Determination of the stress-deformed state of a multilayer composite

Abstract

An analytical determination algorithm was developed in the linear formulation, and a particular case of determining the stress-deformed state of a multilayer composite material was investigated. The algorithm is based on the use of the stress function (Ery) and the dependence of all indicators of the stress-deformed state of the material of each layer on its shape. Possible external factors affecting the composite structure are given. For the general case of building a composite structure, the sequence of adding the matrix of coefficients and the vector of free members of the system of linear algebraic equations is formed. The solution of the system of algebraic equations is proposed to be carried out by a method similar to the pre-race method, but for blocks of four equations supplemented by two equations of the influence of the previous layer in the calculation. As a result of actions similar to direct and reverse pre-race, we will obtain vectors of coefficient values of expressions of indicators of the stress-deformed state of the material of all layers as component sums.
 The acceptability of the algorithm for determining stresses and spatial deformations in a separate case of loading a composite sample with square layers is proven. The possibility of using the algorithm for the case of a significant (infinitely large) thickness the farthest from the loaded layer of the composite structure and single-layer (monolithic) material is shown. The following is established: characteristics of the distribution of normal stresses and displacements in the loaded layer of a two-layer composite material. They qualitatively coincide for different values of the Poisson coefficients of the layer materials. The amplitude of stress relief and displacements across the thickness of the loaded layer increases with a decrease in Poisson's ratio. The ratio of extreme values of normal stresses in the material of the loaded layer depends not only on the ratio of the shear moduli or the longitudinal elasticity moduli but also on the ratio of the values of the Poisson coefficients of the materials of the layers.