Nonlinear Rheological Processes Modeling in Three-Layer Plates with a Polyurethane Foam Core

Abstract

Introduction: Three-layer structures with a polyurethane foam filler are widely used in construction as roofing and wall panels. The purpose of this work is to develop a method for calculating the bending of three-layer plates with a polyurethane foam filler, taking into account the nonlinear creep of the middle layer. The non-linear Maxwell–Gurevich equation is used as the polyurethane foam creep law. Methods: In the article, the system of resolving the equations is obtained, and the solution is carried out numerically by the finite difference method in combination with the Euler method in a MATLAB environment. An analytical solution is also obtained for a plate hinged along the contour. Results: The developed model and calculation algorithms are verified by comparison with the calculation in the ANSYS software package. A comparison with the calculation according to the linear theory is also carried out, and the effects caused by the non-linear creep of polyurethane foam are revealed. Conclusion: It has been established that when nonlinear creep is taken into account, in contrast to the linear law, the stresses in the plate are not constant in time. In the faces, at the initial stage, the stresses increase with a subsequent return to the initial values, and in the filler, on the contrary, the stresses at the initial stage decrease. These results indicate the need to take into account the nonlinear creep of polyurethane foam in the calculation of sandwich panels.