# 330-0310/01 – Introduction to FEM (UMKP)

 Gurantor department Department of Applied Mechanics Credits 2 Subject guarantor doc. Ing. Martin Fusek, Ph.D. Subject version guarantor doc. Ing. Radim Halama, Ph.D. Study level undergraduate or graduate Requirement Optional Year 3 Semester summer Study language Czech Year of introduction 2015/2016 Year of cancellation Intended for the faculties FS Intended for study types Bachelor
Instruction secured by
PRZ031 Ing. Jana Bartecká
FOJ08 Ing. František Fojtík, Ph.D.
FRY72 doc. Ing. Karel Frydrýšek, Ph.D.
FUS76 doc. Ing. Martin Fusek, Ph.D.
HAL22 doc. Ing. Radim Halama, Ph.D.
HOR80 prof. Ing. Petr Horyl, CSc., dr.h.c.
ROJ71 Ing. Jaroslav Rojíček, Ph.D.
SOF007 doc. Ing. Michal Šofer, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent

### Subject aims expressed by acquired skills and competences

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.

### Teaching methods

Lectures
Individual consultations
Tutorials
Project work

### 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.

### Compulsory literature:

[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.

### Recommended literature:

[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

### Way of continuous check of knowledge in the course of semester

Test, example solutions

### E-learning

no

Lecture attendance, not another request

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

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.

### Conditions for subject completion

Combined form (validity from: 2015/2016 Winter semester)
Min. number of points
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
2019/2020 (B2341) Engineering (2302R010) Design of Machines and Equipment (50) Hunting, Sporting, Defense Arms and Ammunition K Czech Uherský Brod 3 Compulsory study plan
2019/2020 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 3 Optional study plan
2018/2019 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
2018/2019 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 3 Optional study plan
2017/2018 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
2017/2018 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 3 Optional study plan
2017/2018 (B2341) Engineering (2302R010) Design of Machines and Equipment (50) Hunting, Sporting, Defense Arms and Ammunition K Czech Uherský Brod 3 Compulsory study plan
2016/2017 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
2016/2017 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 3 Optional study plan
2015/2016 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
2015/2016 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 3 Optional study plan
2015/2016 (B2341) Engineering (2302R010) Design of Machines and Equipment (50) Hunting, Sporting, Defense Arms and Ammunition K Czech Uherský Brod 3 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner