224-0221/01 – Finite Element Method (MeKP)

 Gurantor department Department of Geotechnics and Underground Engineering Credits 5 Subject guarantor doc. RNDr. Eva Hrubešová, Ph.D. Subject version guarantor doc. RNDr. Eva Hrubešová, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language Czech Year of introduction 2003/2004 Year of cancellation 2020/2021 Intended for the faculties FAST Intended for study types Follow-up Master
Instruction secured by
HRU30 doc. RNDr. Eva Hrubešová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 16+0

Subject aims expressed by acquired skills and competences

Course objectives: - definition of basic principles and relationships underlying mathematical theory of elasticity and plasticity - formulation of basic principles of finite element method -definitions of different types of finite element, their analysis and comparison - build the stiffness matrix, analysis of properties of stiffness matrix - formulation of the basic conditions of solvability of equation system, selection of appropriate methods to solve the fundamental system of equations, comparing them - creation of a separate numerical model based on finite element method using available software systems - Discussion of the results of numerical models, the analysis of their explanatory power and sensitivity to input data

Teaching methods

Lectures
Individual consultations
Tutorials
Project work

Summary

The content of the course are the principles and capabilities of the utilization of finite elements method for the solution of various engineering problems, with special emphasis on the role of geotechnical. Students will learn the theoretical basis of this numerical method and the principle of discretization of given area, the various types of finite elements for application in one-dimensional, planar and spatial tasks. The aim is also to familiarize students with the practical use of this method in solving problems in geotechnical engineering and underground construction (the stability of slopes, embankments, spoil banks, the role of the stability of underground works (tunnels, etc.)) through a specialized geotechnical software (Plaxis, 3D Tunnel , Phases, etc.).

Compulsory literature:

Potts, D. Zdravkovic, L. Finite element analysis in geotechnical engineering. Telford, 1999. ISBN 0 72772753 2.

Recommended literature:

Gioda, Z.: Modeling in Geomechanics. Wiley 2000

control tests

not available

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: 1. Introductory lecture, the basic idea of ​​the finite element method, history of method, possibilities of application of the method in engineering problems. 2. Matrix algebra, types of matrices, methods for solving systems of linear algebraic equations, conditions for their solvability. 3. Differential operators, the basic equations of the theory of elasticity and strength. 4. Energy principles, principle of virtual work, Lagrange principle Galerkin method, Ritz method. 5. Discretization of analyzed area, the principle of discretization, finite element types (Linear, planar and spatial). 6. Function approximation for a particular type of finite element, basis functions, stiffness matrix and its properties. 7. One-dimensional role - beam variant of FEM. 8. Two-dimensional problem, the basic equations and relations. 9. Finite elements in spatial tasks. 10. The finite element method in continuum mechanics. 11. Geotechnical software applications of finite element method. 12. Program system PLAXIS (characteristic preeprocesor, postprocessor). 13. Program system TUNNEL 3D modeling spatial problems by finite elements. 14. The possibilities of combination the finite element method and method of boundary integrals. Exercise: 1. Home exercise - introduction to training programs and organizations. 2. Flexible plate deflection equations. 3. Solving boundary value problems using Ritz variational method. 4. One-dimensional finite element task. 5. Static solutions of arc lining using REVYZ. 6. Program system FEAT - creating a model, input data, evaluation of results. 7. Static solutions of the support construction using FEAT. 8. Interpolation of the solution of plane triangle task, setting the base function. 9. Functional of potential energy. 10. Slope stability solution using the program system PLAXIS. 11. Modeling of the stability of underground workings using PLAXIS software system. 12. Utilization of the software PHASES for modeling of geotechnical problems. 13. Spatial modeling of the stability of the tunnel using the program system TUNNEL 3D. 14. Monitoring and evaluation of programs and credits. Tasks: 1. Determination of stress-strain and stability state of the slope using FEM 2. Static and stability design of tunnel supports using finite elements.

Conditions for subject completion

Part-time form (validity from: 1960/1961 Summer semester, validity until: 2011/2012 Winter semester)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (100) 51 3
Exercises evaluation Credit 35 (35) 0 3
Examination Examination 65 (65) 0 3
Written examination Written examination 35  0 3
Oral Oral examination 30  0 3
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2019/2020 (N3607) Civil Engineering (3607T035) Geotechnics K Czech Ostrava 1 Compulsory study plan
2014/2015 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Compulsory study plan
2014/2015 (N3607) Civil Engineering (3607T035) Geotechnics K Czech Ostrava 1 Compulsory study plan
2013/2014 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Compulsory study plan
2013/2014 (N3607) Civil Engineering (3607T035) Geotechnics K Czech Ostrava 1 Compulsory study plan
2012/2013 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Compulsory study plan
2012/2013 (N3607) Civil Engineering (3607T035) Geotechnics K Czech Ostrava 1 Compulsory study plan
2011/2012 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Compulsory study plan
2011/2012 (N3607) Civil Engineering (3607T035) Geotechnics K Czech Ostrava 1 Compulsory study plan
2010/2011 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Compulsory study plan
2010/2011 (N3607) Civil Engineering (3607T035) Geotechnics K Czech Ostrava 1 Compulsory study plan
2009/2010 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Compulsory study plan
2009/2010 (N3607) Civil Engineering (3607T035) Geotechnics K Czech Ostrava 1 Compulsory study plan
2008/2009 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Compulsory study plan
2008/2009 (N3607) Civil Engineering (3607T035) Geotechnics K Czech Ostrava 1 Compulsory study plan
2007/2008 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Compulsory study plan
2007/2008 (N3607) Civil Engineering (3607T035) Geotechnics K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

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