Abstract: The traditional biological growth method only optimizes the sample shape. A modified biological growth method that enables the shape optimization of structures with complex geometry to be achieved in an effective manner is presented. The improvements include three aspects. First, the grids in FEM model are not modified with the node coordinates, the boundary of the structure is described using B-spline curve. Second, the cost function is formulated that allows the weight of the structure to be minimized subject to a set of geometrical and stress constraints. So the ability of the biological growth method is enhanced to optimize the design of the complex geometry. Third, during the evolution of the shape optimization, the penalty method is used to deal with the individual that violates the constraint condition. As an example of application, the modified method has been successfully used to handle the shape optimization of centrifugal impellers.

Key words: Biological growth method, Centrifugal impeller, Shape optimization