Finite elements, genetic algorithms and β-splines:: a combined technique for shape optimization

Shape optimization consist in changing the boundary shape of the structure to find the optimal design by verifying the prescribed constraints. Generally, this problem has been solved by replacing the originally design problem by a sequence of explicit subproblems. They are constructed by means of local approximation concepts based on function values and derivatives at the current design point. The aim of this paper is to propose a different approach to solve bidimensional shape optimization problems by using Genetic Algorithms. Boundary beta-splines curves with an automatic mesh generation are used to obtain the analytical model and finally, the finite element method is used to estimate the fitness function. The versatility and flexibility of the proposed approach is tested and discussed in two numerical examples, showing that the technique is able to deal with real engineering problems. (C) 1999 Elsevier Science B.V. All rights reserved.