Level set based topology optimization using hole creation map

A new level set based topology optimization employing hole creation map is presented. In the conventional level set based topology optimization, the optimum topology strongly depends on the initial level set distribution due to the incapability of hole creation during optimization process. In the present work, in this regard, a hole creation algorithm is proposed, in which the size, position, and number of new holes during the optimization process can be globally and consistently identified by considering both the value of a given criterion for hole creation and the occupied volume (area) of material domain. To facilitate the hole creation process, the hole creation map which corresponds to the discrete valued criterion of hole creation is applied to the level set function. In order to regularize the design domain during the optimization process, the edge smoothing is carried out by solving the edge smoothing partial differential equation (PDE). To update the level set function during the optimization process, in the present work, the least-squares finite element method (LSFEM) is adopted. To demonstrate the flexibility and usefulness of the proposed method, a verification example of two-dimensional structural topology optimization for compliance minimization problem subjected to volume constraint is treated. As an extension, the level set based topology optimization considering curved shell geometry is carried out.