On hole nucleation in topology optimization using the level set methods

Hole nucleation is an important issue not yet fully addressed in structural topology optimization using the level set methods. In this paper, a consistent and robust nucleation method is proposed to overcome the inconsistencies in the existing implementations and to allow for smooth hole nucleation in the conventional shape derivatives-based level set methods to avoid getting stuck at a premature local optimum. The extension velocity field is constructed to be consistent with the mutual energy density and favorable for hole nucleation. A negative extension velocity driven nucleation mechanism is established due to the physically meaningful driving force. An extension velocity filtering approach is developed to allow for nucleation of new holes at the sites where the material is ineffectively used while the ill-posed topology optimization problem can be regularized. To overcome the numerical instabilities caused by the level set evolution, the gradients of the level set function are kept bounded using a rescaling-based reinitialization scheme based on a global representation technique without moving the free boundary. Inconsistencies with the regularization and reinitialization techniques are eliminated and smooth nucleation of new holes becomes possible. The level set-based topology optimization would become more accurate and efficient. The success of the present method is demonstrated with the classical examples in minimum compliance design.