Basics of FEM
| Type of study | BachelorFollow-up Master |
|---|---|
| Language of instruction | Czech |
| Code | 330-0524/01 |
| Abbreviation | ZaMKP |
| Course title | Basics of FEM |
| Credits | 4 |
| Coordinating department | Department of Applied Mechanics |
| Course coordinator | doc. Ing. Zdeněk Poruba, Ph.D. |
Subject syllabus
Lectures:
1. Introduction to the Finite Element Method (FEM): history, fields of application, and fundamental principles.
2. Fundamentals of elasticity theory and formulation of boundary value problems.
3. Discretization of continua, types of finite elements, and their applications.
4. Shape functions, solution approximation, and finite element formulation.
5. Element stiffness matrix and assembly of the global system of equations.
6. Boundary conditions, loading, and solution of linear static problems.
7. Calculation of displacements, strains, stresses, and reaction forces; interpretation of results.
8. Solution accuracy, convergence, error estimation, and model verification.
9. Material modelling and principles of finite element model development.
10. Contact problems, constraints, and connections between structural components.
11. Introduction to geometrically and materially nonlinear analyses.
12. Overview of advanced FEM applications: thermal, dynamic, and coupled-field analyses.
13. Current trends in the development of the Finite Element Method, course summary, and recommended practices for numerical modelling.
Seminars:
1. Introduction to the selected commercial FEM software, user interface, and workflow.
2. Creation of geometric models and their simplification for numerical analysis.
3. Definition of material properties and selection of appropriate finite element types.
4. Mesh generation and basic mesh refinement techniques.
5. Definition of boundary conditions and loading.
6. Solution of a simple linear static problem.
7. Evaluation of displacements, strains, stresses, and reaction forces.
8. Investigation of the influence of mesh density and mesh quality on solution accuracy.
9. Modelling of assemblies, contacts, and connections between components.
10. Practical demonstration of a nonlinear analysis.
11. Demonstration of a thermal or dynamic analysis.
12. Independent solution of an assigned engineering problem using the Finite Element Method.
13. Presentation of results, discussion of the developed model, interpretation of results, and consultation on the semester project.
1. Introduction to the Finite Element Method (FEM): history, fields of application, and fundamental principles.
2. Fundamentals of elasticity theory and formulation of boundary value problems.
3. Discretization of continua, types of finite elements, and their applications.
4. Shape functions, solution approximation, and finite element formulation.
5. Element stiffness matrix and assembly of the global system of equations.
6. Boundary conditions, loading, and solution of linear static problems.
7. Calculation of displacements, strains, stresses, and reaction forces; interpretation of results.
8. Solution accuracy, convergence, error estimation, and model verification.
9. Material modelling and principles of finite element model development.
10. Contact problems, constraints, and connections between structural components.
11. Introduction to geometrically and materially nonlinear analyses.
12. Overview of advanced FEM applications: thermal, dynamic, and coupled-field analyses.
13. Current trends in the development of the Finite Element Method, course summary, and recommended practices for numerical modelling.
Seminars:
1. Introduction to the selected commercial FEM software, user interface, and workflow.
2. Creation of geometric models and their simplification for numerical analysis.
3. Definition of material properties and selection of appropriate finite element types.
4. Mesh generation and basic mesh refinement techniques.
5. Definition of boundary conditions and loading.
6. Solution of a simple linear static problem.
7. Evaluation of displacements, strains, stresses, and reaction forces.
8. Investigation of the influence of mesh density and mesh quality on solution accuracy.
9. Modelling of assemblies, contacts, and connections between components.
10. Practical demonstration of a nonlinear analysis.
11. Demonstration of a thermal or dynamic analysis.
12. Independent solution of an assigned engineering problem using the Finite Element Method.
13. Presentation of results, discussion of the developed model, interpretation of results, and consultation on the semester project.
Literature
[1] ZIENKIEWICZ, O. C., Robert Leroy TAYLOR a J. Z. ZHU. The finite element method: its basis and fundamentals. 6th ed. Oxford: Elsevier Butterworth-Heinemann, 2005. ISBN 0-7506-6320-0.