Structural topology optimization considering connectivity constraint

Topology optimization has been regarded as a powerful design approach for determining optimal topology of a structure to obtain desired functional performances within a defined design domain. Considering manufacturing process constraints in topology optimization becomes increasingly important due to its potential practical applications. In this paper, we propose a novel topology optimization model with manufacturing process related connectivity constraints. A generalized method, named as virtual scalar field method (VSFM), is developed for describing and enforcing desired connectivity constraint. As an illustrative example, the connectivity constraint can be converted to an equivalent maximum temperature constraint when temperature is chosen as the scalar field. The temperature constraint is then easily integrated and implemented in routine topology optimization. The simply-connected constraint, which excludes interior closed cavities and is representative of many advanced manufacturing techniques, e.g. additive manufacturing (AM) or casting, is used as an example to demonstrate the key ideas and the efficiency of the VSF method. Some numerical examples, which consider the connectivity constraint in topology optimization, are presented to show the validity of this method.