Topology optimization with flexible void area

This paper presents a methodology for including fixed-area flexible void domains into the minimum compliance topology optimization problem. As opposed to the standard passive elements approach of rigidly specifying void areas within the design domain, the suggested approach allows these areas to be flexibly reshaped and repositioned subject to penalization on their moments of inertia, the positions of their centers of mass, and their shapes. The flexible void areas are introduced through a second, discrete design variable field, using the same discretization as the standard field of continuous density variables. The formulation is based on a combined approach: The primary sub-problem is to minimize compliance, subject to a volume constraint, with a secondary sub-problem of minimizing the disturbance from the flexible void areas. The design update is performed iteratively between the two sub-problems based on an optimality criterion and a discrete update scheme, respectively. The method is characterized by a high flexibility, while keeping the formulation very simple. The robustness and applicability of the method are demonstrated through a range of numerical examples. The flexibility of the method is demonstrated through several extensions, including a shape measure requiring the flexible void area to fit a given reference geometry.