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

Schedule

Schedule online

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


Part I (P. Tossings) Introduction to numercial methods to solve optimization problems

• Fundamentals of Mathematical Programming (including KKT conditions)
• Unconstrained Optimization: Gradient Methods (including conjugate directions)
• Line Search Techniques
• Unconstrained Optimization: Newton, Newton-like and Quasi-Newton Methods
• Quasi-Unconstrained Optimization
• General Constrained Optimization: Dual Methods
• General Constrained Optimization: Transformation Methods (including SLP and SQP)

• Optimization in Engineering Design
• Fundamentals of Structural optimization
• Optimality Criteria (OC)
• Sensitivity Analysis for Finite Element Model
• Structural approximations
• Solving efficiently CONLIN and MMA using dual sovers
• 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 understand the principles of algorithms and optimization methods,
• 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 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)
• Finite Element Method (basic level)

Planned learning activities and teaching methods

• In person lectures
• Supervised computer work sessions

• For students who have no sufficient skills in MATLAB programmaing and in Finite Element Method, it is strobgly recommended to attend preparation courses or to read recommended self learning material.

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

Live presentation.
Attending 60% of supervised computer work sessions is mendatory (presence is notified by signing the attendance list).

Recommended or required readings

Copy of slides available on line on the platform eCampus
Copies of Prof. Duysinx lectures are also available 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

• There is theory oral exam in January session. Its weight is 60% of the final mark.
• Supervised computer works are evaluated on the basis of the reports and some additional discussion during the oral examen. The computer work weights 40% of the final mark.
• Participation to at least 60% of the practical sessions is mandatory to present the oral examen.
• To get the credits, the student has to pass both the computer work and the oral exam.
• The evaluation of the computer work can not be modified for the september session.

Work placement(s)

Organizational remarks

The lectures are given on Tuessday afternoon (13:45-17:45 during fall semester (September 18 - December 18).
Courses include both lectures and supervised computer work participation.
Question & Answer session is organzed in December.
Exam is scheduled during the January session.
The evaluation of the computer works is based on the reports (beginning of November, and end of Decembeer). An oral feedback is provided on demand and through a discussion during the oral exam.

Contacts

Pierre Duysinx

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

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

Adaptation of teaching commitments following the COVID-19 pandemic for the May-June 2020 session

Teaching methods implemented : distance-learning

The course has been given at Q1 and doesn't need any adaptation

Assessment subjects

Same chapters as in January

Assessment methods

Session June

The first session of exams has taken place in January
 
Session September
If sanitary conditions allow it, the second session will be classically based on the evaluation of the homework and lab reports and an oral exam according to the pedagogical contract. The oral exam includes one question about the theory and one exercise to be solved during the half day session.

Contacts

Pierre Duysinx email: p.duysinx@uliege.be Mobile phone: +32 475 98 22 87 Acronyme SKYPE: pierreduysinx Link LIFESIZE: https://call.lifesizecloud.com/1230571

Adaptation of teaching commitments following the COVID-19 pandemic for the Aug-Sept 2020 session

Assessment subjects

The course being given during the first semester (Q1), the exam topics are the same as in January 2020. The same question list is holding.
Students  will have to discuss one question with Mrs Tossings and one question with Mr Duysinx. Maximum time allocated to each question is 30 minutes, including a short preparation (maximum 5 minutes). To support the discussion, the students can prepare documents that will be shared during the discussion with the professor. The students have to prepare by themselves in advance the documents they want to share. The use of scanned handwritten notes in PDF format is encouraged. The use of copies of teachers' slides is tolerated.
The two questions have the same weight in the oral evaluation.

The Homeworks cannot be submitted twice, but the professors can, if necessary, reduce their weight in the final grade total, always for the benefit of the student.

Assessment methods

Oral exam on the LIFESIZE platform
Room of P. Tossings : https://call.lifesizecloud.com/4378896 (no password)
Room of P. Duysinx : https://call.lifesizecloud.com/4378874 (no password)

Contacts

Pierre Duysinx email: p.duysinx@uliege.be Mobile phone: +32 475 98 22 87 Acronyme SKYPE: pierreduysinx Link LIFESIZE: https://call.lifesizecloud.com/1230571

Items online