All programmes > Finite Elements, Part 2

Finite Elements, Part 2 (B-KUL-H9X21A)

3 ECTSEnglish35 First termCannot be taken as part of an examination contract
François Stijn
POC Bouwkunde

Aims

The finite element method is generally considered of as the most powerful numerical technique to solve continuum problems.
Whereas in the 1960s this method has been developed within structural mechanics, nowadays applications can be found in fluid mechanics, solid mechanics, quantum mechanics... as well as in the study of heat transport, electromagnetism, etc.

The student is offered a broad view on the finite element method. The course starts with the general methodology to convert (differential) equations that describe a certain physical system are converted into a system of algebraic equations by applying the final element method.

Most illustrative examples will be taken from:
• structural mechanics (two- and three dimensional elastic continua, plates and shells, truss and  beams elements);
• heat transport: the differential equation ('quasi-harmonic equation') that describes heat transport has a form that is typical for a number of other disciplines, provided that temperature and derived quantities are translated properly;
• fluid mechanics.

The treatment of the finite element method has two main objectives:
• offer users the necessary theoretical background of finite element programs to be able to use them in a responsible and efficient manner for real practical problems. Therefore, attention will also be paid to aspects such as modelling, interpretation of results...
• offer potential developers of own finite elements programs (for new applications) the necessary basic knowledge.

Previous knowledge

The student should have command of a basic knowledge on continuum mechanics, differential and integral calculation and linear algebra. Preliminaries: elasticity and plasticity theory.

Order of Enrolment


This course unit is a prerequisite for taking the following course units:
H05L8A : Shell and Spatial Structures
H0P92A : Nonlinear Structural Mechanics

Is included in these courses of study

Activities

2 ects. Finite Elements, Part 2: Lectures (B-KUL-H04M3a)

2 ECTSEnglishFormat: Lecture22 First term
François Stijn
POC Bouwkunde

Content

Finite element course, part II: in this second part, the FEM is expanded to two and three dimensional continuum problems.
The following application domains are addressed: heat transport, solid mechanics and fluid mechanics. For each of these applications, the element equations are derived in detail.
Afterwards, element families are introduced (1D, 2D, 3D / linear, quadratic, cubic / straight and curved element boundaries...). For a number of element types, the intra-element variation is given of temperatures, heat fluxes / displacements, strains, stresses / velocities, pressures.
After an in depth treatment of the theoretical background, more application related topics are presented, e.g. symmetry, choice of element type, mesh density, automatic generation of elements, allowable deviations of the 'normal' element form, loads and boundary conditions, error estimators, interpretation of the results, quality of commercial FE packages.

Course material

Study cost: 1-10 euros (The information about the study costs as stated here gives an indication and only represents the costs for purchasing new materials. There might be some electronic or second-hand copies available as well. You can use LIMO to check whether the textbook is available in the library. Any potential printing costs and optional course material are not included in this price.)

  • Course text
  • Cook R.D., Malkus D.S., Plesha M.E., Concepts and Applications of FiniteElement Analysis, John Wiley, 1989
  • Cook R.D., Finite Element Modeling for Stress Analysis, John Wiley, 1995

Is also included in other courses

1 ects. Finite Elements, Part 2: Exercises (B-KUL-H04M4a)

1 ECTSEnglishFormat: Practical13 First term
François Stijn
POC Bouwkunde

Content

Through small manual calculations, insight into the background of this numerical analysis method (FEM) will be sharpened.
The students become familiarized with the most used elements, as present in the element libraries of current finite element programs and learn how to use them.
Finally, the students analyze a real case, in which they extensively check and interpret the results.

Course material

  • Book with exercises published by the Department of Civil Engineering
  • Interactive exercises offered on Toledo

  • Exercises from the recommended literature:
  • Cook R.D., Malkus D.S., Plesha M.E. Concepts and Applications of Finite Element Analysis, John Wiley, 1989
  • Cook R.D., Finite Element Modeling for Stress Analysis, John Wiley, 1995
  • Moaveni S. Finite Element Analysis: Theory and Applications with Ansys, Prentice-Hall, 1999

Format: more information

  • Making exercises
  • Interactive computer sessions
  • Applying the theory to a real-life case
  • Team work

Is also included in other courses

Evaluation

Evaluation: Finite Elements, Part 2 (B-KUL-H2X21a)

Type : Partial or continuous assessment with (final) exam during the examination period
Description of evaluation : Written, Report
Type of questions : Open questions
Learning material : Calculator, List of formulas

Explanation


  • Assessment of the report of the case study (to be handed in after the exercise sessions).
  • Exam during the examination period.  A list of formulas can be used.