Kabysh Y. Investigation of elasticity problems of two-component stochastic composites on the base of static model of inhomogeneous deformation

The thesis is devoted to construction of the mathematical model of inhomogeneous static deforma-tions of unidirectional fibre-reinforced composites which are in a condition of a plane deformation in a plane, perpendicular to a grain flow. It is assumed that the distribution of the fibres is random. The model includes fourth order differential equilibrium equations with respect to the mean displacements (mathematical expectation) and formulas for determining component-wise displacements, strains and stresses through the mean displacements and strains. All coefficients are determined by elastic constants of components and geometric parameters of the structure. The model is correct for arbitrary gradients of external loading. On the base of the model of inhomogeneous static deformations of stochastic composites the fun-damental solutions of equilibrium equations in terms of displacements for granular and unidirectional fibre-reinforced composites are built. On the base of obtained results the displacementfields under the action of point force and point moment are found. With the purpose of illustration of practical application of the model of inhomogeneous static de-formations of stochastic composites two boundary problems are solved - problem of equilibrium of layer, manufactured from granular composite; - problem of stressed state of thick-walled cylinder manufactured from unidirectional fibre-reinforced composite which is under the action of internal and external pressures. The cylinder is in a condition of a plane deformation in a plane, perpendicular to a grain flow. The distributions of component-wise displacement and stresses in these problems are investigated. Boundary-layer effects are analysed. Keywords: two-component elastic stochastic composite, model of inhomogeneous deformations of composites, fundamental solutions of equilibrium equations in terms of displacements, distribution of component-wise displacements and stresses .