Optimal Topology of Aircraft Rib and Spar Structures Under Aeroelastic Loads

Abstract

Several topology optimization problems are conducted within the ribs and spars of a wing box. It is desired to locate the best position of lightening holes, truss/cross-bracing, etc. A variety of aeroelastic metrics are isolated for each of these problems: elastic wing compliance under trim loads and taxi loads, stress distribution, and crushing loads. Aileron effectiveness under a constant roll rate is considered, as are dynamic metrics: natural vibration frequency and flutter. This approach helps uncover the relationship between topology and aeroelasticity in subsonic transport wings, and can therefore aid in understanding the complex aircraft design process which must eventually consider all these metrics and load cases simultaneously.

Coupled aerostructural topology optimization using a level set method for 3D aircraft wings

“…The interested reader is referred to the reviews by Deaton and Grandhi (2014) and van Dijk et al (2013) and the critical comparison of several methods by Gain and Paulino (2013). The level set method employed in this work uses shape sensitivity analysis coupled with the level set method originally developed for implicit front tracking (Sethian 1999;Osher and Fedkiw 2003). In this approach the implicit function is a signed distance function and it is updated by solving a HamiltonJacobi (H-J) type equation using an explicit upwind scheme (Allaire et al 2004;Wang et al 2003).…”

“…Note that (3) is the same as solving (2) using an explicit forward Euler scheme (Osher and Fedkiw 2003).…”

“…Details of how the signed distance function is computed for an unstructured mesh are included in Section 2.2. Maintaining a signed distance function throughout the optimization is important for the stability of the level set method (Sethian 1999;Osher and Fedkiw 2003). Otherwise the implicit function can become too steep or shallow, leading to numerical difficulties when solving the discretized H-J equation, (3).…”

“…It has been observed that this approach requires significantly fewer signed distance re-initializations compared with the natural velocity extension method (Sethian 1999). A velocity extension strategy that maintains the signed distance function is to keep velocity values constant along a line normal to the boundary, which can be obtained by numerically solving (Osher and Fedkiw 2003):…”

“…Again, we want to use an upwind scheme to compute the gradients and promote stability in the solution (Sethian 1999;Osher and Fedkiw 2003). Note that the required upwind gradients for solving the H-J equation are different from those computed during the fast marching method.…”