Risks of linear design of joined wings: a non-linear dynamic perspective in the presence of follower forces

Abstract

Past work on Joined Wings pointed out the importance of including structural geometric non-linearities since the early stages of the design. However, the attention was mainly focused on conservative loading and several open questions needed an answer. In a effort to simulate aerodynamic-pressure-like loads, this research focuses on non-conservative follower forces. Several numerical evaluations demonstrate that follower loading exacerbates the risks of snap instability in Joined Wings. Snap type of instabilities introduce problems which do not pertain only to static responses. In fact, they are associated with the concept of bi-stable regions, with consequent risks of branch-jumping phenomena which are here shown to happen also for small vanishing perturbations and for load levels that are far from the limit one. The here studied phenomena suggest that the design process for Joined Wings has to be revisited and should focus, when stability is concerned, on the evaluation of the post-critical (if any) response: performing a non-linear analysis until the expected nominal limit load (set, for example, by the flight envelope) is reached is thus, a non-conservative approach and could lead to catastrophical consequences. Unfortunately, the above design directions may not be enough to guarantee a safe design: in this study, a case showing an isola-type of bifurcation is presented. Path-tracking techniques (i.e., arc-length family methods) could not detect such phenomena if not combined with ad hoc dynamic perturbation analyses. A further inherent property of the investigated cases is the sensitivity to parameters (e.g. the lower-to-upper-wing bending stiffness ratio): a small perturbation can produce a sudden appearance of a bi-stable region and isola type of bifurcation. This sensitiveness strongly interferes with the design process, being small deviation from the nominal properties (geometry, material, etc.) unavoidable at manufacturing level.