# 337-0510/01 – FEM in Mechanics (MKPVM)

 Gurantor department Department of Mechanics Credits 3 Subject guarantor prof. Ing. Petr Horyl, CSc., dr.h.c. Subject version guarantor prof. Ing. Petr Horyl, CSc., dr.h.c. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language Czech Year of introduction 2004/2005 Year of cancellation 2014/2015 Intended for the faculties FS Intended for study types Follow-up Master
Instruction secured by
HOR80 prof. Ing. Petr Horyl, CSc., dr.h.c.
POR05 doc. Ing. Zdeněk Poruba, Ph.D.
SZW73 Ing. Jan Szweda, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+10

### Subject aims expressed by acquired skills and competences

Define discretization principle in deformation variant of FEM Identify importance of shape function by aproximation of displacement Characterize creation of stiffness matrix of one element Construct glabal stiffness matrix from one element matrixes, Load vector Solve matrix equation for solution eigenvalues and eigenshapes non-damping vibration Introduction to the solution of nonlinear static problems. Compute easy problem of buckling

Lectures
Tutorials

### Summary

1. Diskretization of mechanical structures, variable calculus in mechanics, Ritz method 2. Deformation variant of finite element method 3. One dimension stright element, shape function at bending, stiffness matrix, load vector, 4. Global stiffness matrix and global load vector, optimisation of band matrix, basic matrix equation of FEM and their solution 5. Transformation matrixes, plane and space frame structures 6. Plane and Space elements 7. Dynamic problems and FEM, mass matrix 8. Eigenfrequencies and eigenshapes of vibrations, iterations method of solutions 9. Step by steps methods; modal analysis 10.General problem statement of FEM

### Compulsory literature:

Cook, R.D. et al. Concepts and Applications of Finite Element Analysis. J. Wiley&Sons,2002,pp.719,ISBN 0-471-35605-0

### Recommended literature:

http://www.mece.ualberta.ca/tutorials/ansys/ ( University of Alberta, Canada)

### E-learning

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### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1. Diskretization of mechanical structures, variable calculus in mechanics, Ritz method 2. Deformation variant of finite element method 3. One dimension stright element, shape function at bending, stiffness matrix, load vector, 4. Global stiffness matrix and global load vector, optimisation of band matrix, basic matrix equation of FEM and their solution 5. Transformation matrixes, plane and space frame structures 6. Plane and Space elements 7. Dynamic problems and FEM, mass matrix 8. Eigenfrequencies and eigenshapes of vibrations, iterations method of solutions 9. Step by steps methods; modal analysis 10.General problem statement of FEM

### Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2014/2015 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 35  20
Examination Examination 65  31
Mandatory attendence parzicipation:

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### Occurrence in study plans

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2014/2015 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (40) Design of Machines and Equipment P Czech Ostrava 1 Compulsory study plan
2013/2014 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (40) Design of Machines and Equipment P Czech Ostrava 1 Compulsory study plan
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2011/2012 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling K Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (20) Production Machines and Equipment K Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (70) Earth, Mining and Building Machines K Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling P Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (40) Design of Machines and Equipment P Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (20) Production Machines and Equipment P Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (70) Earth, Mining and Building Machines P Czech Ostrava 1 Choice-compulsory study plan
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2010/2011 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (20) Production Machines and Equipment P Czech Ostrava 1 Choice-compulsory study plan
2010/2011 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (70) Earth, Mining and Building Machines P Czech Ostrava 1 Choice-compulsory study plan
2010/2011 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling K Czech Ostrava 1 Choice-compulsory study plan
2010/2011 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics K Czech Ostrava 1 Choice-compulsory study plan
2010/2011 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 1 Choice-compulsory study plan
2010/2011 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (20) Production Machines and Equipment K Czech Ostrava 1 Choice-compulsory study plan
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2009/2010 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 1 Choice-compulsory study plan
2009/2010 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (70) Earth, Mining and Building Machines K Czech Ostrava 1 Choice-compulsory study plan
2008/2009 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 1 Choice-compulsory study plan
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2008/2009 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 1 Choice-compulsory study plan
2008/2009 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (10) Machines for Mining and Treating Commercial Raw Materials K Czech Ostrava 1 Choice-compulsory study plan
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2007/2008 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 1 Choice-compulsory study plan
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2007/2008 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 1 Choice-compulsory study plan
2007/2008 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (10) Machines for Mining and Treating Commercial Raw Materials K Czech Ostrava 1 Choice-compulsory study plan
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2007/2008 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 1 Choice-compulsory study plan
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2006/2007 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (20) Production Machines and Equipment P Czech Ostrava 1 Choice-compulsory study plan
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2006/2007 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (40) Design of Machines and Equipment P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (10) Machines for Mining and Treating Commercial Raw Materials K Czech Ostrava 1 Choice-compulsory study plan
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2006/2007 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling K Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2301) Mechanical Engineering (2301T032) Production Systems with Industrial Robots and Manipulators K Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (2301T032) Production Systems with Industrial Robots and Manipulators P Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 1 Choice-compulsory study plan
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2005/2006 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling P Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (40) Design of Machines and Equipment P Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (10) Machines for Mining and Treating Commercial Raw Materials K Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics K Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (20) Production Machines and Equipment K Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (30) Earth Moving and Building Machines K Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling K Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (40) Design of Machines and Equipment K Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (2301T032) Production Systems with Industrial Robots and Manipulators K Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (2301T032) Production Systems with Industrial Robots and Manipulators P Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (20) Production Machines and Equipment P Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (30) Earth Moving and Building Machines P Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling P Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (40) Design of Machines and Equipment P Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics P Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (10) Machines for Mining and Treating Commercial Raw Materials K Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (20) Production Machines and Equipment K Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (30) Earth Moving and Building Machines K Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling K Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (40) Design of Machines and Equipment K Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics K Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (2301T032) Production Systems with Industrial Robots and Manipulators K Czech Ostrava 1 Choice-compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner