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Finite Element Method in Mechanics

Type of study Doctoral
Language of instruction English
Code 330-0903/02
Abbreviation MKPME
Course title Finite Element Method in Mechanics
Credits 10
Coordinating department Department of Applied Mechanics
Course coordinator doc. Ing. Jiří Podešva, Ph.D.

Subject syllabus

1. Finite element method - the basic principles.
2. Formulation of the stiffness matrix and mass matrix for the dynamic task.
3. The finite element types, 1D beam or truss element, 2D shell element, 3D volume element.
4. The basic rules for building the model, geometry model, finite element model.
5. The boundary condition definition - the supports, loading.
6. The static case formulation basic rules, equations of equilibrium, solution methods.
7. The natural vibration task, modal analysis, natural frequencies and mode shapes, solution methods.
8. Harmonically excited forced vibration, vibration due to centrifugal force, phase shift, damping, solution methods.
9. Harmonically excited forced vibration, postprocessing, time curves, amplitude characteristics.
10. Numerical integration of the equations of motion, transient analysis, solution methods.
11. Numerical integration of the equations of motion, the solution set-up rules.
12 Spectral analysis, fourier decomposition, random excitation, “white noise”.

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

REDDY, J.N., An Introduction Nonlinear Finite Element Analysis, Oxford
University Press, 2004, p. 463, ISBN 0-19-852529-X

WRIGGERS, P., Nichtlineare Finite-Element Metoden, Springer, 2005, p. 495, ISBN
3-540-67747

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

Advised literature

Examples for ANSYS solutions: http://www.mece.ualberta.ca/tutorials/ansys/

Zhi-Hua Zhong. Finite Element Procedures for Contact-Impact Problems. Oxford
University Press, 1993, p. 371, ISBN 0-19 856383-3 

WRIGGERS, P., Nichtlineare Finite-Element Metoden, Springer, 2005, p. 495, ISBN
3-540-67747