330-9001/02 – Numerical Methods (NUMET)

Gurantor departmentDepartment of Applied MechanicsCredits10
Subject guarantordoc. Ing. Karel Frydrýšek, Ph.D.Subject version guarantorprof. Ing. Radim Halama, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory type B
YearSemesterwinter + summer
Study languageEnglish
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFMT, FSIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
HAL22 prof. Ing. Radim Halama, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 20+0
Part-time Examination 20+0

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

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (P0715D270010) Mechanical Engineering Technology K English Ostrava Choice-compulsory type B study plan
2021/2022 (P0715D270010) Mechanical Engineering Technology P English Ostrava Choice-compulsory type B study plan
2020/2021 (P0713D070002) Thermal engineering and fuels in industry K English Ostrava Choice-compulsory type B study plan
2020/2021 (P0713D070002) Thermal engineering and fuels in industry P English Ostrava Choice-compulsory type B study plan
2020/2021 (P0788D270004) Material sciece and Engineering K English Ostrava Choice-compulsory type B study plan
2020/2021 (P0788D270004) Material sciece and Engineering P English Ostrava Choice-compulsory type B study plan
2020/2021 (P0715D270010) Mechanical Engineering Technology P English Ostrava Choice-compulsory type B study plan
2020/2021 (P0715D270010) Mechanical Engineering Technology K English Ostrava Choice-compulsory type B study plan
2019/2020 (P0713D070002) Thermal engineering and fuels in industry K English Ostrava Choice-compulsory type B study plan
2019/2020 (P0713D070002) Thermal engineering and fuels in industry P English Ostrava Choice-compulsory type B study plan

Occurrence in special blocks

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