MECA0027-1

Duration

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

Number of credits

	Master of Science (MSc) in Aerospace Engineering	5 crédits
	Master of Science (MSc) in Electromechanical Engineering	5 crédits
	Master of Science (MSc) in Mechanical Engineering (EMSHIP+, Erasmus Mundus)	5 crédits
	Master of Science (MSc) in Mechanical Engineering (EMSHIP+, Erasmus Mundus)	5 crédits
	Master of Science (MSc) in Engineering Physics	5 crédits

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)

Part II Application to structural and multidisciplinary optimization

Fundamental Concepts in Structural and Multidisciplinary Optimization
Finite Element and 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)
Mechanical Vibrations: eigenfrequencies, eigenmodes, mechanical systems with N-degrees of freedom

Planned learning activities and teaching methods

In person lectures
Supervised computer work sessions
Exercice session

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, hybrid learning)

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

Organisational adjustments related to the current health context

Assessment methods and criteria

Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.

Any session :

- In-person

oral exam

- Remote

oral exam

- If evaluation in "hybrid"

preferred in-person

Additional information:

There is theory oral exam in January session. Its weight is 60% of the final mark.
The personnal homework and the 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

Patricia Tossings

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

Items online

Site web du cours
Course Web site

http://www.ingveh.ulg.ac.be/index.php?page=meca0027

Structural and multidisciplinary optimization