# 330-0326/03 – Finite Element Method and Boundary Element Method (MKPMHP)

 Gurantor department Department of Applied Mechanics Credits 4 Subject guarantor doc. Ing. Radim Halama, Ph.D. Subject version guarantor doc. Ing. Radim Halama, Ph.D. Study level undergraduate or graduate Study language Czech Year of introduction 2016/2017 Year of cancellation Intended for the faculties USP Intended for study types Follow-up Master
Instruction secured by
PRZ031 Ing. Jana Bartecká
FUS76 doc. Ing. Martin Fusek, Ph.D.
HAL22 doc. Ing. Radim Halama, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

### Subject aims expressed by acquired skills and competences

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.

Lectures
Tutorials

### 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.

### Compulsory literature:

[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.

### Recommended literature:

[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.

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### Další požadavky na studenta

This course is a continuation of the subject Numerical methods.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

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.

### Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2018/2019 (N2658) Computational Sciences (2612T078) Computational Sciences P Czech Ostrava 1 Choice-compulsory study plan
2017/2018 (N2658) Computational Sciences (2612T078) Computational Sciences P Czech Ostrava 1 Choice-compulsory study plan
2016/2017 (N2658) Computational Sciences (2612T078) Computational Sciences P Czech Ostrava 1 Choice-compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner