On the strength of many-layer fiber-reinforced plates

Abstract

In Kolpakov and Rakin (2021), the concept of a representative model for multilayer plates was introduced. It was shown that a three-layer representative plate model provides us with complete information about the local stress-strain state (SSS) in a multilayer plate formed from an arbitrary number of layers. In this paper, it is shown that for a many-layer plate (the number of layers is more than 300), the periodicity cell problems (PCPs) corresponding to in-plane (tension/shear) make the main contribution to the local SSS. On one hand, it is a similarity with the uniform plate. On another hand, the solutions to the PCPs corresponding to in-plane (tension/shear) for fiber-reinforced plate are very different from the solutions corresponding to uniform plate.If the number of layers is less than 60, it is necessary to take into account the solutions to the bending/torsion cell problem. In both cases, it is necessary to take into account the skin-boundary layers (which occurs both in tension/shear and bending/torsion PCPs).Using the idea of a representative model, we construct a homogenized strength criterion (HSC) for fiber reinforced plates. As a result of the complex form of the local stress-strain stale in the components of composite, the HSC is built as a computer procedure. Since the representative model is low-dimension one, the procedure is fast.In general, the failure surface is a 5-dimensional surface in 6-dimensional space. For a multilayer plate, the strength criterion depends on three variables (three combinations of tension/shear and bending/torsion). In this case, the failure surface is a 2D surface in 3D space and can be visualized. In multilayer plates, we find many similarities with the classical theory of plates, but at the same time we clearly see quantitative and qualitative differences between multilayer plates and classical information plates. In particular, we see that the maximum of the local stress in composite plate occurs not at the top/bottom surfaces of the plate, but in the deep of the plate.