| Course Unit Code | 330-3008/01 |
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| Number of ECTS Credits Allocated | 5 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First 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 | There are no prerequisites or co-requisites for this course unit |
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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 subject forms the basis for the use of finite element method in engineering practice.
Contents are general formulation of continuum mechanics, fundamentals linearization, introduction to variational methods, finally FEM applications to specific types of problems of linear elasticity.
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| Learning Outcomes of the Course Unit |
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| Students gain the theoretical foundations of the finite element method (FEM) and the procedures for solving problems of elasticity using the numerical method. Basic training of FEM application on the selected tasks from engineering practice especially focused on the biomechanics. |
| Course Contents |
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1. The first issue of modeling, analytical and numerical approaches to solving problems
2. Revision of mathematics necessary for further study (vectors, matrices, solving systems of equations, transformation)
3. Numerical Mathematics (interpolation, approximation, solving systems of equations, errors).
4. Revision of basic knowledge of mechanics (statics, kinematics, dynamics, flexibility and strength)
5. The Finite Element Method - FEM history and its applications in biomechanics, basic ideas, direct stiffness method (introduction).
6. Direct stiffness method (completion).
7. Variational formulation of the problem of elasticity - the principle of minimum potential energy
8. General formulation of FEM - Analysis of elements
9. General formulation of FEM - structural analysis
10. Types of elements and their use
11. Steady and unsteady problems solved by FEM (static analysis, stability)
12. Steady and unsteady problems solved by FEM - (modal analysis, transient analysis)
13. Introduction to nonlinear FEA Thermal analysis by FEM, Coupled problems.
14. Application Notes - using FEM for solving problems of biomechanics. |
| Recommended or Required Reading |
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| Required Reading: |
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[1] Zienkiewicz, O. C., Taylor, R. L. The Finite Element Method (Volume 1 - 3), Butterworth-Heinemann, Oxford 2000, ISBN 0-7506-5049-4
[2] Singiresu S. Rao. The Finite Element Method in Engineering. 5th edition, Elsevier 2011, doi:10.1016/B978-1-85617-661-3.00024-6 |
[1] Zienkiewicz, O. C., Taylor, R. L. The Finite Element Method (Volume 1 - 3), Butterworth-Heinemann, Oxford 2000, ISBN 0-7506-5049-4
[2] Lenert, J.: Úvod do metody konečných prvku, VŠB – TU Ostrava, 1999, ISBN 80 – 7078 – 686 – 8 |
| Recommended Reading: |
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LARSON, M. G., BENGZON F. The Finite Element Method: Theory, Implementation, and Applications. Springer Science & Business Media, 2013. ISBN-13: 978-3642332869.
BEER, G., WATSON, J.O.: Introduction to Finite and Boundary Element Methods for Engineers, New York, 1992.
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BITTNAR, Z. a J. ŠEJNOHA. Numerické metody mechaniky 1,Praha: Vydavatelství ČVUT,1992.
LARSON, M. G., BENGZON F. The Finite Element Method: Theory, Implementation, and Applications. Springer Science & Business Media, 2013. ISBN-13: 978-3642332869. |
| 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 | 15 |
| Examination | Examination | 65 | 16 |