Numerical Methods

Type of study	Doctoral
Language of instruction	English
Code	330-9001/02
Abbreviation	NUMET
Course title	Numerical Methods
Credits	10
Coordinating department	Department of Applied Mechanics
Course coordinator	prof. Ing. Radim Halama, Ph.D.

Subject syllabus

1. Strain variant of FEM for elastostatic problems.
2. Determination of basic equation for FEM.
3. Element types. Approximation of displacement. Serendipity family elements, Hermitian and Lagrangian elements.
4. Local stiffness matrix. Reference elements and natural coordinates. Gauss integration.
5. Transformation matrix of 1D and 2D elements. Isoparametric, subparametric and superparametric elements.
6. Global stiffness matrix and its assembling.
7. Solution of global equation of equilibrium. Gauss elimination method and Frontal method. Convergence.
8. Aposterior error estimation and adaptive algorithms of FEM.
9. Types of nelinear problems. Newton-Raphsonova method and its incremental variant.
10. Material nonlinearity and FEM. Elastoplastic matrix assembly.
11. Incremental theory of plasticity. Yield condition – idealy plastic material, isotropic and kinematic hardening.
12. Kinematic hardening rule – Prager, Besseling, Chaboche.
13. Nonlinear isotropic model (Voce) and Chaboche combined model. Calibration of material models.
14. Numerical integration of constitutive equations. Radial return method.

Literature

BEER, G., WATSON, J.O. Introduction to Finite and Boundary Element Methods for Engineers, New York, 1992.
CHABOCHE, J.L., LEMAITRE, J. Mechanics of Solid Materials, Cambridge University Press, Cambridge, 1990.
BLAHETA, R. Numerical Methods in Elasto-Plasticity, Peres Publishers, Nové Město blízko Chlumce nad Cidlinou, 1999.
HALAMA, R., SEDLÁK, J., ŠOFER, M. Phenomenological Modelling of Cyclic Plasticity, Chapter in: Numerical Modelling, Peep Miidla (Ed.), InTech, 2012, p. 329-354.
MADENCI, E., GUVEN, I. The Finite Element Method and Applications in Engineering Using ANSYS®, Springer, 2005, 686 p.

Advised literature

PARÍS, F., CAŃAS, J. Boundary Element Method - Fundamentals and Applications, Oxford University Press, New York,1997.
DUNNE, F, PETRINIC, N. Introduction to Computational Plasticity. Oxford University Press, 2005. 256 p.

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