# 339-0312/01 – Introduction to FEM (UMKP)

 Gurantor department Department of Mechanics of Materials Credits 2 Subject guarantor doc. Ing. Radim Halama, Ph.D. Subject version guarantor doc. Ing. Radim Halama, Ph.D. Study level undergraduate or graduate Requirement Compulsory 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
LoginNameTuitorTeacher giving lectures
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.
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
Combined 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

### Další požadavky na studenta

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: 1960/1961 Summer semester, validity until: 2014/2015 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Graded exercises evaluation Graded credit 100 (100) 0
Project Project 50  0
Other task type Other task type 50  0
Mandatory attendence parzicipation:

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### Occurrence in study plans

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2011/2012 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Compulsory study plan
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2011/2012 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment K Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines K Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Šumperk 3 Compulsory study plan
2011/2012 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control K Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (3907R009) Operation of Energy Equipment K Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2302R003) Transport Machinery and Material Handling K Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering K Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2301R013) Robotics (70) Robotics K Czech Ostrava 3 Compulsory study plan
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2011/2012 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Optional study plan
2011/2012 (B2341) Engineering (2301R040) Industrial Engineering K Czech Ostrava 3 Optional study plan
2011/2012 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials K Czech Chomutov 3 Compulsory study plan
2010/2011 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Compulsory study plan
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2010/2011 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology (10) Transport Equipment P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology (10) Transport Equipment P Czech Šumperk 3 Compulsory study plan
2010/2011 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 3 Compulsory study plan
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2010/2011 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (3907R009) Operation of Energy Equipment P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Compulsory study plan
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2010/2011 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Optional study plan
2010/2011 (B2341) Engineering (2301R040) Industrial Engineering K Czech Ostrava 3 Optional study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines K Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Šumperk 3 Compulsory study plan
2010/2011 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control K Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment K Czech Šumperk 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment K Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology (10) Transport Equipment K Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology (10) Transport Equipment K Czech Šumperk 3 Compulsory study plan
2010/2011 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport K Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology (20) Surface Transport K Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (3907R004) Energy Management K Czech Ostrava 3 Compulsory study plan
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2010/2011 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R003) Transport Machinery and Material Handling K Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment K Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (50) Hunting, Sporting, Defense Arms and Ammunition K Czech Uherský Brod 3 Compulsory study plan
2010/2011 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering K Czech Ostrava 3 Compulsory study plan
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2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment (10) Transport Equipment and Technology P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment (10) Transport Equipment and Technology K Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 3 Compulsory study plan
2009/2010 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Optional study plan
2009/2010 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Šumperk 3 Compulsory study plan
2009/2010 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R002) Transport Equipment K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R002) Transport Equipment K Czech Šumperk 3 Compulsory study plan
2009/2010 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (3907R004) Energy Management K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R013) Robotics (70) Robotics K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R003) Transport Machinery and Material Handling K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (50) Hunting, Sporting, Defense Arms and Ammunition K Czech Uherský Brod 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R040) Industrial Engineering K Czech Ostrava 3 Optional study plan
2008/2009 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 3 Compulsory study plan
2008/2009 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Šumperk 3 Compulsory study plan
2008/2009 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Třinec 3 Compulsory study plan
2008/2009 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control K Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R002) Transport Equipment K Czech Šumperk 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R002) Transport Equipment K Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport K Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (3907R004) Energy Management K Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (3907R004) Energy Management K Czech Třinec 3 Compulsory study plan
2008/2009 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering K Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R013) Robotics (70) Robotics K Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R003) Transport Machinery and Material Handling K Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials K Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment K Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment K Czech Třinec 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines K Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (50) Hunting, Sporting, Defense Arms and Ammunition K Czech Uherský Brod 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Optional study plan
2008/2009 (B2341) Engineering (2301R040) Industrial Engineering K Czech Ostrava 3 Optional study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner