Variational-difference Approach to calculation of a Three-layer beam taking into account the creep of the middle layer

Objective. This article presents a calculation method for a three-layer beam with lightweight filler taking into account the creep of the middle layer. A significant development of deformations over time under a constant load is presented.

Method. A beam hinged at the ends is investigated under a uniformly distributed load; the solution is carried out using the variational-difference method. The linear Maxwell-Thompson equation is used as the creep law. The Euler and Runge-Kutta methods are used to calculate the growth rate of highly elastic deformations.

Result. A graphical analysis of changes in stresses and deformations over time is presented. It is found that the ratio of elastic and creep deformations at different points in time varies significantly. A program has been developed for calculations in the MATLAB package with the ability to vary the initial data and output a graph of the dependence of displacements and bending moment on time. A comparison of the maximum deflection in the elastic stage (at the initial moment of time) with the solution in the LIRA SAPR software package is presented. It is noted that the stresses remain virtually unchanged during creep.

Conclusion. The proposed approach can be applied to the analysis of the stress-strain state and bearing capacity for any sandwich panels of arbitrary cross-section. There are no restrictions on the boundary conditions and type of loading, and the material of the beam's bearing layers can be not only metal, but also any other material, in particular, composite.

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