A NEW APPROACH TO VARIABLE-TOPOLOGY SHAPE DESIGN USING A CONSTRAINT ON PERIMETER

This paper introduces a method for variable-topology shape optimizatio n of elastic structures called the perimeter method. An upper-bound co nstraint on the perimeter of the solid part of the structure ensures a well-posed design problem. The perimeter constraint allows the design er to control the number of holes in the optimal design and to establi sh their characteristic length scale. Finite element implementations g enerate practical designs that are convergent with respect to grid ref inement. Thus, an arbitrary level of geometric resolution can ns be ac hieved, so single-step procedures for topology design and detailed sha pe design are possible. The perimeter method eliminates the need for r elaxation, thereby circumventing many of the complexities and restrict ions of other approaches to topology design.