2011 Volume 6 Issue 3 Pages 567-578
Topology optimization has been successfully used in many industries, especially those engaged in the design and manufacturing of mechanical devices, but numerical problems are often encountered, such as grayscale representations of obtained composites. A type of structural optimization method using the level set theory for boundary expressions has been proposed, in which the outlines of target structures are implicitly represented using the level set function, and optimal configurations are obtained by updating this function based on the shape sensitivities. Level set-based methods typically have a drawback, however, in that topological changes that increase the number of holes in the material domain are not allowed. To overcome the above numerical and topological problems, this paper proposes a new topology optimization method incorporating level set boundary expressions based on the concept of the phase field method, which we apply to a minimum mean compliance problem. First, a structural optimization problem is formulated based on a boundary expression, using the level set function. Next, a time evolutionary equation for updating the level set function is formulated based on the concept of the phase field method, and the minimum mean compliance problem is formulated using a level set boundary expression. An optimization algorithm for the topology optimization incorporating the level set boundary expression based on the concept of the phase field method is then derived. Several examples are provided to confirm the usefulness of the proposed structural topology optimization method.