A stress-based criterion to identify and control intersections in 2D compliance minimization topology optimization

Topology optimization typically generates designs that exhibit significant geometrical complexity, which can pose difficulties for manufacturing and assembly. The number of occurrences of an important design feature, in particular intersections, increases with geometrical complexity. Intersections are essential for load transfer in many engineering structures. For certain upcoming manufacturing processes, such as direct metal deposition, the size of an intersection plays a role. During metal deposition, slim intersections are more prone to manufacturing defects than bulkier ones. In this study, a computationally tractable methodology is proposed to both control occurrence and size of intersections in topology optimization. To identify intersections, a stress-based quantity is proposed, denoted as Intersection Indicator. This quantity is based on the local degree of multi-axiality of the stress state, and identifies material points at intersections. The proposed intersection indicator can identify intersections in both single as well as multi-load case problems. To detect the relative size of intersections, the average density in the vicinity of an intersection is used to penalize or promote intersection sizes of interest. The corresponding sensitivity analysis involves solving a set of adjoint equations for each load case. Numerical 2D experiments demonstrate a controllable reduction of penalized slim intersections compared to the designs obtained from conventional compliance minimization. The overall geometrical complexity of the design is reduced due to the promotion of bulkier intersections which leads to an increase in compliance. The designs obtained are more suitable for manufacturing processes such as direct metal deposition.