| Course title | Continuum Mechanics |
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| Course code | KME/MK |
| Organizational form of instruction | Lecture + Tutorial |
| Level of course | Master |
| Year of study | 2 |
| Semester | Winter |
| Number of ECTS credits | 6 |
| Language of instruction | Czech, English |
| Status of course | Compulsory-optional |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course 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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| Learning activities and teaching methods |
Lecture, Practicum
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| prerequisite |
| Knowledge |
| 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 |
| 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 |
| N/A |
| N/A |
| N/A |
| N/A |
| N/A |
| learning outcomes |
| Knowledge |
| 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 |
| 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 |
| N/A |
| N/A |
| N/A |
| teaching methods |
| Knowledge |
| Lecture |
| Practicum |
| Skills |
| Lecture with visual aids |
| Practicum |
| Individual study |
| Competences |
| Lecture |
| Practicum |
| Lecture with visual aids |
| Individual study |
| assessment methods |
| Knowledge |
| Oral exam |
| Seminar work |
| Skills |
| Individual presentation at a seminar |
| Oral exam |
| Competences |
| Oral exam |
| Individual presentation at a seminar |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester |
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