Course syllabus

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Contact information

Lecturer and examiner

Teaching assistants

    Calling name is underlined.

 

Aim

Mathematical modelling of phenomena studied in science and engineering frequently lead to partial differential equations or boundary value problems. The finite element method (FEM) is a powerful tool to obtain approximate solutions to such equations and has become a standard tool in analysis, design and simulation.

The course aims to show the theory behind FEM and how the method is used to solve some of the most common problems in mechanical engineering and physics. The course content includes both deriving finite element equations as well as implementing these in some programming language. Furthermore, the course also gives some insight into modern computational mechanics and show examples on how FEM is used in industrial applications.

Finally, the course gives a firm basis for continued studies in advanced FEM (for example methods for transient and nonlinear problems) and related topics such as advanced solid mechanics, continuum mechanics, structural mechanics/dynamics, etc.

 

Schedule

TimeEdit

 

Literature

  • N Ottosen & H Petersson: Introduction to the Finite Element Method, Prentice Hall, New York, 1992. Sold at STORE.
  • CALFEM - A Finite Element Toolbox to MATLAB V3.4, Division of Structural Mechanics and the Department of Solid Mechanics, Lund University, 2004. (Available for download).

 

Organization 

The learning activities consist of about 35 h of lectures, 12 h of tutorials, and 20 h of consultations in computer rooms.

The lectures cover the theory of the finite element method and related numerical techniques. During the lectures, numerical examples are also solved to illustrate some of the course material. Most weeks there are also a tutorial class focusing on problem solving and numerical implementation. Each week, there are four hours of computer labs during which the students work on the hand-in assignments with teachers available for consultation.

If possible, a guest speaker will be invited to describe and show how the finite element method is used in industry.

 

Changes made since the last occasion

  • New examiner
  • Course given in English
  • Back to campus-teaching
  • Exam is carried out in computer rooms
  • Using FE software as subtasks on the hand-in assignments

 

Examination

  • Written exam:
    • Maximum 9 points
    • Permissible aids: Distributed formula sheet
  • Computer assignments that need to be passed
    • May give up to 3 bonus points for the written exam (1 point/assignment)
  • The final course grade is determined from the points on the written exam and the hand-in assignments, according to the following table:
Grading rubric

Bonus p \ Exam p

1

2

3

4

5

6

7

8

9

0

U

U

U

U

3

3

4

4

5

1

U

U

U

3

3

4

4

5

5

2

U

U

U

3

4

4

4

5

5

3

U

U

3

3

4

4

5

5

5

 

Learning objectives

The course treats primarily linear stationary problems with applications on field equations (such as e.g. heat conduction, torsion of prismatic members, deflection of membranes, porous media flow, etc.), theory of elasticity, and beam bending. For each of these problems and subsequent to the course, the student should be able to:

  • Derive a weak form that has the same solution as the original boundary value problem and, using test functions according to the Galerkin method,
  • Derive a global and local FE formulation from the weak formulation.
  • Explain how different types of boundary conditions affect the weak formulation as well as the FE formulation, and show how the different types of conditions are approximated.
  • Show how the FE approximation is constructed when a problem involves one or more unknown functions.
  • Derive expressions for element stiffness matrices and element load vectors and explain how these are assembled to structure stuffiness and structure loads.
  • Use numerical integration to evaluate stiffness matrices and load vectors.
  • Conclude the suitable number of integration points for a given element type.
  • Derive expressions for element stiffness matrices using isoparametric mapping, and describe restrictions on element geometries in such a context.
  • Implement, in a given programming language, a function that uses numerical integration to obtain the element stiffness matrix of an isoparametric element.
  • Describe the conditions a FE approximation must fulfill to guarantee convergence, and give physical interpretations of these conditions.
  • Construct computer codes that solve any of the treated problem types by a FE method, and use the code to solve given examples.
  • Use industrial FE software to solve problems covered in the course.

 

 

Course summary:

Date Details Due