Syllabus 2010/2011 FHLN01

Syllabus academic year 2010/2011
(Created 2010-07-25.)

STRUCTURAL OPTIMIZATION

FHLN01

Credits: 7,5. Grading scale: TH. Cycle: A (Second Cycle). Main field: Technology. Language of instruction: The course might be given in English. Optional for: F4, F4bem, I4, M4bem, M4fo, M4pu, MD4, Pi4, Pi4bs. Course coordinator: Docent Mathias Wallin, mathias.wallin@solid.lth.se, Solid Mechanics. Recommended prerequisits: FHL064, FHLF01Finite Element Method or similar course. The course might be cancelled if the number of applicants is less than 16. Assessment: The examination in the course consists of one mid-term exam and one project. The mid-term exam will cover theoretical aspects of the underlying optimization algorithms and their connection with structural optimization whereas the project is related to the implementation of the optimization algorithms in a finite element environment. The mid-term exam will be given two times per year whereas the project is given once in conjunction with the course. Home page: http://www.solid.lth.se.

Aim
In stuctural optimization the problem of finding the 'optimal' design is considered. The term 'optimal' design can apply to various aspects and the common features are minimum weight or maximum stiffness of a structure. The course is aimed to give the student knowledge and fundamental understanding of modern tools that are commercially available.

Knowledge and understanding
For a passing grade the student must

be able to explain and understand goal function, constraints, global and local minima
be able to explain and understand the underlying optimization algorithms used in structural optimization
be able to explain and identify the causes for numerical instabilities associated with numerical topology optimization

Skills and abilities
For a passing grade the student must

be able to formulate a mathematical optimization problem from engineering structural optimization problems.
be able to describe numerical solution strategies suitable for structural optimization.

Judgement and approach
For a passing grade the student must

be able to solve simple discrete structural optimization problems analytically
be able to solve simple continual stiffness optimization problems using variational principles.
implement simple optimization algorithms in a finite element environment

Contents
The following topics will be considered in the course

Formulation of optimization problems, goal functions, constraints, global/local optima.
Convex optimization
Convex approximation techniques for structural optimization problems
size and shape optimization
topology optimization
filter

Literature
An introduction to structural optimization,
Christensen, P and Klarbring, A
Springer-Verlag, 2008
ISBN: 978-1-4020-8665-6
CALFEM - A finite element toolbox to MATLAB. Studentlitteratur.