330-3008/01 – Finite Element Method (MKP)

Gurantor departmentDepartment of Applied MechanicsCredits5
Subject guarantorprof. Ing. Radim Halama, Ph.D.Subject version guarantorprof. Ing. Radim Halama, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2016/2017Year of cancellation
Intended for the facultiesFMTIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
FRY72 doc. Ing. Karel Frydrýšek, Ph.D.
FUS76 doc. Ing. Martin Fusek, Ph.D.
HAL22 prof. Ing. Radim Halama, Ph.D.
ROJ71 Ing. Jaroslav Rojíček, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+3

Subject aims expressed by acquired skills and competences

Students gain the theoretical foundations of the finite element method (FEM) and the procedures for solving problems of elasticity using the numerical method. Basic training of FEM application on the selected tasks from engineering practice especially focused on the biomechanics.

Teaching methods

Lectures
Tutorials

Summary

The subject forms the basis for the use of finite element method in engineering practice. Contents are general formulation of continuum mechanics, fundamentals linearization, introduction to variational methods, finally FEM applications to specific types of problems of linear elasticity.

Compulsory literature:

[1] Zienkiewicz, O. C., Taylor, R. L. The Finite Element Method (Volume 1 - 3), Butterworth-Heinemann, Oxford 2000, ISBN 0-7506-5049-4 [2] Singiresu S. Rao. The Finite Element Method in Engineering. 5th edition, Elsevier 2011, doi:10.1016/B978-1-85617-661-3.00024-6

Recommended literature:

LARSON, M. G., BENGZON F. The Finite Element Method: Theory, Implementation, and Applications. Springer Science & Business Media, 2013. ISBN-13: 978-3642332869. BEER, G., WATSON, J.O.: Introduction to Finite and Boundary Element Methods for Engineers, New York, 1992.

Way of continuous check of knowledge in the course of semester

test, unassisted analyses

E-learning

Other requirements

performing FE analyses, self computing of one task

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. The first issue of modeling, analytical and numerical approaches to solving problems 2. Revision of mathematics necessary for further study (vectors, matrices, solving systems of equations, transformation) 3. Numerical Mathematics (interpolation, approximation, solving systems of equations, errors). 4. Revision of basic knowledge of mechanics (statics, kinematics, dynamics, flexibility and strength) 5. The Finite Element Method - FEM history and its applications in biomechanics, basic ideas, direct stiffness method (introduction). 6. Direct stiffness method (completion). 7. Variational formulation of the problem of elasticity - the principle of minimum potential energy 8. General formulation of FEM - Analysis of elements 9. General formulation of FEM - structural analysis 10. Types of elements and their use 11. Steady and unsteady problems solved by FEM (static analysis, stability) 12. Steady and unsteady problems solved by FEM - (modal analysis, transient analysis) 13. Introduction to nonlinear FEA Thermal analysis by FEM, Coupled problems. 14. Application Notes - using FEM for solving problems of biomechanics.

Conditions for subject completion

Full-time form (validity from: 2016/2017 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 35  15
        Examination Examination 65  16
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (N0788A270001) Biomechanical Engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (N3923) Materials Engineering (3901T077) Biomechanical Engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (N0788A270001) Biomechanical Engineering P Czech Ostrava 1 Compulsory study plan
2018/2019 (N3923) Materials Engineering (3901T077) Biomechanical Engineering P Czech Ostrava 1 Compulsory study plan
2017/2018 (N3923) Materials Engineering (3901T077) Biomechanical Engineering P Czech Ostrava 1 Compulsory study plan
2016/2017 (N3923) Materials Engineering (3901T077) Biomechanical Engineering P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner