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 |
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:
Recommended literature:
Gioda, Z.: Modeling in Geomechanics. Wiley 2000
Additional study materials
Way of continuous check of knowledge in the course of semester
control tests
E-learning
not available
Other requirements
no additional requirements
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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