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SHAPE OPTIMIZATION OF SHAFTS UNDER TORSION USING GENETIC ALGORITHMS AND BOUNDARY ELEMENTS

This paper discusses shape optimization problems for elastic shafts under torsion using genetic algorithms (GA) coupled to the boundary element method (BEM). A GA is proposed to evolve the shape optimization involving the objective function that minimizes the area of the cross-section where the constraint imposed is a minimum value of torsional stiffness. The design variables of the problem are coordinates of the nodes used to define the boundary element discretization of the cross section. These values are generated by the GA and handled by a mesh generator which defines a candidate solution to the problem. The value of the torsional stiffness for each individual is evaluated using an implementation of the direct boundary element method. For a given pair of values of cross-sectional area and torsional stiffness, the value of the fitness function of an individual is obtained. In this case the constrained optimization problem is replaced by an unconstrained one by means of a penalty function. In order to investigate the robustness of the proposed scheme, an optimization problem were tackled. The binary-coded generational GA uses a Gray code, rank-based selection, and elitism. Standard one-point, two-point, and uniform crossover as well a mutation operator were applied.