Modeling of elastic properties of the reinforced layer of composite elements of structures of complex shape

Abstract

One of the distinctive properties of composite materials is their anisotropy, which allows, in particular, to use their strength properties as efficiently as possible. Elements of structures that are made of composite materials, for structural reasons and to ensure strength, can have a geometric shape, which is characterized by a change in characteristic geometric dimensions along a certain coordinate. This can lead to an increase in the distance between the fibers, and, as a result, to a change in the reinforcement density along one of the coordinates. This is characteristic, for example, when increasing the length of the parallel of the conical shell in height when reinforcing the shell along the meridian, or increasing the length of the circle of the spherical belt when it is reinforced along the radius. The case of rectangular panels (plates or slabs) of variable thickness can be highlighted separately. In order to take into account the influence of these circumstances on the physical and mechanical characteristics of the layer, the variable reinforcement parameter characterizing the volume fraction of the fiber material is introduced from the characteristic coordinate. It is assumed that the fiber and matrix materials are in perfect contact at the separation boundary, local changes in the stress state are not taken into account there. The material of the fibers perceives compressive and tensile stresses, the fibers are arranged regularly. To formalize the description, the shape of the fibers is assumed to be rectangular. On the basis of these provisions, the relations for describing the elastic properties of a layer of a unidirectional fibrous composite material with a variable reinforcement ratio in one of the characteristic directions of the layer are obtained - the components of the stiffness matrix of the orthotropic composite, on the basis of which the effective characteristics of the composite material can be determined in the future (moduli of elasticity and Poisson's ratios in the directions along and across the fibers).