An Introduction to Shape and Topology Optimization - WMM9AM28

This course is intended to go half-way between the theoretical and the practical, algorithmic stakes of shape and topology optimization.
The precise contents of the course will depend on the reactions of the audience; however, it is expected that the following theoretical topics will be discussed:

• Existence and non existence of an optimal design.
• Homogenization of partial differential equations, and applications in shape optimization.
• The method of Hadamard for defining shape variations and shape derivatives.
• The practical calculation of shape derivatives, involving the adjoint method.

The numerical issues tackled during the course include:

• The device of a basic, shape gradient algorithm.
• The use of a basic mesh deformation algorithm.
• The level set method for shape and topology optimization.
• Density-based topology optimization methods.

A basic knowledge in the mathematical analysis of PDE and numerical programming is assumed from the attendants; the first lectures will provide refreshers about a number of such issues.

The grading will be based on a written exam and / or an oral presentation of a research article.

The grading will be based on a written exam and / or an oral presentation of a research article.

L'examen existe uniquement en anglais

Le cours est programmé dans ces filières :

• Cursus ingénieur - Master Math. et Applications - Semestre 9 (ce cours est donné uniquement en anglais )

Code de l'enseignement : WMM9AM28
Langue(s) d'enseignement :

Vous pouvez retrouver ce cours dans la liste de tous les cours.

[1] G. Allaire, C. Dapogny, and F. Jouve, Shape and topology optimization, Hal preprint:
https://hal.archives-ouvertes.fr/hal-02496063, (2020).

[2] G. Allaire and M. Schoenauer, Conception optimale de structures, vol. 58, Springer, 2007.

[3] M. P. Bendsoe and O. Sigmund, Topology optimization: theory, methods, and applications, Springer Science & Business Media, 2013.

[4] C. Dapogny, An introduction to shape and topology optimization, exercise sessions available at:
https://github.com/dapogny/GDR-MOA-Course, 2018.

[5] , An introduction to shape and topology optimization, online course available at:
https://hal.archives-ouvertes.fr/cel-01923097v1, 2018.

[6] F. Hecht, New development in freefem++, Journal of numerical mathematics, 20 (2012), pp. 251--266.

[7] A. Henrot and M. Pierre, Variation et optimisation de formes: une analyse géométrique, vol. 48, Springer Science & Business Media, 2006.

[8] B. Mohammadi and O. Pironneau, Applied shape optimization for fluids, Oxford university press, 2010.