A structural optimization method incorporating level set boundary expressions based on the concept of the phase field method

Topology optimization has been successfully used in many industries, such as mechanical industries, but it often encounters numerical problems 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 optimal criteria. However, this method has a drawback that it does not allow topological changes that either introducing a hole in the material domain. To overcome the above two problems, this paper proposes a new topology optimization method incorporating level set boundary expressions based on the concept of the phase field method, and we apply it to the minimum mean compliance problem. First, a structural optimization problem is formulated based on a boundary expression using the level set function. Next, a time evolution 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 the 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 derived. Finally, several examples are provided to confirm the usefulness of the proposed structural optimization method.