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Fundamentals of Continuum Mechanics - NDGF017

Title:	Základy mechaniky kontinua
Guaranteed by:	Department of Geophysics (32-KG)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016
Semester:	both
E-Credits:	3
Hours per week, examination:	2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Note:	you can enroll for the course in winter and in summer semester

Guarantor:	prof. RNDr. František Gallovič, Ph.D.
Teacher(s):	prof. RNDr. František Gallovič, Ph.D. Mgr. Jan Premus, Ph.D.

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Annotation -

Tensor of finite strain and tensor of infinitesimal strain. Stress tensor. Equation of motion in integral and differential forms. Generalised Hooke's law. Hooke's law for an isotropic medium. Equation of motion for a homogeneous isotropic medium. Wave equations. Foundations of hydrodynamics.

Last update: T_KG (29.03.2016)

Aim of the course -

Students will be acquainted with the foundations of the continuum mechanics that are needed in geophysics, in particular in seismology.

Last update: T_KG (11.04.2008)

Course completion requirements -

Oral exam

Last update: Gallovič František, prof. RNDr., Ph.D. (10.06.2019)

Literature - Czech

M. Brdička: Mechanika kontinua. NČSAV, Praha 1959.

O. Novotný: Mechanika kontinua. MFF, Universita Karlova, Praha 1976 (Skripta).

I.S. Sokolnikov: Mathematical Theory of Elasticity. McGraw-Hill, New York 1946.

Y.C. Fung: Foundations of Solid Mechanics. Prentice-Hall, Englewood Cliffs 1965.

Y.C. Fung: A First Course in Continuum Mechanics. Prentice-Hall, Englewood Cliffs 1969.

O. Novotny: Seismic Surface Waves. UFBA, Salvador, Bahia 1999 (Lecture notes).

Last update: T_KG (14.04.2008)

Teaching methods -

Lecture

Last update: T_KG (11.04.2008)

Course assessment methods and requirements for successful completion, grading scheme - Czech

Zkouška je ústní, požadavky odpovídají sylabu v rozsahu prezentovaném na přednášce.

Last update: Gallovič František, prof. RNDr., Ph.D. (06.10.2017)

Syllabus -

Mathematical models in physics

Displacement vector

Strain tensor
Tensor of finite strain. Physical meaning of the components of the tensor of finite strain. Principal axes of strain. Tensor of infinitesimal strain. Volume dilatation.

Stress vector and related problems
Body forces and surface forces. Stress vector. Conditions of equilibrium in integral form. Equations of motion in integral form.

Stress tensor
Components of the stress tensor. Cauchy's formula. Conditions of equilibrium in differential form. Equations of motion in differential form.

Stress-strain relations
Rheological classifications of substances. Generalised Hooke's law.

Equations of motion
Equations of motion for a homogeneous isotropic medium. Wave equations.

Foundations of hydrodynamics
The equations of motion in the Eulerian coordinates. Ideal fluid, equation of continuity, Bernoulli's equation. Viscous fluid, the Navier-Stokes equation.

Last update: T_KG (07.05.2012)

Course registration requirements - Czech

P?ednáška je ur?ena pro studenty, kte?í neabsolvovali úvod do mechaniky kontinua v základním kurzu fyziky, zejména pro absolventy magisterského studia z jiných fakult.

Last update: T_KG (18.01.2007)