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Syllabus for

Academic year
MMS050 - Finite element simulations in design
Konstruktionsberäkningar med finita elementmetoden
Syllabus adopted 2021-02-11 by Head of Programme (or corresponding)
Owner: MPPDE
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: Second-cycle
Main field of study: Mechanical Engineering, Industrial Design Engineering

Teaching language: English
Application code: 33114
Open for exchange students: Yes
Block schedule: A+

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0119 Examination 4,5 c Grading: TH   4,5 c   12 Jan 2022 am J_DATA,  11 Apr 2022 am J_DATA,  24 Aug 2022 pm J_DATA
0219 Written and oral assignments 3,0 c Grading: UG   3,0 c    

In programs

MPPDE PRODUCT DEVELOPMENT, MSC PROGR, Year 1 (compulsory elective)
TIMAL MECHANICAL ENGINEERING - Machine Design, Year 3 (compulsory)


Jim Brouzoulis

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General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Mathematics courses in linear algebra and calculus in several dimensions.


The finite element method (FEM) is a numerical method, to solve partial differential equations, enabling the analysis of many enigneering problems. This course provides the theoretical basis of FEM as well as practical training in performing finite element simulations, to analyze and design mechanical and thermal systems.

Learning outcomes (after completion of the course the student should be able to)

  • Summarize what the Finite Element Method (FEM) is and exemplify what it could be used for.
  • Describe the theoretical basis of FEM and explain strong form, weak form, and FE-form.
  • Compare FEM to Finite Element Analysis (FEA) and illustrate the steps involved in each.
  • Identify and choose relevant boundary conditions for a given problem. 
  • Select and motivate the appropriate choice of element type for a given analysis. 
  • Judge the quality of a given mesh. Can identify and motivate regions where the mesh density must be high.
  • Explain essential and natural boundary conditions, also list these conditions for all studied elements. Exemplify boundary conditions of mixed type. 
  • Recognize the governing equations for different mathematical models and explain their constituents.
  • Perform a convergence study and evaluate the results.
  • Derive FE-equations for linearized buckling and free vibration.
  • Construct FE-models and perform: 
    • static structural analysis to determine deformations, stresses, and strains.
    • linearized buckling analysis to estimate critical buckling loads and buckling modes.
    • free-vibration analysis to estimate natural-frequencies and modal shapes.
    • steady-state thermal analysis to determine temperature and heat flow.
    • sequential thermo-mechanical analysis to determine thermal stresses.
  • Use FEA to guide the design of a component, with respect to given criteria, in an iterative process.
  • Summarize the following element types: bars, beams, plates, shells, 2D solids (plane stress/strain, axisymmetry) and 3D solids.
  • Explain the difference between linear and nonlinear problems and how they are solved. List sources leading to a nonlinear FE-problems.
  • Set up, solve and evaluate results from FEA containing:
    • Contact formulations (Penalty, Lagrange, Augmented-Lagrange). 
    • Linear material models (Hooke's law, Fourier's law), elastic-plastic models (elastic-ideally-plastic, linear hardening), fiber reinforced composites (transverse isotropy).
  • Prepare CAD-geometry for FEA (defeaturing and repairing).
  • Explain what topology optimization is and be able to perform an analysis where the compliance is minimized. 


  • Theoretical basics of the Finite Element Method (FEM).
  • Practice using commercial software to set up and perform Finite Element Analysis (FEA). 
  • Common types of FE-analyses: static structural analysis, steady-state heat flow, linearized buckling, natural vibration analysis.
  • Iterative design based on one or more criteria: stiffness/deformation, allowable stress, fatigue, weight, etcetera.
  • Introduction to non-linear problems.
  • Modeling aspects: choosing boundary conditions (loads and supports), preparing CAD geometry, meshing, choosing element types, contact formulations. 
  • Common material models for metals, polymers and fiber reinforced composites.
  • Introduction to topology optimization.


The course contains about 40 h of lectures and about 30 h of computer labs. The lectures cover the theory and exemplify practical aspects of FEA. During the computer labs, students work on hand-in assignments under teacher supervision.

The course relates to the UN's sustainable development goals, especially:

  • Goal 9: Industry, Innovation and Infrastructure
  • Goal 11: Sustainable Cities and Communities
  • Goal 12: Sustainable Consumption and Production


Will be notified prior to the course start. 

Examination including compulsory elements

A written exam determines the final grade. To pass the course, all the computer assignments need to be approved.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.

Page manager Published: Mon 28 Nov 2016.