Course detail

FEM in Engineering Computations I

FSI-RIVAcad. year: 2025/2026

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)

Entry knowledge

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

Rules for evaluation and completion of the course

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.

Attendance at practical training is obligatory. Study progress is checked in seminar work during the whole semester.

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.
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.

Study aids

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
M.Španiel, Z.Horák: Úvod do metody konečných prvků, Nakladatelství ČVUT, 2011 (CS)
V.Kolář, I.Němec, V.Kanický: FEM principy a praxe metody konečných prvků, Computer Press, 2001

Classification of course in study plans

  • Programme N-ETI-P Master's

    specialization FLI , 2 year of study, winter semester, compulsory

  • Programme N-IMB-P Master's

    specialization IME , 1 year of study, winter semester, compulsory
    specialization BIO , 1 year of study, winter semester, compulsory

  • Programme N-MTI-P Master's 1 year of study, winter semester, elective
  • Programme N-SLE-P Master's 1 year of study, winter semester, elective
  • Programme N-SUE-P Master's 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Jindřich Petruška, CSc.

Syllabus

Discretisation in Continuum Mechanics by different numerical methods

Variational formulation of FEM, historical notes

Illustration of FE algorithm on the example of 1D elastic bar

Line elements in 2D and 3D space - bars, beams, frames

Plane and axisymmetrical elements, mesh topology and stiffness matrix structure

Isoparametric formulation of elements

Equation solvers, domain solutions

Convergence, compatibility, hierarchical and adaptive algorithms

Plate and shell elements

FEM in dynamics, consistent and diagonal mass matrix

Explicit FE solution

FEM in heat conduction problems, stationary and transient analysis

Optimization with FEM

 

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

prof. Ing. Jindřich Petruška, CSc.

Syllabus

Illustration of algorithm of Finite Difference Method on selected elasticity problem

Commercial FE packages - brief overview

ANSYS - Introduction to environment and basic commands

Frame structure in 2D

Frame structure in 3D

Plane problem of elasticity

3D problem, pre- and postprocessing

Post processing with Workbench

Consultation of individual projects

Modal analysis by ANSYS

Consultation of individual projects

Transient problem of dynamics, stress vaves

Problem of heat conduction and thermal stress analysis

Presentation of semester projects