A new approach to variable-topology shape design using a constraint on perimeter

This paper introduces a method for variable-topology shape optimization of elastic structures called the perimeter method. An upper-bound constraint on the perimeter of the solid part of the structure ensures a well-posed design problem. The perimeter constraint allows the designer to control the number of holes in the optimal design and to establish their characteristic length scale. Finite element implementations generate practical designs that are convergent with respect to grid refinement. Thus, an arbitrary level of geometric resolution can ns be achieved, so single-step procedures for topology design and detailed shape design are possible. The perimeter method eliminates the need for relaxation, thereby circumventing many of the complexities and restrictions of other approaches to topology design.