Course syllabus

TME245 Finite element method - structures lp3 VT24 (7.5 hp)

Course is offered by the department of Industrial and Materials Science

Contact details

Lecturer/examiner:
Martin Fagerström (MF), martin.fagerstrom@chalmers.se, ph. 070-2248731

Lecturer:
Magnus Ekh (ME), magnus.ekh@chalmers.se 
Carolyn Oddy (CO), carolyn.oddy@chalmers.se

Teaching assistants:
Caroline Ansin (CA), caroline.ansin@chalmers.se
Lei Liu (LL), lei.liu@chalmers.se
Afroditi Tzanetou (AT), tzanetou@chalmers.se
Rauan Al-Emrani (RA), rauan@chalmers.se

Course aim

The aim of the course is to provide a deeper knowledge and increased understanding of how to apply the finite element method (FEM) to more advanced problems in solid and structural mechanics. In particular, problems involving nonlinearities, structural components (such as beams and plates) and stability analysis are considered.

Schedule

See TimeEdit and here

Course literature

  • Niels S. Ottosen and Hans Peterson. Introduction to the finite element method. Prentice-Hall, New York 1992. - only a few chapters, mainly for background information
  • Fredrik Larsson and Kenneth Runesson, Introduction to FE analysis of plates. Dept. of Applied Mechanics, Chalmers, 2014. Available on the course homepage for downloading.
  • Fredrik Larsson. Introduction to nonlinear finite element analysis. Dept. of Applied Mechanics, Chalmers, 2010. Available on the course homepage for downloading.

Course design

The course is organised into approximately 38 h of lectures and 38 h of computer classes. The main theory is presented in the lectures. The main part of the computer classes is dedicated to group work with the computer exercises (2 to be reported by the computer) and computer assignments (2 hand-in reports that are graded). However, during computer class, small size problems may be solved by the students and/or the instructors, exemplifying the theory. Two compulsory computer exercises (reported orally), giving an introduction to the FE-software Abaqus, are included in the course.

The computer exercises and hand-in assignments are to be solved in groups of preferably two students. More than two students will not be allowed. As we strongly believe that you will learn better by working with the project in pairs, we strongly recommend two students in each group. The main intention with these projects is to give all the students the opportunity to really work with the theory and to apply the theory to solve “real” FE problems. The best way to study the finite element method is “learning-by-doing”! So make sure to take an active part in solving the tasks.

The computer assignments are also a key part of the course examination, cf. below. Consequently, finalising these projects with good grades will require considerable effort, and more time than what is set aside for the supervised computer classes will in general be required. 

Examination

Computer exercises and assignments

The main course work consists of two mandatory computer exercises (to be reported orally at the computers, no credits) and two semi-mandatory computer assignments (hand-in reports to be graded). Both the computer exercises and computer assignments involve FE-analysis using the Matlab toolbox CALFEM as well as the commercial FE-software Abaqus. The CALFEM package can be downloaded from the course homepage or from  http://sourceforge.net/projects/calfem/ (please note that on the course homepage, the CALFEM function extract.m has been renamned as extract_dofs.m to avoid conflicts with a standard MATLAB-function with the same name).

The exercises and assignments are to be solved in groups of maximum two students where both students should contribute equally in solving the tasks. Computer classes are scheduled where you will have access to teaching assistants for asking questions about the computer exercises and assignments. Please note however, that we will not answer direct questions like “Is this correct?”. It is up to each individual group to make sure that the answers are reasonable.

A written report for each computer assignment must be submitted via Canvas by the deadline (see course schedule). Reports may be handwritten, but in such cases extra care should be taken so that reports are readable and understandable. In order to be able to submit the report, you need to sign-up for one of the project groups.

Each hand-in computer assignmentwill give a maximum of 7 credits. Altogether, 14 credit points can thus be obtained towards the final grade, see below. These points will remain valid until the course is given next time. Please note that project reports for the two computer assignments will be graded without any possibility for modifications or improvements in a second stage.

Late submission policy

Computer assignments should be submitted before the deadline. Non-agreed late submissions will lead to point deductions according to the following scheme:

  • Submission after the deadline, but before 9h after deadline: -1p
  • Submission more than 9h after deadline but before 24 hours after deadline: -2p
  • Submission more than 24h after deadline but before 48 hours after deadline: -3p
  • Submission more than 48h after deadline: No grade

Since the computer assignments are a significant part of the examination, it is essential that each group solves the tasks separately. To clarify better, it is OK to:

  • collaborate and discuss around derivations asked for in different subtasks. HOWEVER, each group should in the end do the derivations themselves and hand-in their own written solutions
  • discuss around implementation strategies in MATLAB for different subtasks. HOWEVER, limit the discussions to pen and paper discussions otherwise you will know that you are on the border of what is not OK.

 It is NOT OK to:

Directly copy other groups derivations and hand them in as your own. This applies also to codes from students from previous years.

  • Show or share any amount of MATLAB-code or Abaqus files between groups. 
  • Copy and hand-in code which is partly written by another group. This is true for code written by other students this year as well as from previous years.

Computer assignment reports will be analysed trough Urkund. Any suspected cheating (including things like copying MATLAB code or parts of someone else’s report) will be directly reported to the Disciplinary Committee, please refer to the collection of rules:

https://student.portal.chalmers.se/en/chalmersstudies/joint-rules-and-directives/Documents/20090920_Academic_Honesty.pdf Please note that failure to comply with the rules may lead to warnings or in worst case time limited suspension form Chalmers.

Regarding the ambition level and quality of the assignments reports, imagine the current situation: The person correcting and grading the report is your manager at the consultancy company where you work. You have been given an FE assignment and when you hand in the results your manager should be able to send the report directly to the client without further modification. For additional guidance, you may also refer to the Report_instructions.pdf document available on Canvas.

Final exam

The final written exam takes place in the morning on Saturday, 16 March at 8:30. During the exam, no aids will be allowed. The exam will have questions/problems which altogether can give 14 credit points.

Grading

The final course grade is given as a combination of the credit points obtained at the exam and from the computer exercises and computer assignments according to the table below:

Grades are awarded as follows:

Required credit points

Chalmers grade

<16

U

16 (minimum 6 from the final exam)

3

22

4

28

5

 

NOTE: To obtain a passing grade it is necessary to obtain at least 6 points in the final exam.

Changes made since the last occasion

The credits associated with the mandatory exercises have been removed and the grade limits adjusted.

Learning objectives (after completion, the students should be able to:) 

  • apply the finite element method to solve problems for structural components, such as plates,
  • apply the finite element method to non-linear problems, e.g. for non-linearities with respect to non-linear constitutive relations (e.g. material behavior) or geometrical non-linearities,
  • evaluate and choose suitable iterative method for solving a non-linear problem,
  • apply the finite element method to linearized pre-buckling theory to solve structural problems,
  • explain the fundamental aspects of general stability problems for a fully nonlinear problem,
  • explain the inputs, connections and steps in a FEM program required for solving nonlinear problems and linearized pre-buckling stability analysis,
  • implement a simple finite element code for non-linear problems and linearized pre-buckling analysis in MATLAB or Python, using the finite element toolbox CALFEM,
  • critically review the capabilities of commercial finite element codes,
  • compute solutions to basic solid mechanics problems using commercial FE-software, e.g. Abaqus and/or Comsol Multiphysics.

A more detailed and explicit list of expected learning outcomes will be made available on the course homepage.

Link to the syllabus on Studieportalen.

Study plan