This paper deals with a shape and topology optimization for fluid field problem. For the topology optimization, based on Borrvall's research, body force due to the object in fluid is expressed by using a fluid fraction whose distribution represents the topology of solid or fluid domain. An optimization problem for minimization of fluid drag is formulated, and applied to design a cross sectional shape of columnar objects in fluid flow. In the shape optimization, we propose a new method which utilized Poisson's equation to obtain a smooth shape in the optimization process. For a basic study of the method before an application to a fluid field problem, a hole shape in a plate for minimization of stress concentration is designed.
