Course detail

# FEM in Engineering Computations

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.

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.

Recommended optional programme components

Not applicable.

Zienkiewicz, O. C., Taylor, R. L., Zhu, J. Z., The Finite Element Method: Its Basis and Fundamentals, Elsevier, 2005
Z.Bittnar, J.Šejnoha: Numerické metody mechaniky 1, 2, Vydavatelství CVUT, Praha, 1992
R.D.Cook: Concepts and Applications of Finite Element Analysis, J.Wiley, 2001
J.Petruška: Počítačové metody mechaniky II, http://www.umt.fme.vutbr.cz/images/opory/MKP%20v%20inzenyrskych%20vypoctech/RIV.pdf
K.-J.Bathe: Finite Element Procedures, Prentice Hall, 1996
V.Kolář, I.Němec, V.Kanický: FEM principy a praxe metody konečných prvků, Computer Press, 2001

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.

Language of instruction

Czech

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

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

Classification of course in study plans

• Programme B3A-P Bachelor's

branch B-MET , 3. year of study, winter semester, 5 credits, compulsory

• Programme M2A-P Master's

branch M-IMB , 1. year of study, winter semester, 5 credits, compulsory
branch M-MTI , 1. year of study, winter semester, 5 credits, elective (voluntary)

• Programme M2I-P Master's

branch M-FLI , 2. year of study, winter semester, 5 credits, compulsory

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

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.Explicit FE solution

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

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

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