Panel-Method Loads in Density-Based Topology Optimization of Wing Interiors: Consistent Load Transfer, Design-Uniform Stability, and Verification

Wing topology optimization often uses different aerodynamic and structural meshes, and the effect of the load transfer and of load errors on the optimum is rarely quantified. We study both for a fixed wing shape under one-way panel-method loads. The analysis and its full verification are two-dimensional. In 2D the load is transferred exactly by the adjoint of the finite element trace, so the discrete problem is a Galerkin approximation without consistency error from the transfer. With a clamped, load-carrying passive skin, we prove that the square root of the compliance, and of its optimum, is Lipschitz continuous in the load, in the energy norm of the passive set, uniformly in the design and the void stiffness. At 400 panels the compliance of a fixed rib is 0.53% below its value at 12,800 panels. Under measured-pressure loads, the best panel-optimal rib is within 0.35% of the best design found, less than the scatter between local optima. The three-dimensional study, with up to 63 million active voxels on one graphics processing unit, is a feasibility demonstration with a transfer that conserves force and moment but is not the adjoint of the trace; the hypotheses of the stability result are checked directly.