Kundelyev A. Hydroelastic deformation of physically nonlinear cylindrical shells

The subject of the thesis is the deformation of hyperelastic cylindrical vessels caused by inner time-varying flow of viscous liquid. The aim of the thesis is the development of effective methods of solution of fluid-shell interaction problem taking into account hyperelasticity of the shell and Newtonian characteristics of fluid. We used combination of analytical and numerical methods in this work. Scientific novelty of present work consists in development of the theory and methods of the solving of problems of hydroelastic deformation of physically nonlinear cylindrical shells. On the basis of the theory of large deformations and the Navier-Stokes equations for incompressible viscous Newtonian liquid, an improved mathematical model of thick-walled hyperelastic vessel is developed. In order to solve the resulting equations, a new effective numerical method is proposed based on Galerkin method and the finite difference centered scheme. We studied the influence of changes to the physical and geometricalparameters of the shell to the mode of deformation, shear stress, pressure wave speed etc on the basis of real functions of stress strain energy. A new method of blood system's characteristics estimating is proposed. The methods and the results presented in this thesis can be used the engineering decisions when investigating viscous flows in the pipelines with deformable walls as well as in biomechanics and medicine.