OGACA: Geometrical optimization with Code_Aster

7 May 2010

by Frédéric Renou, Structural Engineer, frederic.renou[at]gmail.com

Code_Aster is used to carry out a geometrical optimization of forms. The form is described by a level line function and uses the XFEM method initially developed for the computation of cracks. The presence of XFEM elements and the availability of the source code were crucial factors in the choice of Code_Aster for this application. The availability of Code_Aster’s source code enabled me to customise the developments necessary to carry out this optimization (mainly in python).

Figure 1

In this example an asymmetrical foot of quadripode (fig. 1) supporting 4 different forces was optimized. The first stage consists in meshing the volume in which we would accept the presence of material at the end of the optimization (fig. 2). Thereafter the program determines the best distribution of the level line function (fig. 3).

Figure 2	Figure 3
Figure 2	Figure 3

Eventually the final geometry is obtained (fig. 4). This result depends on the curvature of the parameterized surface (fig. 5). Moreover the use of a level line function allows this geometrical optimization to propose changes of topology, here the creation of a hole in the form. The mathematical principles of the forms’ optimization on which this program is based were developed per G. Allaire and F.Jouve

Figure 4	Figure 5
Figure 4	Figure 5