Course detail

FEM in Engineering Computations

FSI-RIVAcad. year: 2013/2014

The course presents an introduction to selected numerical methods in Continuum Mechanics (finite difference method, boundary element method) and, in
particular, a more detailed discourse of the Finite Element Method. The relation to Ritz method is explained, algorithm of the FEM is presented together with
the basic theory and terminology (discretisation of continuum, types of elements, shape functions, element and global matrices of stiffness, pre- and
post-processing). Application of the FEM in different areas of engineering analysis is presented in theory and practice: static linear elasticity, dynamics
(modal analysis and transient problem), thermal analysis. In the practical part students will learn how to create an appropriate computational model and
realise the FE analysis using commercial software.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Ing. Jindřich Petruška, CSc.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Learning outcomes of the course unit

Students learn how to formulate appropriate computational models of typical problems of applied mechanics. They will become experienced in preparation,
running and postprocessing of FE models and able to use any of the commercial FE packages after only a short introductory training.

Prerequisites

Matrix notation, linear algebra, function of one and more variables, calculus, differential equations, elementary dynamics, elasticity and thermal conduction.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

The course-unit credits award is based on the individual preparation of two semester projects, proving students have mastered the work with a selected FE
package. Examination has the form of a written test and following discussion

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Aim of the course is to present numerical solution of problems of Structural and Continuum Mechanics by Finite Element Method and to give a general view
of the possibilities of commercial FE packages.

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

Study progress is checked in seminar work during the whole semester.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

K.-J.Bathe: Finite Element Procedures, K.-J.Bathe, 2014
R.D.Cook: Concepts and Applications of Finite Element Analysis, J.Wiley, 2001
Zienkiewicz, O. C., Taylor, R. L., The Finite Element Method for Solid and Structural Mechanics, Elsevier, 2013

Recommended reading

J.Petruška: MKP v inženýrských výpočtech http://www.umt.fme.vutbr.cz/images/opory/MKP%20v%20inzenyrskych%20vypoctech/RIV.pdf
V.Kolář, I.Němec, V.Kanický: FEM principy a praxe metody konečných prvků, Computer Press, 2001
Z.Bittnar, J.Šejnoha: Numerické metody mechaniky 1, 2, Vydavatelství CVUT, Praha, 1992

Classification of course in study plans

  • Programme B3901-3 Bachelor's

    branch B-MET , 3 year of study, winter semester, compulsory

  • Programme N3901-2 Master's

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

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Jindřich Petruška, CSc.

Syllabus

1. Discretisation in Continuum Mechanics by different numerical methods
2. Variational formulation of FEM, historical notes
3. Illustration of FE algorithm on the example of 1D elastic bar
4. Line elements in 2D and 3D space - bars, beams, frames
5. Plane and axisymmetrical elements, mesh topology and stiffness matrix structure
6. Isoparametric formulation of elements
7. Equation solvers, domain solutions
8. Convergence, compatibility, hierarchical and adaptive algorithms
9. Thin-walled elements in bending, hermitean shape functions
10.Plate and shell elements
11.FEM in dynamics, consistent and diagonal mass matrix
12.FEM in heat conduction problems, stationary and transient analysis
13.Weakly coupled thermal-deformation problem

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

prof. Ing. Jindřich Petruška, CSc.
doc. Ing. Tomáš Návrat, Ph.D.

Syllabus

1. Illustration of algorithm of Finite Difference Method on selected elasticity problem
2. Application of Ritz Method on the same problem
3. Commercial FE packages - brief overview
4. ANSYS - Introduction to environment and basic commands
5. Frame structure in 2D
6. Frame structure in 3D
7. Plane problem of elasticity
8. 3D problem, pre- and postprocessing
9. Consultation of individual projects
10.Consultation of individual projects
11.Modal analysis by ANSYS
12.Transient problem of heat conduction and thermal stress analysis
13.Presentation of semester projects