# 339-0312/02 – Introduction to FEM (UMKP)

 Gurantor department Department of Mechanics of Materials Credits 2 Subject guarantor prof. Ing. Radim Halama, Ph.D. Subject version guarantor prof. Ing. Radim Halama, Ph.D. Study level undergraduate or graduate Requirement Optional Year 3 Semester summer Study language Czech Year of introduction 2007/2008 Year of cancellation 2014/2015 Intended for the faculties FS Intended for study types Bachelor
Instruction secured by
PRZ031 Ing. Jana Bartecká
FOJ08 doc. Ing. František Fojtík, Ph.D.
FRY72 doc. Ing. Karel Frydrýšek, Ph.D.
FUS76 doc. Ing. Martin Fusek, Ph.D.
HAL22 prof. Ing. Radim Halama, Ph.D.
HOR80 prof. Ing. Petr Horyl, CSc., dr.h.c.
KLU106 Ing. Richard Klučka
PEC204 Ing. Luboš Pečenka, Ph.D.
ROJ71 Ing. Jaroslav Rojíček, Ph.D.
SED301 Ing. Josef Sedlák, Ph.D.
SIV020 Ing. Milan Sivera
SMI133 Ing. Jakub Šmiraus, Ph.D.
SOF007 doc. Ing. Michal Šofer, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Graded credit 0+2
Part-time Graded credit 0+8

### 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.

Lectures
Tutorials
Project work

### Summary

Subject includes an explication of FEM foundations for linear structural problems and also has practical focus: 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.

### Compulsory literature:

1] BEER,G.-WATSON,J.O.: Introduction to Finite and Boundary Element Methods for Engineers, John Wiley & Sons,1992 [2] BROWN,D.K.: An Introduction to the Finite Element Method using BASIC Programs, Surrey University Press, Blackie & Son Ltd, 1990, 2nd ed.

### Recommended literature:

1] BEER,G.-WATSON,J.O.: Introduction to Finite and Boundary Element Methods for Engineers, John Wiley & Sons,1992 [2] BROWN,D.K.: An Introduction to the Finite Element Method using BASIC Programs, Surrey University Press, Blackie & Son Ltd, 1990, 2nd ed.

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

Test, example solutions

no

### Other requirements

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

Full-time form (validity from: 2011/2012 Summer semester, validity until: 2014/2015 Winter semester)
Task nameType of taskMax. number of points
Min. number of points
Graded exercises evaluation Graded credit 100  51
Mandatory attendence parzicipation:

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### Occurrence in study plans

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2014/2015 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
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2013/2014 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Šumperk 3 Optional study plan
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2012/2013 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Optional study plan
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2012/2013 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (3902R001) Applied Informatics and Control P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (3907R009) Operation of Energy Equipment P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (3904R016) Environmental Engineering P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Design of industrial products P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2302R010) Design of Machines and Equipment (21) Design of Production Machines and Equipment P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (3902R001) Applied Informatics and Control K Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2302R007) Hydraulics and Pneumatics K Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2303R002) Mechanical Engineering Technology K Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2303R002) Mechanical Engineering Technology K Czech Šumperk 3 Optional study plan
2012/2013 (B2341) Engineering (2301R040) Industrial Engineering K Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (3907R009) Operation of Energy Equipment K Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (3904R016) Environmental Engineering K Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management K Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines K Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2302R010) Design of Machines and Equipment (21) Design of Production Machines and Equipment K Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Šumperk 3 Optional study plan
2012/2013 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 3 Optional study plan
2012/2013 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Šumperk 3 Optional study plan

### Occurrence in special blocks

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