FEM in Engineering Computations I (FSI-RIV)

Academic year 2023/2024
Supervisor: prof. Ing. Jindřich Petruška, CSc.  
Supervising institute: ÚMTMB all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
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.
Learning outcomes and competences:
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.
Course contents:
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.
Teaching methods and criteria:
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.
Controlled participation in lessons:

Attendance at practical training is obligatory. Study progress is checked in seminar work during the whole semester.
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Computer-assisted exercise  13 × 2 hrs. compulsory                  
Course curriculum:
    Lecture

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

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
Literature - fundamental:
1. Zienkiewicz, O. C., Taylor, R. L., The Finite Element Method for Solid and Structural Mechanics, Elsevier, 2013
2. R.D.Cook: Concepts and Applications of Finite Element Analysis, J.Wiley, 2001
3. K.-J.Bathe: Finite Element Procedures, K.-J.Bathe, 2014
Literature - recommended:
1. Z.Bittnar, J.Šejnoha: Numerické metody mechaniky 1, 2, Vydavatelství CVUT, Praha, 1992
2. J.Petruška: MKP v inženýrských výpočtech http://www.umt.fme.vutbr.cz/images/opory/MKP%20v%20inzenyrskych%20vypoctech/RIV.pdf
7. V.Kolář, I.Němec, V.Kanický: FEM principy a praxe metody konečných prvků, Computer Press, 2001
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
N-MTI-P full-time study --- no specialisation -- Cr,Ex 5 Elective 2 1 W
N-ETI-P full-time study FLI Fluid Engineering -- Cr,Ex 5 Compulsory 2 2 W
N-SLE-P full-time study --- no specialisation -- Cr,Ex 5 Elective 2 1 W
N-IMB-P full-time study IME Engineering Mechanics -- Cr,Ex 5 Compulsory 2 1 W
N-IMB-P full-time study BIO Biomechanics -- Cr,Ex 5 Compulsory 2 1 W