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Course, academic year 2023/2024
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Foundations of continuum mechanics - MG452P80
Title: Základy mechaniky kontinua
Czech title: Základy mechaniky kontinua
Guaranteed by: Institute of Hydrogeology, Engineering Geology and Applied Geophysics (31-450)
Faculty: Faculty of Science
Actual: from 2020
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
Explanation: Výuka probíhá s ohledem na situaci dle nařízení hyg. stanice hl.m. Prahy a MŠMT
Note: enabled for web enrollment
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.
doc. RNDr. Oldřich Novotný, CSc.
Annotation -
Last update: Mgr. Zdeňka Sedláčková (14.05.2012)
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.
Literature -
Last update: Mgr. Zdeňka Sedláčková (15.05.2012)

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).

Requirements to the exam - Czech
Last update: Mgr. Zdeňka Sedláčková (15.05.2012)

Zkouška formou ústní.

Syllabus -
Last update: Mgr. Zdeňka Sedláčková (14.05.2012)

Outlook

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. Homogeneous strain. Relations among the elastic coefficients.

Equations of motion

Equation 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.

 
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