Structural analysis and finite elements

Course content

The course teaches the linear elastic numerical analysis of structures using the finite element method. It starts with a brief recall of the main prerequisites for this course to set a common basis of notations: solid mechanics and linear elasticity. The link between the strong form of the governing equations in solid mechanics and their weak form is established next. The main concept of the Finite Element Method by spatial discretization is introduced in the following. From this basis isoparametric finite elements are presented and subsequently beam, membrane, plate and 3D finite elements are treated (including the application of loads and boundary conditions). Solution methods of the system of equations resulting from applying the FEM are briefly exposed. The use of the FEM for structural dynamics is introduced (modal basis).

Objectives (and/or specific learning outcomes)

After successfully attending the course, the students will be able to perform an in depth computational linear elastic analysis of a complex mechanical machine part, product or a civil engineering construction using the finite element method with a critical mind with respect to the numerical results.

The learning outcomes comprise:

capacity to link the presented theory of the Finite Element Method (FEM) to its implementation and functioning in engineering software,
development of a critical awareness of the sources of errors inherent to this computational method and its implications on FE modelling practice,
acquisition of a first practical experience in the application of the FEM to realistic problems in the domain of electromechanical and civil engineering,
capacity to engage in structural modelling in 1D (beams), 2D (membranes, plates) and 3D using FEM,
development of an awareness of the impact of modelling assumptions on the computational results and on the domain of validity of the model with respect to the investigated physical problem,
development of a critical mind with respect to the validity of numerical results.

Teaching methods and learning activities

Lectures on the theory and project assignments performed in group work. The project assignments consists of two parts: 1) the implementation of a simple finite element computer program (missing parts in an existing code skeleton need to be completed) and 2) the practical application of the FEM to a realistic problem from the domains of civil engineering and electromechanical engineering.

References, bibliography, and recommended reading

A complete set of references is available in the course material. The main ones are:

Irons, B. and Ahmad, S. (1980). Techniques of Finite Elements. Ellis Horwood Ltd.
Zienkiewicz, O. C. and Taylor, R. L. (2000a). The Finite Element Method – Volume 1: The Basis. Elsevier Butterworth-Heinemann.
Oñate, E. (2013). Structural Analysis with the Finite Element Method, Linear Statics – Volume 2: Beams, Plates and Shells. Springer.

Course notes

Université virtuelle

Contribution to the teaching profile

This teaching unit contributes to the following competences:

In-depth knowledge and understanding of exact sciences with the specificity of their application to engineering
In-depth knowledge and understanding of the advanced methods and theories to schematize and model complex problems or processes
Reformulate complex engineering problems in order to solve them (simplifying assumptions, reducing complexity)
Correctly report on research or design results in the form of a technical report or in the form of a scientific paper
Collaborate in a (multidisciplinary) team
A critical attitude towards one’s own results and those of others

Other information

Contacts

Prof. Peter Berke

Building, Architecture & Town planning (BATir) Department

Brussels School of Engineering/École polytechnique de Bruxelles

Université libre de Bruxelles (ULB)

Avenue F.D. Roosevelt, 50 (CP 194/2), B-1050 Brussels (Belgium)

Phone: +32 2 650 6552 - Email: peter.berke@ulb.be

Prof. Lincy PYL

MEMC - Mechanics of Materials and Constructions

Vrije Universiteit Brussel (VUB)

Pleinlaan 2, B-1050 Brussels (Belgium)

Phone: 02/6292920

E-mail: lincy.pyl@vub.be

Campus

Solbosch, Other campus

Evaluation

Method(s) of evaluation

written examination
Project
Group work
Written report

written examination

Open question with developed answer

Project

Group work

Written report

The student evaluation is twofold, composed of a written examination and a project grade. Partial grade transfer (i.e. for the examination or for the project) between academic years is not allowed.

During the written examination no course notes, textbooks, syllabus, personal notes, calculators, computers, etc., are allowed. The aim of the written examination is to check the students' ability to understand and master the general concepts covered during the course.

The project is a “single shot” assignment, i.e. performed once per academic year. It is evaluated on the basis of a written report. This report is used to verify the proper application of the FEM to a practical engineering problem and the critical mind of the students with respect to the computational results. The project assignment cannot be repeated or reworked upon after submission of the project report in the same academic year, independently of the grade received (even if it’s below 10/20).

The final project grade may be different for each member of a same group. Such grade dissociation is justified by the observed/proven significant difference in the performance and/or workload of the members. Unjustified absence from the computer labworks can impact the project grade.

Mark calculation method (including weighting of intermediary marks)

The final grade is calculated as follows:

if the written examination grade is equal to or over 7/20: 50% written examination grade and 50% project grade,
if the written examination grade is below 7/20: 100% of the written examination grade.

Language(s) of evaluation

english