Boundary Element Method Applied to 3D Optimum Design

Abstract

CETIM has developed a method to optimize the shape of bidimensional elastic structures using the Finite Element method to determine the mechanical behaviour of the component at each step of the algorithm. This method prooved to be very efficient and in now applied to three dimensional structures using the Boundary Element method as analysis tool. The principle of the shape optimization method is to repeatedly modify the shape of the structure according to the results of the previous analysis. These results are only evaluated on the moving boundary of the component according to the mechanical criterion selected. Furthermore technological constraints can be taken into account : geometrical and physical ones. The main advantage of the proposed method lies in the fact that no functional or gradient of functional with respect to the shape variable, needs to be computed.

Furthermore the use of the Boundary Element method avoids all problems related to volume meshes, especially those of their evolution at each iteration.

The first part of this paper describes the shape optimization method. Then considerations related to the use of the Boundary Element method are developed. Finally a simple example is presented.