| Course Unit Code | 330-0310/01 |
|---|
| Number of ECTS Credits Allocated | 2 ECTS credits |
|---|
| Type of Course Unit * | Optional |
|---|
| Level of Course Unit * | First Cycle |
|---|
| Year of Study * | Third Year |
|---|
| Semester when the Course Unit is delivered | Summer Semester |
|---|
| Mode of Delivery | Face-to-face |
|---|
| Language of Instruction | Czech |
|---|
| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
|---|
| Name of Lecturer(s) | Personal ID | Name |
|---|
| HAL22 | prof. Ing. Radim Halama, Ph.D. |
| Summary |
|---|
| 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. |
| Learning Outcomes of the Course Unit |
|---|
| Student should learn elementary procedures for solution of elasticity and strength problems by means of finite element method (FEM). Guaranty an understanding of a discussed topic. Student will gain theoretical knowledge of FEM, which they will learn to apply at a solution of selected problems out of a technical practice. |
| Course Contents |
|---|
1. Lecture – Elementary thought of FEM. Selection of interpolator functions. Types of elements. Derivation of stiffness matrix of a truss element. Equations of an elasticity mathematical theory. Minimal principle of potential energy. Process at FEM calculation. Conditions of convergence.
2. Lecture – assembly of global stiffness matrix and right side. Foundations of Ansys Workbench (description of individual models, work with help). Example 1: application example – beam in 3D.
3. Lecture – Computational modelling. Simplified exercises from 3D to 1D and 2D. Example 2: wrenche.
4. Lecture – Choice of boundary conditions. Singularity. Reading geometry from CAD model and its modification. Example 3: symmetry usage.
5. Lecture- Error of FEM calculation (aposteriori estimate). Adaptive FEM algorithm (h-method). Example 4: Think walled pressure tin.
6. Lecture - Seminary work.
7. Lecture – Seminary work.
8. Lecture – Seminary work.
9. Lecture – Final test, finalization and handing over a seminary work.
|
| Recommended or Required Reading |
|---|
| Required Reading: |
|---|
[1] MADENCI, E., GUVEN, I. The Finite Element Method and Applications in Engineering Using Ansys®. Springer, 2006, 686p. ISBN 978-0-387-28290-9
[2] ZIENKIEWICZ, O. C., TAYLOR,R.L. a ZHU, J.Z. The finite element method: its basis and fundamentals. 6th ed. Oxford: Elsevier Butterworth-Heinemann, 2005. ISBN 0-7506-6320-0.
|
[1] FUSEK, Martin, ROJÍČEK, Jaroslav, Metoda konečných prvků I [online], Ostrava: VŠB-TU Ostrava, 2013, ISBN 978-80-248-3023-0, Dostupné z: http://projekty.fs.vsb.cz/463/edubase
[2] LENERT, Jiří. Úvod do metody konečných prvků. Ostrava: VŠB-Technická univerzita, 1999. ISBN 80-7078-686-8.
[3] SZWEDA, Jan, Zdeněk PORUBA, Roman SIKORA a Ondřej FRANTIŠEK. Matematika v pozadí inženýrských úloh [online]. Ostrava: VŠB-TU Ostrava, 2012 [cit. 2018-01-11]. Dostupné z: http://mi21.vsb.cz/modul/matematika-v-pozadi-reseni-inzenyrskych-uloh
[4] ZIENKIEWICZ, O. C., TAYLOR,R.L. a ZHU, J.Z. The finite element method: its basis and fundamentals. 6th ed. Oxford: Elsevier Butterworth-Heinemann, 2005. ISBN 0-7506-6320-0.
[5] LENERT,J. Základy matematické teorie pružnosti. 1. vyd. Ostrava : VŠB-TU, 1997. 96 s. ISBN 80-7078-437-7 |
| Recommended Reading: |
|---|
| [1] BEER,G.-WATSON,J.O. Introduction to Finite and Boundary Element Methods for Engineers. John Wiley & Sons, 1992, 509p.ISBN 0-471-92813-5 |
[1] FUSEK, Martin, MKP v Nastranu a Patranu [online], Ostrava: VŠB-TU Ostrava, 2011, ISBN 978-80-248-2730-8, Dostupné z: http://projekty.fs.vsb.cz/147/ucebniopory/978-80-248-2730-8.pdf
[2] FUSEK, Martin, Týmová cvičení předmětu MKP I [online], Ostrava: VŠB-TU Ostrava, 2011, ISBN 978-80-248-2729-2, Dostupné z: http://projekty.fs.vsb.cz/147/ucebniopory/978-80-248-2729-2.pdf
[3] KOLÁŘ, Vladimír, Ivan NĚMEC a Viktor KANICKÝ. FEM: principy a praxe metody konečných prvků. Praha: Computer Press, 1997. ISBN 80-7226-021-9.
[4] BITTNAR,Z.-ŠEJNOHA,J. Numerické metody mechaniky 1. Praha : Vydavatelství ČVUT, 1992. 310 s. ISBN 80-01-00855-X.
[5] BITTNAR,Z.-ŠEJNOHA,J. Numerické metody mechaniky 2. Praha : Vydavatelství ČVUT, 1992. 261 s. ISBN 80-01-00901-7.
[6] BEER,G.-WATSON,J.O. Introduction to Finite and Boundary Element Methods for Engineers. John Wiley & Sons, 1992, 509p.ISBN 0 471 92813 5
[7] MADENCI, Erdogan. a Ibrahim. GUVEN. The finite element method and applications in engineering using ANSYS. New York: Springer, c2006. ISBN 0-387-28289-0. |
| Planned learning activities and teaching methods |
|---|
| Lectures, Individual consultations, Tutorials, Project work |
| Assesment methods and criteria |
|---|
| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
|---|
| Graded credit | Graded credit | 100 | 51 |