The stiffness of plate structures can be significantly improved by adding reinforcing ribs. In this paper, we are in particular concerned with stiffening of panels using ribs made of constant-thickness plates that may be, for example, welded to the panel. These ribs are common in, for example, the reinforcement of ship hulls, aircraft wings, pressure vessels and storage tanks. Existing methods either produce rib designs that cannot be fabricated with plates, or employ heuristics that produce non-optimal designs. This paper presents a method for optimally designing the topology, locations and dimensions of rectangular ribs to reinforce a panel. To this end, we smoothly project an analytic, explicit geometry representation of a set of ribs onto a continuous density field over a design envelope. This density field is discretized in an element-wise manner on a uniform grid for analysis. The initial design consists of a prescribed set of ribs, constrained to remain perpendicular to the panel to facilitate manufacturing and joining of the ribs.

The advantages of our method are two-fold. On one hand, as in classical density-based topology optimization, we circumvent re-meshing by using a fixed finite element grid for the analysis, and the differentiability of the projection allows us to employ efficient and robust gradient-based optimization methods. On the other hand, the explicit geometry representation provides a direct translation into CAD, it produces reinforcement designs that conform to available plate cutting and joining processes, and it allows us to impose a constraint on the minimum separation between any two ribs to guarantee clear gaps for weld gun access. Also, bounds on the ribs dimensions can be naturally and directly accommodated. We present numerical examples of our panel reinforcement design under different types of loadings to demonstrate the applicability of the proposed method.

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