Shape optimization of mechanical structure by an adjoint variables method and genetic algorithm

Abstract

The shape optimization of machine elements or structures consists in searching the optimal form satisfying the imposed mechanical, technological and geometrical criteria. In this paper two methods, developed for shape optimization of uni and bidimensional mechanical structures are offered. The first one, known as the adjoint variables method, is based upon the evaluation of the sensitivity or the derivatives of the functional with respect to the evolution of the structure shape. It requires the use of a mathematical optimization code in order to converge towards the solution. The second method deals with Genetic Algorithms whose principle rises from the evolution of individuals living in nature. Within the framework of structures optimization, a new Genetic Algorithm has been developed. The analysis is carried out by the finite element method. The first part of this article is devoted to optimal shape research of unidimensional structures such as beams while the second treats the shape optimization of bidimensional parts. To show the effectiveness of each of the two methods, examples are presented, and the numerical results obtained show that a good convergence was obtained in each case.