4 semester


Name of the discipline

Continuum mechanics


Course of study, specialty

2, specialty “mechanics and mathematical modeling”


Semester of training



Amount of credits



FULL NAME. lecturer

Doctor of Phys.-Math. Sciences, Professor Mihasev GI


Objectives of studying the discipline

The aim of the course is to study the models, methods and methods for solving the problems of all the sections of continuum mechanics.

 As a result of the study, the student should be able to:

–         use the basic equations of continuum mechanics in the formulation of specific educational and applied problems;

–         apply knowledge in the field of differential and integral equations, the theory of functions of a complex variable in the solution of these problems;

–         apply approximate, asymptotic and numerical methods for solving the problems of mechanics of a deformable solid



Theoretical Mechanics


Contents of the discipline

– The subject of continuum mechanics. Scope of applications, perspective directions.

 – Stress state analysis. The concept of a continuous medium. Uniformity. Isotropy. Mass density Mass forces. Surface forces. Principle of Cauchy stress. The stress vector. Stress state at the point. Stress tensor. The connection between the stress tensor and the stress vector. Symmetry of the stress tensor. Invariants of the stress tensor. The maximum and minimum shear stress. Plane stressed state. Deviator and ball stress tensor

 – Deformations. Eulerian and Lagrangian motion description. Transition from Lagrange variables to Euler variables and back. Vector of displacement. The tensor of small deformations. Main axes, principal values, invariants of the strain tensor. The mechanical meaning of the components of the strain tensor. Equivalence equations for the components of the tensor of small deformations.

 Linear theory of elasticity. The generalized law of Hooke. Deformation energy function. Isotropic and anisotropic media. Symmetry of elastic properties. Isotropic media. Elastic constants. Static and dynamic problems of the theory of elasticity


Recommended literature

1.     Morozov N.F. Lectures on selected issues of continuum mechanics. – L.: Publishing house leningr. University, 1975.

2.     Atanatskovich T., Guran A., Lectures on the theory of elasticity (edited by AL Smirnov and PE Tovstika), St. Petersburg State University, 2003.

3.     Lurie A.I. Theory of elasticity. – Moscow: Nauka, 1980, 940 p.

4.     Muskhelishvili NI, Some basic problems of the mathematical theory of elasticity. – Moscow: Nauka, 1966, 634 p.

5.     Vasizu Quitri. Variational methods in the theory of elasticity and plasticity. – Moscow: Mir, 1987, 542 p.

6.     Ishlinsky A.Yu., Ivlev D.D. Mathematical theory of plasticity. – Moscow: Fizmatlit, 2001. – 704 p.

7.     Continuum mechanics in problems. Ed. M.E. Eglith. – Moscow: Moscow Lyceum, vols. I – II, 1996.


Teaching Methods

Lectures. Practical lessons. Individual tasks. Test papers


Language of instruction



Conditions (requirements)

The score on the exam is set taking into account:

40% – work in practical classes, 60% – verbal response in the exam.


Format of the current certification

Examination, credit