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| MECA0027-1 | Structure Optimization
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| Duration : | 30h Th, 30h Pr |
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| Credits/ECTS : |
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| Holder(s) : | Claude Fleury |
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| Substitute(s) : | Pierre Duysinx |
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| Language : | French language |
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| Course contents : | Numerical optimization methods have now reached a stage where they can be routinely applied by practicing engineers to many design tasks. Because these methods help achieving an ordered approach to design decisions, their impact on the design methodology is becoming stronger and stronger in most leading industries. For example, the introduction of optimization capabilities into commercially available finite element systems like SAMCEF has deeply modified the way to design aircraft structures. Therefore education in this field should benefit to any scientist, engineer or manager involved in the design process.
The course begins with a short historical overview showing why and how many engineering design processes should be stated, and solved iteratively, as numerical optimization problems. Next, after exposing the necessary mathematical background, some well established intuitive approaches to optimum design are briefly reviewed. It is shown that these "Optimality Criteria" techniques, mainly based on engineering judgment and experience, often lead to a dead end when difficult practical problems are dealt with.
A more rational approach, based on rigorous "Mathematical Programming" theories, is then described in detail, starting from simple, one-dimensional unconstrained problems, and moving gradually toward large, complicated constrained problems. Approximation concepts are introduced, that can considerably reduce the computational cost of the iterative optimization process. Recent efficient methods based on duality theory are exposed, that reconciliate optimality criteria and mathematical programming approaches. Next, attention turns toward sensitivity analysis, i.e. how to evaluate the partial derivatives (gradients) required by the optimizer. The course terminates with a discussion of current trends: in order to fully computerize the design cycle, the integration of CAD and FEM technologies within an interactive optimization loop is increasingly needed.
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.
Content
1. Historical Overview and Fundamental Concepts
2. Mathematical Bases: Nonlinear Programming
3. Optimality Criteria Techniques
4. Introduction to Mathematical Programming Methods
5. Linearly Constrained Minimization
6. General Nonlinear Programming Methods
7. Approximation Concepts
8. Sensitivity Analysis for Finite Element Models
9. Shape Optimal Design using Geometric CAD modelling
10. Large Scale Topology Optimization
11. Applications to real-life design problems |
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| Course objective : | 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. 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 fieldof 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. |
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| Workshops : | Exercises (20H)
Computer project (2 students/group) |
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| Organization : | 1st semester |
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| Written notes : | Optimisation des Structures: Théorie
Optimisation des Structures: Exercices
Centrale des Cours
All the class notes are in English |
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| Assessment : | Oral exam, open book (50%).
Project par group of 2 students (50%).
In June. |
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| Contacts : | Prof. Claude Fleury
c.fleury@ulg.ac.be |
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