On the Basic Systems of Equations of Continuum Mechanics and Some Mathematical Problems for Anisotropic Thin-Walled Structures

摘要

A dynamic system of partial differential equations (PDEs) which is 3D with respect to spatial coordinates and contains as a particular case both: Navier-Stokes equations and the nonlinear systems of PDEs of the elasticity theory is proposed. Mathematical models for anisotropic, poroelastic media are created and justified. These models are applied to dynamic and steady-state nonlinear problems for thin-walled structures. A direct method of constructing von Karman type equations in dynamical case is proposed.