Bohuslavska A. Thermomechanical characteristics of a fibrous composite material with anisotropic components

The thesis is devoted to the solution of the problem of determining the effective thermomechanical characteristics for a fibrous composite with transversely isotropic components and their application to the solution of boundary-value problems of thermoelasticity. The effective temperature coefficients of linear expansion are found by solving two boundary value problems. The first is the task of jointly deforming a composite cylinder with transtropic components. Further, for the composite, which is considered to be a homogeneous transtropic material, an analogous boundary value problem is solved. From the matching conditions, the effective temperature coefficients of the linear expansion of the transtropic material are found, which depend on the thermoelastic constants of the matrix material and the fiber material, as well as the volume content of each of them in the composite. The analytical relations proposed for the temperature coefficients of linear expansion are used in the work to determine the thermoelastic constants of a composite reinforced with two grades of unidirectional fibers. There are two types of cells. As a result of the homogenization of each cell type, two regions are obtained. Taking the first fiber as “conditional” and the second one as “conditional” matrix, homogenization is performed once more. A comparison of the results obtained with those known in the literature is presented. The developed approach is used to determine the temperature coefficients of linear expansion of a three-component composite material when its constituents have transversely isotropic properties. Using the obtained thermomechanical characteristics, an analytical solution is found for the problem of the stress-strain state of a hollow cylinder of a fibrous composite under the influence of temperature and strength loads. On the basis of the finite element method using the proposed thermomechanical characteristics, the thermoelasticity problem for a hollow cylinder, a conically-cylindrical structure of a fibrous composite is solved, and the stress-deformed state of a rubber acoustic vibration isolator with composite inserts under the influence of force and temperature loading is considered.