Course Unit Code | 330-0326/03 |
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Number of ECTS Credits Allocated | 4 ECTS credits |
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Type of Course Unit * | Choice-compulsory type A |
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Level of Course Unit * | First Cycle |
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Year of Study * | Third Year |
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Semester when the Course Unit is delivered | Winter Semester |
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Mode of Delivery | Face-to-face |
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Language of Instruction | Czech |
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Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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Name of Lecturer(s) | Personal ID | Name |
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| FUS76 | doc. Ing. Martin Fusek, Ph.D. |
| HAL22 | prof. Ing. Radim Halama, Ph.D. |
Summary |
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The course extends the foundation for the use of finite element methods and explains important aspects of the application and implementation of the Boundary Element Method. It formulates the nonlinear continuum mechanics. It contains general formulations of continuum mechanics, the basics of linearization, finally the application of FEM and BEM to specific types of linear and nonlinear elasticity tasks. |
Learning Outcomes of the Course Unit |
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Student completing the course will be able to:
- Build a model describing the behavior of of elastic body (system).
- Implement the solution of the model one of the methods described above.
- Evaluate and draw conclusions. |
Course Contents |
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1. Revision of Fundamental Knowledge and Terms in the Field of Continuum Mechanics.
2. Modelling of Continuum Mechanics Problems. Analytical and Numerical Solutions. Finite Difference Method.
3. Finite Element Method – Principle, Basic Equation Solution, Application to Thermal and Electric Fields Linear Problems. Stationary and Non-stationary Processes.
4. Finite Element Methods – Reference Points, Gaussian Integral, Errors and Adaptive Finite Element Method and Its Application. Convergence.
5. Boundary Element Method – Principle, Differences between FEM and BEM, Basic Equation Solution, Fundamental Solution, Application to Thermal and Electric Fields Linear Problems. Stationary and Non-stationary Processes.
6. Boundary Element Method – Boundary Discretization and Types of Elements. Constructing System of Equations. Application of Boundary Conditions. Solutions of System of Equations.
7. Boundary Element Method – Generalized Formulation of BEM Using the Method of Weighted Residiuals.
8. Selected Practical Problems Solved by FEM and BEM. Comparative Study.
9. Possible FEM and BEM Combinations.
10. Non-linear Problems – Introduction to Non-linearities (geometrical, material, and contact non-linearities). Possible solutions. |
Recommended or Required Reading |
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Required Reading: |
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[1] BEER, G., WATSON, J.O. Introduction to Finite and Boundary Element Methods for Engineers. John Wiley & Sons, 1992. 509 p. ISBN 0 471 92813 5. |
[1] FUSEK, F.; HALAMA, R.: MKP a MHP. 1. vyd. Ostrava: VŠB-TU, 2012. 104 s. Skriptum. URL: http://mi21.vsb.cz/sites/mi21.vsb.cz/files/unit/metoda_konecnych_prvku_a_hranicnich_prvku.pdf.
[2] LENERT, J.: Úvod do metody konečných prvků. 1. vyd. Ostrava: VŠB-TU, 1999. 110 s. ISBN 80-7078-686-8.
[3] KATSIKADELIS, J., T. Boundary Elements: Theory and Application. Elsevier Science Ltd., 2002. ISBN 0-080-44107-6
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Recommended Reading: |
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[1] BEER, G., SMITH, I., DUENSER, Ch.: The Boundary Element Method with Programming for Engineers and Scientists. Springer, 2008. 494 p. ISBN 978-3-211-71574-1. |
[1] LENERT, J.: Základy matematické teorie pružnosti. 1. vyd. Ostrava: VŠB-TU, 1997. 96 s. ISBN 80-7078-437-7.
[2] BITTNAR, Z., ŠEJNOHA, J. Numerické metody mechaniky 1. Praha: Vydavatelství ČVUT, 1992. 310 s. ISBN 80-01-00855-X.
[3] BITTNAR, Z., ŠEJNOHA, J. Numerické metody mechaniky 2. Praha: Vydavatelství ČVUT, 1992. 261 s. ISBN 80-01-00901-7.
[4] BEER, G., SMITH, I., DUENSER, Ch.: The Boundary Element Method with Programming for Engineers and Scientists. Springer, 2008. 494 p.
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Planned learning activities and teaching methods |
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Lectures, Tutorials |
Assesment methods and criteria |
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Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing |
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Credit and Examination | Credit and Examination | 100 (100) | 51 |
Credit | Credit | 35 | 20 |
Examination | Examination | 65 | 16 |