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The fundamental statements of the continuum mechanics basics are set out. In particular, the paper deals with the nonlinear problems in curvilinear coordinate systems. The first five lectures are devoted to the basics of tensor calculus: the metric tensor, tensor coordinate transformation, differentiation of the basis vectors of curvilinear coordinate, transformation laws of tensor components by changing the coordinate system. The remaining lectures are devoted to the mathematical formulation of stationary and non-stationary nonlinear problems of continuum mechanics: heat and mass transfer systems equations for non-stationary continuum mechanics problems of incompressible and compressible fluids, Euler equations for ideal fluid equations and Navies-Stokes equations for viscous fluid, continuum turbulent motion with regard to the classical Reynolds stress turbulence models.

Oriented on the students of higher educational establishments studying “Industrial Engineering” and related disciplines: Mechanical Engineering, building disciplines, heat power engineering and oil processing industry.


Continuum mechanics – 2. Nonlinear problems of continuum mechanics [Digital resource]: Lecture materials for students studying “Industrial Engineering”, specialized in “Engineering, equipment and technologies for production of polymers and building materials and products” / Contrib.: A. Ya. Karvatskii – K. : Igor Sikorsky Kyiv Polytechnic Institute, 2017. – 94 p.: fig. – Ref.: p. 87–90.