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Syllabus for

Academic year
MHA021 - The finite element method
 
Owner: TMASA
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: C
Department: 42 - APPLIED MECHANICS


Course round 1


Teaching language: English

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0197 Examination 5,0 c Grading: TH   5,0 c   15 Mar 2007 am V

In programs

TMASA MECHANICAL ENGINEERING - Naval Architecture, Year 4 (elective)
TMASA MECHANICAL ENGINEERING - Applied Mechanics, Year 4 (elective)
TTFYA ENGINEERING PHYSICS, Year 4 (elective)
AUMAS MSc PROGRAMME IN AUTOMOTIVE ENGINEERING, Year 1 (elective)
NAMAS MSc PROGRAMME IN NAVAL ARCHITECTURE - Structural Engineering, Year 1 (elective)

Examiner:

Univ lektor  Peter Möller



Course round 2


Teaching language: Swedish

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0197 Examination 5,0 c Grading: TH   5,0 c   22 Dec 2006 pm M,  17 Jan 2007 am V,  29 Aug 2007 am M

In programs

TMASA MECHANICAL ENGINEERING, Year 3 (elective)
TMASA MECHANICAL ENGINEERING, Year 4 (elective)

Examiner:

Univ lektor  Peter Möller




Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

No formal requirements; however, MATLAB is extensively used, so the student is expected to have a basic knowledge in how to use this software.
It is also beneficial to have some basic knowledge in mechanics and strength of materials, e.g. to be familiar with concepts such as stress, strain, Hookes law, equilibrium and the like.
Some basic knowledge in mathematics and linear algebra will also be necessary; e.g. rules for integration, derivatives, Taylor series, ordinary and partial differential equations, algebra of matrices.

Aim

The student is expected to get a general understanding of how and why the finite element method works, as well as an ability to solve some of the most common engineering problems (governed by boundary value problems) by use of the method. The course content is such that it should be possible for the student to do a computer implementation of a FE-method.
We also provide an insight into modern computational mechanics and how FE is used in industrial applications.
Finally, the student should be well prepared for advanced courses in finite element methods (treating e.g. non-linear and transient problems) and in other realted topics, such as (advanced) strength of materials, structural mechanics and dynamics, constitutive modelling, etc.
Course web page

Content

Finte element methods are used to approximate solutions to partial differential equations. Here we concentrate on some of the most common problem types in engineering mechanics, such as stationary field problems (e.g. heat conduction and the Prandtl stress function) and linear elasticity (including bending of beams). The mathematical modelling of physical problems (i.e. the derivation of the governing differential equations and appropriate boundary conditions) is only briefly described. Instead we focus on how the respective boundary value problems may be formulated as variational problems (e.g. the principle of virtual work) or minimization problems (e.g. the the principle of minimum potential energy), and on how finite element methods approximate the solutions of these latter formulations. We also treat various numerical methods and techniques that are common in this context: numerical integration, mappings, substitution of variables, element approximations, solotion of large spase systems of equations, convergens, error estimation, and adaptivity.

Organisation

The course embrace a series of lectures and computer exercises.
The lectures give a theoretical description of the finite element method and related numerical techniques. We also solve a few numerical examples in order to illustrate some of the material. At the computer exercises we use MATLAB and a toolbox (CALFEM) to construct our own FE-programs. Four of the exercises embrace assignments that should be solved and reported (written or oral).
Guest speakers are invited to describe and show how the finite element method is used in an industrial environment.

Literature

N Ottosen & H Petersson: "Introduction to the Finite Element Method", Prentice Hall, New York, 1992.
CALFEM - A Finite Element Toolbox to MATLAB V3.3, Division of Structural Mechanics and the Department of Solid Mechanics, Lund University, 1999.
P W Möller: "Error Estimation and Adaptivity in the Finite Element Method", Publication U73, Department of Applied Mechanics, Chalmers, 1998.
K-G Olsson: "Introduction to the Finite Element Method - Problems", Division of Structural Mechanics, Lund University, 1999.

Examination

Written examination and 4 computer assignments.
Grading: TH


Page manager Published: Thu 03 Nov 2022.