Mikulich O. Development of boundary integral equation method for the dynamic problems of heterogeneous and structurally heterogeneous media in the Cosserat elasticity

The dissertation is devoted of the development of the stress state determination method of inhomogeneous and structurally inhomogeneous media with tunnel cavities or holes of arbitrary cross-section for the time-varying distributed and localized loads. This method is based on the application of Fourier transformation over the time and the development of the boundary integral equations method with using the apparatus of the theory of functions of a complex variable. In Cosserat elasticity for the application of the indirect approach of the boundary element method and the weighted-residual approach, the representations for the determination of displacements and microrotations are written. The fundamental functions, which the components is determined the influence of the shear-rotation deformations, are performed. The dynamic stress state of foam media with negative Poisson's ratio (auxetics) and positive Poisson's ratio under the action of distributed and localized non-stationary load is investigated.