Introduction to Continuum Dynamics

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Code	Completion	Credits	Range	Language
01DYK	Z	2	0+2	Czech

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

This course is an introduction to the mathematical description of continuum dynamics. It summarizes the necessary mathematical apparatus with emphasis on vector and tensor calculus, differential forms, and integration on manifolds. It includes the basic concepts of continuum mechanics such as strain and stress tensors or substantial derivative, by means of which it is possible to derive the fundamental laws of conservation of mass, momentum, angular momentum, and energy in integral and differential form. In the last part of the course, these conservation laws are adapted to the case of viscous and inviscid fluid and linear and nonlinear elastic body.

Requirements:

Basic courses in calculus, linear algebra, theoretical physics and differential equations (according lectures at CTU in Prague 01DIFR, 01LA1, 01LAA2, 01MA1, 01MAA2, 01MAA3, 02TEF1).

Syllabus of lectures:

1. Mathematical background

a) vector and tensor calculus

b) differential forms

c) integration on manifolds

2. Basic concepts of continuum mechanics

a) movement and deformation of continuum

b) the strain tensor and small strain tensor

c) decomposition of deformation, rotation

d) substantial derivative of scalar, vector and volume quantities

3. Conservation laws

a) conservation of mass

b) conservation of momentum

c) conservation of angular momentum

d) conservation of mechanical energy

e) conservation of total energy

4. Constitutive relations

a) inviscid fluid

b) viscous fluid

c) non-linear elastic body

d) linear elastic body

5. Selected applications

Syllabus of tutorials:

Study Objective:

Knowledge:

The basic principles of continuum mechanics description. Conservation laws for mass, momentum, angular momentum, and energy. Constitutive equations for viscous and inviscid fluid. Constitutive relations for linear and nonlinear elastic body.

Abilities:

Derivation of basic conservation laws. Derivation of the constitutive relations for the case of fluid or elastic body.

Study materials:

Mandatory reading:

[1] Gurtin, Morton E. An introduction to continuum mechanics. Vol. 158. Academic Pr, 1981.

[2] Anderson, John D. Computational Fluid Dynamics: The Basics with Applications. McGraw-Hill, 1995.