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Main menu for Browse IS/STAG
Course info
KME / TP
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Course description
Department/Unit / Abbreviation
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KME
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TP
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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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Theory of Plasticity
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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,
5
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
2
[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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No
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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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No
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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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1 / -
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2 / -
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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 |
No
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Fundamental course |
Yes
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Fundamental theoretical course |
No
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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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KME/PME
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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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The main aim of this course is to introduce students into the basic principles of plasticity theory to be able to solve simple one-dimensional and two-dimensional problems.
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Requirements on student
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Credit requirements:
Elaboration of terminal paper.
Credit obtained in previous years of study is not accepted.
Examination requirements:
Active knowledge of theory and the ability to apply it to particular problems.
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Content
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1. Deformation of bodies. Mathematical model of boundary value problem in plastic state. Stress analysis: stress tensor, stress deviator tensor and stress spherical tensor, principal stresses, invariants of stress tensor.
2. Invariants of stress deviator tensor, equivalent stress. Density of deformation energy. Strain analysis: relative displacement tensor, pure deformation tensor and rotation tensor, strain deviator tensor and strain spherical tensor, invariants of strain deviator tensor. Equivalent deformation in elastic and plastic state. Volumetric change.
3. Natural strain. Deformation rate. Approximations of stress-strain curves. Static isometric plastic deformation, Bauschinger effect.
4. - 5. Initial yield criteria. Tresca and Mises yield criteria. Comparison of both criteria.
6. - 7. Axisymmetric problems: Rotating discs and thick-walled vessels, elasto-plastic and plastic state.
8. Residual stresses. Drucker's rule of stability. Initial and sequential yield surfaces. Loading function and surface.
9. Loading criteria. Drucker's postulate of stability for triaxial state of stress. Associative law of plastic flow, compatibility condition. Initial yield surface.
10. Yield surface in deviatoric plane. Sequential yield surfaces. Theory of plasticity - theory of small elasto-plastic strains.
11. Theory of plasticity - theory of plastic flow. The comparison of plasticity theories.
12. Elasto-plastic and plastic potential. Elasto-plastic torsion of cylindrical bars.
13. Membrane analogy of torsion.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Recommended:
Hearn, E. J. Mechanics of Materials 2: The Mechanics of Elastic and Plastic Deformation of Solids and Structural Materials. Third Edition. Oxford : Butterworth-Heinemann, 1997. ISBN 978-0750632669.
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Recommended:
Chen, Wai-Fah; Han, D. J. Plasticity for structural engineers. Ft. Lauderdale : J. Ross, 2007. ISBN 978-1-932159-75-2.
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Recommended:
Servít, Radim. Teorie pružnosti a plasticity II. Vyd. 1. Praha : SNTL, 1984.
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Recommended:
Chakrabarty, Jagabanduhu. Theory of Plasticity. Third Edition..
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Recommended:
Plánička, František; Kuliš, Zdeněk. Základy teorie plasticity. Praha : ČVUT, 2004. ISBN 80-01-02876-3.
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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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Contact hours
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52
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Preparation for an examination (30-60)
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40
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Graduate study programme term essay (40-50)
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50
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Total
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142
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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: |
definovat základní pojmy z oblasti lineární teorie pružnosti |
disponovat základními znalostmi v oblasti integrálního a diferenciálního počtu |
orientovat se v základních metodách řešení obyčejných diferenciálních rovnic |
mít základní znalosti z teorie maticového a tenzorového počtu |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
derivovat a integrovat základní matematické funkce |
provádět základní operace s maticemi a vektory (sčítání, násobení, inverze, apod.) |
řešit obyčejné lineární diferenciální rovnice metodou separací proměnných |
sestavit model lineární úlohy pružnosti |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
definovat zobecněné napětí a deformaci |
popsat matematický model okrajové úlohy v plastickém stavu |
vysvětlit význam jednotlivých invariantů tenzoru napětí a deformace a jejich deviátorů |
vysvětlit pojmy počáteční a následná podmínka plasticity a popsat základní modely zpevnění |
popsat základní typy aproximací pracovního diagramu |
Skills - skills resulting from the course: |
formulovat Trescovu či Misesovu podmínku plasticity pro zadanou 1D a 2D úlohu |
provést analýzu napjatosti v elasto-plastickém stavu u vybraných rotačně symetrických úloh |
sestavit rovnice popisující jednoduché úlohy tváření |
řešit základní typy namáhání těles (tah, krut, ohyb) při uvažování plastických deformací |
stanovit zbytková napětí při odlehčení z plně plastického a elasto-plastického stavu pro základní typy namáhání (tah, krut, ohyb) |
Competences - competences resulting from the course: |
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: |
Seminar work |
Oral exam |
Skills - skills achieved by taking this course are verified by the following means: |
Seminar work |
Oral exam |
Competences - competence achieved by taking this course are verified by the following means: |
Seminar work |
Oral exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Practicum |
Self-study of literature |
Lecture supplemented with a discussion |
One-to-One tutorial |
Skills - the following training methods are used to achieve the required skills: |
Lecture supplemented with a discussion |
Practicum |
One-to-One tutorial |
Competences - the following training methods are used to achieve the required competences: |
Lecture with visual aids |
Practicum |
Task-based study method |
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