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# A FreeFem++ Toolbox

# for shape optimization (geometry and topology)

# CMAP, Ecole Polytechnique, January 2008

We propose several FreeFem++ routines which
allow the users to optimize the thickness, the geometry or the
topology of elastic structures. All examples are programmed in
two space dimensions (a 3-d version is under current development).
These routines have been written by G. Allaire, B. Boutin,
C. Dousset, O. Pantz.

**Warning :**
Although they have been written and tested with great care, these FreeFem++
programs come with absolutely no warranty. Their authors decline any responsability
linked to their use.

** What is shape optimization ?**
In the context of solid mechanics it is also called structural optimization.
It is the mathematical theory which makes possible the ``automatic'' optimization
of mechanical structures. By ``automatic'' it is meant that these methods
and algorithms can be implemented on a computer which can analyse and
improve the designs of numerous successive configurations without any
help from the engineer or designer. For more details on this topic we
refer to the book "Conception optimale de structures" quoted below.

** What is FreeFem++ ?**
FreeFem++ is a software for solving partial differential equations by
the finite element method. It is a free software, written in C++,
developed by F. Hecht, O. Pironneau, A. Le Hyaric, K. Ohtsuka,
and it runs on several Unix, Windows and MacOS platforms.
It can be freely downloaded
here.

# Useful links

# List of FreeFem++ computer programs