Using Genetic Algorithms and Boundary Elements to Optimize the Topology of 2D Potential Problems

C.ANFLOR; R.MARCZAK; A.P.CISILINO

Ouro Preto, Brasil

Congreso; International Congress of Mechanical Engineering COBEM 2005; 2005

Asociación Brasileña de Ciencias Mecánicas

This work is concerned with the use of genetic algorithms (GA) applied to the search of optimal topologies in potential problems using boundary element methods (BEM). The main objective is to investigate how a domain initially filled with holes evolve during an optimization process and, more importantly, to verify how the final shapes compare with other available solutions. The paper summarizes the basis of GA applied to shape optimization along with the BEM. The external boundary of the problem remains fixed while the positions and dimensions of the cavities within the domain are optimized in order obtain prescribed values of temperature and/ or flux on selected portions of the boundary. Two approaches are followed for the localization of the cavities: Circular holes of arbitrary radii and general convex cavities defined by straight segments. The GA parameters used in the former one are the center coordinates and the radii of the holes, while the vertex coordinates of the cavities are used as optimization parameters in the second one. The performance of the proposed algorithm is discussed trough a member of elementary numerical examples.