Course code: wb1416

Course name: Numerical Methods for Dynamics

This concerns a Course 

DUT credit points: 2

ECTS credit points: 3

Faculty of Mechanical Engineering and Marine Technology

Section of Engineering Mechanics

Lecturer(s): Prof. Dr. Ir Daniel Rixen

Tel.:  015 - 27 81523 / 85733

Catalog data:

engineering dynamics, computational mechanics, finite elements, time-integration, mode superposition, model reduction, linear solvers, eigensolvers

Course year:

MSc 1^st year

Semester:

2A / 2B

Hours per week:

2

Other hours:

16

Assessment:

Oral exam

Assessment period:

2B, August

(see academic calendar)

Prerequisites (course codes):

Statics and Strength of materials (e.g. wb1214 and wb1309), Dynamics (e.g. wb1308), Linear Algebra (e.g. wi1311wb), Numerical Analysis (e.g. wi3097wb)

Follow up (course codes):

Detailed description of topics:

Using engineering tools as black boxes can be dangerous and inefficient. This is especially true when performing dynamic analysis of structures in a finite element package. Choosing the right finite element types and the suitable solution procedure is critical to get accurate results and to compute solutions efficiently. In order to discuss basic principles of numerical methods for dynamics and to explain fundamental concepts related to dynamic analysis, the course will cover the following topics:

• Finite element discretization and procedures in linear dynamics

• Free vibration modes and mode superposition techniques

• linear solvers (direct/iterative, parallel) and eigensolvers for finite element models

• model reduction, including dynamic substructuring

• time-integration of linear and non-linear systems

• handling of constrains in dynamic models

In this courses emphasis will be put on understanding fundamental concepts of numerical methods and how they relate to the mechanics of structures.  Specific topics such as dynamic analysis of cyclic symmetric structures can be discussed if time permits.

Course material:

• lecture notes

References from literature:

• Mechanical Vibrations, Theory and Application to Structural Dynamics, M. Géradin and D. Rixen, Wiley, 1997.
• The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, T.J.R. Hughes Prentice-Hall, 1987.
• Finite Element Procedures, K.J. Bathe, Prentice-Hall, 1996
• Structural Dynamics: an introduction to computer methods, R.R. Craig, Wiley, 1981, ISBN 0-471-04499-7
• Matrix Computation, G.H. Golub and C.F. Van Loan, Johns Hopkins University Press, 1996.

Remarks assessment, entry requirements, etc.:

An assignment will be given in ANSYS/Matlab (topic can be defined by students)

Learning goals:

The objective of the course is to explain basic concepts specific to numerical methods typically used in dynamic analysis codes for engineers.

Computer use:

Use of ANSYS and/or Matlab for assignment and illustration

Laboratory project(s):

Design content:

Percentage of design:     %