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Identical coursesFinite Elements (B-KUL-H04M0B)
Cannot be taken as part of an examination contract
Lombaert Geert (coordinator) | François Stijn | Lombaert Geert Aims
The finite element method (FEM) is generally perceived of as the most appropriate numerical analysis technique to solve different continuum problems.
Where in the 1960s this method obtained its first success in the domain of structural mechanics, nowadays one finds applications in fluid mechanics, solid mechanics, quantum mechanics... as well as in the study of heat transport, electromagnetism, etc.
A wide view on the FEM is presented in the course: it is shown how (differential) equations that describe a certain physical system can be converted into a system of algebraic equations.
Illustrative examples are mostly taken from structural mechanics (two- and three dimensional continua, plates..., trusses, beams); from heat transport (the differential equation -'quasi-harmonic equation' - that describes heat transport has a typical form also found in many other disciplines after proper translation of temperature and derived variables); from fluid mechanics.
Objectives of the course:
- offer users of the FEM the necessary theoretical background to use existing FE-programs for real-life problems in a correct and efficient, though critical way. Therefore a lot of attention is also paid to aspects such as modeling, interpretation of results...
- offer potential developers of FE-programs (for new applications) the necessary start platform.
The student should be able
- To understand the mathematical background and the underlying limitations of this numerical method;
- To apply the method to simple examples with a few elements;
- To translate a real structural problem into a suitable FE Model (choice of kind of analysis, element type, element mesh, loads, kinematic boundary conditions);
- To evaluate and interpret the results of a FE-Analysis and to adapt the model if necessary.
Previous knowledge
The student has a basic knowledge on Continuum Mechanics, Structural Mechanics, Differential and Integral Calculus and Linear Algebra.
Order of Enrolment
Mixed prerequisite:
You may only take this course if you comply with the prerequisites. Prerequisites can be strict or flexible, or can imply simultaneity. A degree level can be also be a prerequisite.
Explanation:
STRICT: You may only take this course if you have passed or applied tolerance for the courses for which this condition is set.
FLEXIBLE: You may only take this course if you have previously taken the courses for which this condition is set.
SIMULTANEOUS: You may only take this course if you also take the courses for which this condition is set (or have taken them previously).
DEGREE: You may only take this course if you have obtained this degree level.
FLEXIBLE(H01I0B) OR FLEXIBLE(H01I0A)
The codes of the course units mentioned above correspond to the following course descriptions:
H01I0B : Bouwmechanica
H01I0A : Sterkteleer 3 / bouwmechanica (No longer offered this academic year)
This course unit is a prerequisite for taking the following course units:
H04M9A : Dynamics of Structures
H03Q3A : Projectwerk hoogbouw (No longer offered this academic year)
H05L8A : Shell and Spatial Structures
H0T88A : Structural Optimization
H0P89A : Structural Components: Steel, Part 2
H0P92A : Nonlinear Structural Mechanics
H0P94A : Project Structural Engineering 1
H0P96A : Project Structural Engineering 3
H0N81A : Project gebouwentechniek 3
H0O31A : Geotechnical Design and Practice
Identical courses
This course is identical to the following courses:
H0N67A : Eindige elementen
Is included in these courses of study
Activities
2 ects. Finite Elements, Part 1: Lectures (B-KUL-H04M1a)
Content
The Finite Element Method, part 1 (frame and truss structures): in this first part, the finite element method is applied to frame and truss structures, composed of one-dimensional elements.
During the lectures, stiffness matrices of two- and three-dimensional truss, beam, and frame elements are derived. It is shown how the global stiffness matrix of a structure is assembled from these element matrices. Modelling of connections (stiff, flexible) and boundary conditions are discussed. An introduction is given to geometrically non-linear analysis (buckling instabilities ...).
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.)
- Slides
- Software manual
Is also included in other courses
1 ects. Finite Elements, Part 1: Exercises (B-KUL-H04M2a)
Content
The Finite Element Method, part 1 (frame and truss structures): in this first part, the finite element method is applied to frame and trusse structures, composed of one-dimensionnal elements.
During the exercises, students use an educational software tool that allows them to analyse and control each step in the calculation process and to verify the link with the underlying theory. The aim is to learn students to critically assess and interpret results obtained by means of finite-element programs.
As part of the exercises, students are also asked to select and model (choice of element type, boundary conditions, loads...) a real frame or truss structure described in the literature. The report should also include a detailled analysis and interpretation of the results.
Course material
- Slides (VTK)
- Software manual
Format: more information
- exercises
- computer lab
- case study
Is also included in other courses
2 ects. Finite Elements, Part 2: Lectures (B-KUL-H04M3a)
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)
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 (B-KUL-H24M0b)
Explanation
Continuous evaluation with final exam:
- Case study: for both parts of the course, the assessment of the case study is based on the report which needs to be handed in after the exercise sessions.
- Final exam during the exam period: written exam.
Information about retaking exams
- The exam during the second exam period is similar to the one during the first exam period.
- The score of the case studies in the first exam period is maintained for the calculation of the total score on the course in the second exam period.