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Course info
KME / MK
:
Course description
Department/Unit / Abbreviation
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KME
/
MK
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Continuum Mechanics
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
6
Cred.
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Type of completion
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Written
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Type of completion
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Written
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Time requirements
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Lecture
3
[Hours/Week]
Tutorial
2
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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Yes in the case of a previous evaluation 4 nebo nic.
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Included in study average
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YES
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Language of instruction
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Czech, English
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Occ/max
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Automatic acceptance of credit before examination
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Yes in the case of a previous evaluation 4 nebo nic.
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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5 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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10
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech, English
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
Yes
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Fundamental course |
No
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Fundamental theoretical course |
Yes
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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KMA/MIM, KMA/MMBI, KME/AME, KME/MMB, KME/SZAME, KME/SZMMK, UMS/MFM
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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Student will become acquainted with
- a description of deformations and deformation rates of the continuum
- a description of the stress and temperature fields in the continuum
- formulation of physical laws in the continuum framework
- selected constitutive relations and the foundations of constitutive theory
- variational formulations for the elastic continuum
- basic methods of solving initial-boundary value problems in continuum mechanics
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Requirements on student
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Credit Requirements:
Elaboration and submission of semestral work at the appropriate level.
Exam requirements:
Active knowledge of lectured material and ability to apply theoretical knowledge to solving specific problems of continuum mechanics.
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Content
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1. Definition of the continuum. Scopes and contents of the course. Mathematical description and basics of the tensor calculus. Curvilinear coordinates, physical and practical components of tensors.
2. Continuum kinematics, description of motion in material and spatial configuration. Deformation gradient, strain tensors. Polar decomposition of the deformation gradient.
3. Invariants of tensors. Transformation of volumes and surfaces. The notion of tension and its transformation. Time rates. Compatibility equation.
4. Conservation laws. General formulation of balance relations, mass conservation, mechanical equilibrium of forces and moments.
5. Thermodynamic system and its state. Energy Balance, 2nd Law of Thermodynamics. Clausius-Duhem's inequality.
6. Theory of constitutive laws, classification of materials. Generalized Hooke's law, viscous Newtonian fluids.
7. Problems in continuum mechanics. Elastostatics and elastodynamics, plain strain and plain deformation problems, thermoelastodynamics. Material constants. Duhamel-Neumann's relationship.
8. Variational formulation for problems in continuum mechanics. The virtual works principle (weak formulation). Minimum potential energy principle, dual formulation, maximum of the complementary energy.
9. Numerical methods for solving the problems in continuum mechanics. Ritz and Galerkin methods.
10. Finite Element Method. Algorithmization.
11. Viscoelasticity, 1D rheological models, generalization for continuum.
12. Problems in fluid mechanics. Stationary and non-stationary flows, isothermal and non-isothermal flows. Physical similarity, dimensionless form of equations of continuum mechanics.
13. Models of the elasto-plastic body. Formulation of problems.
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Activities
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Fields of study
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Pro přednášky v tomto předmětu jsou studentům k dispozici podklady ve formě PDF prezentace jednotlivých přednášek a doplňujících textů k některým vybraným přednáškám.
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Guarantors and lecturers
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Literature
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Basic:
Rosenberg, Josef; Křen, Jiří. Mechanika kontinua. 1. vyd. Plzeň : ZČU, 1995. ISBN 80-7082-209-0.
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Basic:
Křen, Jiří; Rosenberg, Josef. Mechanika kontinua. 2., upr. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-908-7.
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Recommended:
Obetková, Viera; Košinárová, Anna; Mamrillová, Anna. Teoretická mechanika. 1. vyd. Bratislava : Alfa, 1990. ISBN 80-05-00597-0.
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Recommended:
Servít, Radim. Teorie pružnosti a plasticity II. Vyd. 1. Praha : SNTL, 1984.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Graduate study programme term essay (40-50)
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45
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Contact hours
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65
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Preparation for an examination (30-60)
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50
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Total
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160
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
orientovat se v základech maticového počtu, lineární algebry, vektorové analýzy, diferenciálního a integrálního počtu, numerických metod |
popsat jednoduché diskrétní mechanické soustavy |
popsat principy algoritmizace jednoduchých problémů |
vysvětlit základní fyzikální zákony |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
používat některý programovací jazyk na úrovni implementace základních numerických algoritmů a jednoduchých operací s datovými strukturami |
zmíněné znalosti použít pro řešení jednoduchých úloh pro diskrétní mechanické soustavy |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
popsat základní pojmy popisu kontinua, zejména pojmy deformace, napětí, energie, disipace |
znát obecné zásady formulace bilančních vztahů ve vztahu k fyzikálním zákonům |
orientovat se v základních konstitutivních vztazích |
znát metodiku formulace úloh pro termo-elastická tělesa |
Skills - skills resulting from the course: |
aplikovat teoretické poznatky při řešení jednodušších úloh pro elastické a termoelastické kontinuum, či pro vazké tekutiny |
formulovat úlohy pro termo-viskoelastické kontinuum kontinuum pro běžné případy silového zatížení a působení teplotního pole |
analyzovat a interpretovat výsledky |
Competences - competences resulting from the course: |
N/A |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Oral exam |
Seminar work |
Skills - skills achieved by taking this course are verified by the following means: |
Individual presentation at a seminar |
Oral exam |
Competences - competence achieved by taking this course are verified by the following means: |
Oral exam |
Individual presentation at a seminar |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Practicum |
Skills - the following training methods are used to achieve the required skills: |
Lecture with visual aids |
Practicum |
Individual study |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Practicum |
Lecture with visual aids |
Individual study |
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