Course Unit Code | 470-8725/01 |
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Number of ECTS Credits Allocated | 4 ECTS credits |
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Type of Course Unit * | Compulsory |
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Level of Course Unit * | First Cycle |
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Year of Study * | Second Year |
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Semester when the Course Unit is delivered | Summer 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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| LUK76 | doc. Ing. Dalibor Lukáš, Ph.D. |
Summary |
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Within this subject students will become familiar with new terms in the field of computer modeling necessary for understanding of modern computational methods. They will study different approaches of solving basic problems in mechanics using Finite Element Method and further they will try their application to selected problems from technical practice.
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Learning Outcomes of the Course Unit |
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Graduate students will be able:
- to use actively new terms in the field of computer modeling necessary for understanding of modern computational methods
- to solve standard engineering problems in mechanics using FEM
- to apply different discretization techniques to the numerical solution of selected engineering problems. |
Course Contents |
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Content:
1. Principle of FEM in static problems, discretization, deformation parameters.
2. Stiffness matrix of a truss element, load vector.
3. Assembling of global matrices and vectors, fundamental matrix equation in statics.
4. Solution of displacement and reactions in practical exercises with truss elements.
5. Transformation from the local to the global coordinate system.
6. Applications for lattice design.
7. Beam element stiffness matrix and application statics on the plane frames.
8. Mathematical formulation of the Finite Element Method (weak formulation of the problem, its discretization, solving the linear system of equations).
9. Finite differences method and its application to solving selected statics and transient problems of mechanics.
10. Introduction of boundary element methods and its applications.
11. Introduction of discrete elements and its applications.
12. Error analysis (a prior and a posterior estimates), visualization tools. |
Recommended or Required Reading |
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Required Reading: |
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[1] COOK R. D., MALKUS D.S., PLESHA M.E., WITT R.J. CONCEPTS AND APPLICATIONS OF FINITE ELEMENT ANALYSIS. 4th edition. J. Wiley & Sons, Inc. NY, 2002, p. 719, ISBN 0-471-35605-0.
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[1] LENERT, J. Úvod do metody konečných prvků. Ostrava 1999: VŠB-Technická univerzita Ostrava. p. 110. ISBN 80-7078-686-8.
[2] COOK R. D., MALKUS D.S., PLESHA M.E., WITT R.J. CONCEPTS AND APPLICATIONS OF FINITE ELEMENT ANALYSIS. 4th edition. J. Wiley & Sons, Inc. NY, 2002, p. 719, ISBN 0-471-35605-0.
[3] KOZUBEK, T., BRZOBOHATÝ, T., HAPLA, V., JAROŠOVÁ, M., MARKOPOULOS, A. Lineární algebra s Matlabem, VŠB-TU Ostrava 2012, http://mi21.vsb.cz/modul/linearni-algebra-s-matlabem.
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Recommended Reading: |
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[1] REDDY, J. N. An introduction to the finite element method. 2nd Edition. McGraw-Hill, 1993.
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[1] REDDY, J. N. An introduction to the finite element method. 2nd Edition. McGraw-Hill, 1993.
[2] BLAHETA, R. Matematické modelování a metoda konečných prvků, VŠB-TU Ostrava 2012, http://mi21.vsb.cz/modul/matematicke-modelovani-metoda-konecnych-prvku-numericke-metody-2
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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 | 30 | 15 |
Examination | Examination | 70 | 21 |