Numerical performance of Poisson method for restricting enclosed voids in topology optimization

Suppressing enclosed voids in topology optimization is an important problem in design for manufacturing. The method of Poisson equation-based scalar field constraint (i.e., Poisson method) can effectively address this problem. Nevertheless, the numerical performance of this method is not well understood. This paper investigates the numerical functionality and characteristics of the Poisson method. An electrostatic model is developed to describe this method instead of the previous temperature model. Moreover, an efficient constraint scheme is proposed, which combines density filtering, Heaviside projection, regional measure, and normalization techniques to overcome various numerical issues and difficulties associated with the method. Particularly, the key constraint relation between the constraint threshold and the optimized result in this method is clarified. Numerical examples are presented to assess the Poisson method and demonstrate the effectiveness of the proposed constraint scheme. It is shown that the choice of constraint boundary conditions affects the obtained design. And the constraint effect of the Poisson method depends on the constraint threshold. Besides, the approximation error variations have a significant impact on the constraint relation for the aggregation techniques-based constraint implementation. These findings are essential in obtaining reasonable designs by the Poisson method.