Local stresses in the reinforced plate with orthogonal sytems of fibers

Abstract

We discuss the methods of computation of local stress–strain state (SSS) in the reinforced plate with orthogonal systems of fibers. Although the problem seems similar to fiber-reinforced solids [1], the final results are more different rather than similar. The main differences between the solids and plates are related to the top and the bottom surfaces of the plate and bending/torsion deformation of the plate. We investigate local stresses corresponding to the basic macroscopic deformations of plate: macroscopic in-plane strain/shift and bending/torsion. Investigation of the boundary layer (BL) near the top and the bottom of the plate demonstrates that the boundary layer thickness is less than the thickness of one structural layer. On this basis, we introduce a new notion of the representative model of a multi-layer plate. Namely, we demonstrate that the three-layer plate provides us with complete information about the local SSS in the multi-layer plate formed of an arbitrary number of layers. This fact allows drastically reduces the dimension of the problems of the calculation of multi-layer fiber-reinforced plates. We discuss the application of these results to the construction of the homogenized strength criterion (HSC) for the fiber-reinforced plates.