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Course Unit Code | 330-0512/02 | |||||
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Number of ECTS Credits Allocated | 5 ECTS credits | |||||

Type of Course Unit * | Choice-compulsory | |||||

Level of Course Unit * | Second Cycle | |||||

Year of Study * | ||||||

Semester when the Course Unit is delivered | Summer Semester | |||||

Mode of Delivery | Face-to-face | |||||

Language of Instruction | Czech, English | |||||

Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester | |||||

Name of Lecturer(s) | Personal ID | Name | ||||

POD10 | doc. Ing. Jiří Podešva, Ph.D. | |||||

MAW007 | Ing. Pavel Maršálek, Ph.D. | |||||

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 | ||||||

Learning Outcomes of the Course Unit | ||||||

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 | ||||||

Course Contents | ||||||

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 | ||||||

Recommended or Required Reading | ||||||

Required Reading: | ||||||

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 HORYL, P. FEM Finite Element Method Introduction,2014,https://www.fs.vsb.cz/330/cs/MKP-II/ | ||||||

Cook R. D., MaFElkus 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 HORYL, P. FEM Finite Element Method Introduction,2014,https://www.fs.vsb.cz/330/cs/MKP-II/ | ||||||

Recommended Reading: | ||||||

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 | ||||||

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 | ||||||

Planned learning activities and teaching methods | ||||||

Lectures, Tutorials, Project work | ||||||

Assesment methods and criteria | ||||||

Tasks are not Defined |