Structural and multidisciplinary optimization

Duration

30h Th, 12h Pr, 18h Proj.

Number of credits

Lecturer

Pierre Duysinx, Patricia Tossings

Language(s) of instruction

English language

Organisation and examination

Teaching in the first semester, review in January

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

The primary objective of the course is to present a systematic and critical overview of the various numerical methods available to solve optimization problems.
A second important goal is to familiarize participants with the introduction of optimization concepts into the design process in aerospace or in mechanical engineering. The basic concepts are illustrated throughout the course by solving simple optimization problems. In addition, several examples of application to real-life design problems are offered to demonstrate the high level of efficiency attained in modern numerical optimization methods. Although most examples are taken in the field of structural optimization, using finite element modeling and analysis, the same principles and methods can be easily applied to other design problems arising in various engineering disciplines such as structural engineering, electromagnetics systems or multidisciplinary optimization.

Content

• Optimization in Engineering Design
• Fundamentals of structural optimization
• Introduction to Mathematical Programming
• Algorithms for Unconstrained Optimization: Gradient Methods
• Line Search Techniques
• Algorithms for Unconstrained Optimization: Newton and Quasi-Newton Methods
• Quasi-Unconstrained Optimization
• Linearly Constrained Minimization
• General Constrained Optimization: Dual Methods
• General Constrained Optimization: Transformation Methods
• From Optimality Criteria (OC) to Sequential Convex Programmming
• Structural approximations
• CONLIN and MMA
• Sensitivity Analysis for Finite Element Model
• Introduction to shape optimization
• Introduction to topology optimization

Learning outcomes of the learning unit

At the end of the course the participants will be familiar with the fundamental optimization concepts applied to automatic design process.
They will be able:

• to develop solution schemes to simple engineering optimization problems related to design or parameter identification (including the development of computer program written in MATLAB language),
• to choose efficient formulations and optimization algorithms to solve their own problems using commercial tools,
• to read, understand and take advantage of scientific papers from the field,
• to get started with using an industrial optimization software tool (NX-TOPOL)

Prerequisite knowledge and skills

• Functional analysis of real functions
• Matrix algebra
• Matlab programming (basic level)

Planned learning activities and teaching methods

• In person lectures
• Practical work sessions
• Supervised computer work sessions

Mode of delivery (face-to-face ; distance-learning)

Live presentation.
Attending 60% of supervised computer work sessions is mendatory.

Recommended or required readings

Copy of slides available on line on the web site of Automotive Engineering Labs. www.ingveh.ulg.ac.be
All the class notes are in English
Reference books (not mandatory)

• Programmation mathématique: théorie et algorithmes (Tome 1). M. Minoux. Dunod, Paris, 1983.
• Foundations of Structural Optimization: A Unified Approach. A.J. Morris. John Wiley & Sons Ltd, 1982
• Haftka, R.T. and Gürdal, Z., Elements of Structural Optimization, 3rd edition, Springer, 1992
• J. Nocedal and S. Wright. Numerical Optimization. Springer 2006.

Assessment methods and criteria

Exam in January:

• Oral theory exam
• Report of supervised computer works
• Computer works: Evaluation of the reports and their oral presentation
• Participating the supervised work sessions is mendatory to pass the oral examen
• The evaluation of the computer work can not be modified for the september session.

Work placement(s)

Organizational remarks

The lectures are given on Thursday morning (9:00-12:30) during fall semester (September 15 - December 22).
Exam during January session.
Computer works: deadlines for reports beginning of November and before Christmas.

Contacts

Pierre Duysinx

• LTAS-Automotive Engineering
• Institut de Mécanique B52 0/514
• Tel 04 366 9194
• Email: P.Duysinx@ulg.ac.be

• Mathématiques Générales
• Institut de Mathématique B37 0/57
• Tél: 04 366 9373
• Email. Patricia.Tossings@ulg.ac.be

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