330-9001/02 – Numerical Methods (NUMET)
| Gurantor department | Department of Applied Mechanics | Credits | 10 |
| Subject guarantor | prof. Ing. Karel Frydrýšek, Ph.D., FEng. | Subject version guarantor | prof. Ing. Radim Halama, Ph.D. |
| Study level | postgraduate | Requirement | Choice-compulsory type B |
| Year | | Semester | winter + summer |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FS, FMT | Intended for study types | Doctoral |
Subject aims expressed by acquired skills and competences
To teach students the basics of FEM with a focus on solving problems with material non-linearity.
Teaching methods
Lectures
Individual consultations
Project work
Summary
In this course students learn the basic theoretical and practical knowledge of numerical methods of mechanics of deformable bodies, especially the finite element method (FEM).
Compulsory 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.
Recommended 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.
Way of continuous check of knowledge in the course of semester
Validation of the learning outcomes will be done through an oral exam. Practical experience with numerical methods will be demonstrated by the protocol describing performed simulations.
E-learning
Other requirements
Technical report creation.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
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.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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