# 337-0504/01 – FEM II (MKPII)

 Gurantor department Department of Mechanics Credits 5 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.
POD10 doc. Ing. Jiří Podešva, 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
Part-time Credit and Examination 10+10

### Subject aims expressed by acquired skills and competences

Outline principle of derivation mass matrix in slope-deflection variant of FEM Identify meaning solution of natural frequencies and mode shapes and classify differences for Bernoulli and Timoshenko beam Define methods for numerical computing of eigenvalues and eigenvectors for undamped systems Construct reduction method for easy problem of natural frequency Solve matrix equation of motion by modal method Classify direct integration method, compare implicit and explicit method Clarify solution principle of nonlinear static problems Relate methods for analysis contacts problem by FEM

Lectures
Tutorials
Project work

### Summary

1. Dynamics and FEM 2. Mass matrix 3. Equations of motion of elastic systems 4. Natural frequencies and mode shapes - properties and normalization of mode shapes - methods for computing eigenvalues and eigenvectors 5. Reduction of the number of DOf in dynamics 6. Response history: modal method - proportional damping matrix - vibration caused by initial conditions - harmonic response - general excitation 7. Response history: direct integration method (implicit and explicit methods) 8. Principles of solution nonlinear static problems, fundamental numeric solution of contacts in FEM 9. Newton-Raphson method, arc-length method

### Compulsory literature:

Cook R. D., Malkus D.S., Plesha M.E., Witt R.J. CONCEPTS AND APPLICATIONS OF FINITE ELEMENT ANALYSIS. 4th edition. J. Wiley & Sons, Inc. NY, 2002, p. 719, ISBN 0-471-35605-0 Examples for ANSYS solutions: http://www.mece.ualberta.ca/tutorials/ansys/ REDDY, J.N., An Introduction Nonlinear Finite Element Analysis, Oxford University Press, 2004, p. 463, ISBN 0-19-852529-X BHATTI, M. A., Fundamental Finite Element Analysis and Applications: with Mathematica and Matlab Computations, Wiley, 2005, p.590, ISBN 0-471-64808-6

### Recommended literature:

BHATTI,M.A., Advanced Topics in Finite Element Analysis of Structures: with Mathematica and Matlab Computations, Wiley, 2006, p.590, ISBN-13 978-0-471- 64807-9

### Other requirements

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### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1. Dynamics and FEM 2. Mass matrix 3. Equations of motion of elastic systems 4. Natural frequencies and mode shapes - properties and normalization of mode shapes - methods for computing eigenvalues and eigenvectors 5. Reduction of the number of DOf in dynamics 6. Response history: modal method - proportional damping matrix - vibration caused by initial conditions - harmonic response - general excitation 7. Response history: direct integration method (implicit and explicit methods) 8. Principles of solution nonlinear static problems, fundamental numeric solution of contacts in FEM 9. Newton-Raphson method, arc-length method

### 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  0
Examination Examination 65 (65) 0
Oral Exam Oral examination 65  31
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2014/2015 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2013/2014 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2012/2013 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2011/2012 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2010/2011 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2009/2010 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2008/2009 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2007/2008 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2006/2007 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2005/2006 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
ECTS - MechEng 2014/2015 Full-time Czech Choice-compulsory 301 - Study and International Office stu. block
ECTS - MechEng 2013/2014 Full-time Czech Choice-compulsory 301 - Study and International Office stu. block
ECTS - MechEng 2012/2013 Full-time Czech Choice-compulsory 301 - Study and International Office stu. block