PVC plate as an example, it is shown that stresses change insignificantly during creep.

Conclusion. The proposed approach can be applied to the analysis of the stress-strain state and the load-bearing capacity of a reinforced concrete slab. There are no restrictions on boundary conditions or loading type, and the plate material can be not only polymers and composites for construction purposes, but also concrete.

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