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Finite Element Method and Boundary Element Method

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code330-0326/03
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Choice-compulsory type A
Level of Course Unit *First Cycle
Year of Study *Third Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
FUS76doc. Ing. Martin Fusek, Ph.D.
HAL22prof. Ing. Radim Halama, Ph.D.
Summary
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
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
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
Required Reading:
[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
Recommended Reading:
[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.
Planned learning activities and teaching methods
Lectures, Tutorials
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit35 20
        ExaminationExamination65 16