Course detail

Finite Element Method

FSI-ZSY-AAcad. year: 2010/2011

Solving problems in mechanics of the continuum. Variational formulation of FEM. Algoritm of FEM. Basic equation and its solution. Finite element types. Convergence and error estimation. Solving nonlinear problems. ANSYS (Classic a Workbench) software system - solving of practical problems. User interface, preprocessing - modelling of geometry, discretization; solution, postprocessing - presentation and analysis of results.

Language of instruction

English

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Ing. Martin Hartl, Ph.D.

Department

Institute of Machine and Industrial Design (ÚK)

Offered to foreign students

Of all faculties

Learning outcomes of the course unit

The students will understand the basics of the finite-element method with the emphasis placed on practical applications. Students will be able to provide stuctural analysis using finite element method.

Prerequisites

The knowledge from the courses of mechanics of solids, mathematics, numerical methods, machine design and CAD systems are assumed.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Graded course-unit credit requirements: active participation in seminars, semestral project in ANSYS Classic or ANSYS Workbenchelaboration, passing the test based on finite element method theory, answering of tutor questions

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The objective of the course is to make students familiar with the fundamentals of finite element method and computational modelling of mechanical problems. The education is focused on modelling in ANSYS software systems, which is wide-spread in companies, universities, and research centers.

Specification of controlled education, way of implementation and compensation for absences

Participation in lectures is recommended, participation at seminars is checked and recorded. Two absences are allowed.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme N2301-2 Master's

    branch M-KSI , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

13 hod., optionally

Teacher / Lecturer

Ing. Michal Vaverka, Ph.D.
prof. Ing. Martin Vrbka, Ph.D.

Syllabus

1. Introduction to finite element method. Basic terms and basic quantities in Strenght of materials.
2. Variational approach of Lagrange. Ritz method, FEM based on variational approach.
3. Ilustration of FEM on 1D problem. Equilibrium equations in FEM.
4. Link elements.
5. Beam elements.
6. Solid elements - introduction, linear tetrahedral elements.
7. Solid elements - isoparametric elements; element type selection, free and mapped mesh, discretization of load.
8. Direct and iterative solvers in FEM.
9. Shell elements.
10 Nonlinear problems I. - contact analysis.
11. Nonlinear problems II. - geomatrical and material nonlinearity.
12. Convergence and error estimation. Adaptive mesh (h-method, p-method).
13. Introduction to ANSYS Workbench.

Computer-assisted exercise

39 hod., compulsory

Teacher / Lecturer

Ing. Michal Vaverka, Ph.D.
prof. Ing. Martin Vrbka, Ph.D.

Syllabus

1. Introductory example - tensile test.
2. Modelling of 2D geometry.
3. Modelling of 3D geometry.
4. Link elements transferring tension and compression.
5. Beam elements (2D and 3D analysis). Gravity load.
6. Stress and strain analysis in 2D.
7. Stress and strain analysis in 3D.
8. Stress and strain analysis in of machine part with notch. Assigment of semestral project.
9. Shell elements, stress analysis of T-shape pipeline (thin-walled construction).
10. Contact of the ball with flat bottom - creation of computational model.
11. Contact of the ball with flat bottom - solution and analysis of results.
12. Material nonlinearity (plasticity).
13. Stress and strain analysis of conecting rod using Workbench. Semestral project evaluation, theoretical test. Course-credit.