Post-Critical Analysis of Joined Wings: the Concept of Snap-Divergence as a Characterization of the Instability

Abstract

The concept of snap divergence and post-critical states are theoretically formulated for Joined Wings with the arc length technique. The true critical condition is compared with the divergence speed evaluated by solving an eigenvalue problem about a steady state equilibrium, showing how in some cases this last approach is not reliable and even nonconservative.The work assesses the difference of the nonlinear responses relative to mechanical loads (both conservative and follower ones) used to mimic the real loading condition and the aerodynamic forces.Two joined-wing configurations, characterized by a different location of the joint, are investigated. It is demonstrated that the lift/displacement response may hide the physical snap divergence occurrence, leading to non-physical interpretation of the stability properties of the system. Thus, as a consequence, use mechanical loading to mimic aerodynamic effects should be meditated since they may not give a reliable picture. Aeroelastic stiffening and softening effects are observed for the different cases, and it is discussed how practical instability situation may not be encompassed by the formal mathematical criterion (singularity of the system tangent matrix).Finally, physical interpretation of the static aeroelastic deformation is provided with particular emphasis on the conditions that lead to the snap divergence. The bending/torsion coupling at geometric (sweep angle of the wings) and material (composite materials) level for each wing can not be thought as an isolate property, since, due to the overconstrained nature of the system, the actions are transferred between different parts of the system. In other words, an intuitive approach that tries to fine tune the design of a part as an isolate entity may not lead to meaningful results.

Risks of Linear Design of Joined Wings: a Nonlinear Dynamic Perspective in the Presence of Follower Forces

“…In the present effort the magnitude is considered to be constant and the reference followed direction is parallel the normal to an element vector. In reference [60] a case in which the magnitude only depends on the deformation. Before further proceeding, in the following of this contribution, the terms array and vector are differently used: when referring to the Euclidean space the terminology vector is used, whereas, referring to finite element degree of freedoms space the word array is employed.…”

“…Not only could linear analysis tools be strongly nonconservative, recommending the employment of expensive nonlinear tools (see [27,60]). But it is also suggested that, for static analysis the post-critical branch should be pursued in order to assess the existence of different static equilibrium points for the same load level (speed).…”

Phenomenology of Nonlinear Aeroelastic Responses of Highly Deformable Joined-wings Configurations

“…The numerical investigations presented in references [4,5,11,13,16] characterized the response of Joined Wings on a conceptual level. In particular, a snap-instability was first found when statically loading the structure with mechanical forces.…”

“…In reference [13] the snap-divergence was compared to the traditional divergence analysis, performed through an eigenvalue analysis about particular configurations (usually the undeformed one). Discrepancy between the critical speeds predicted by these two approaches was substantial.…”

“…When assessing joined-wing behaviour from a static aeroelastic perspective, similar problems were noticed [13] in terms of presence of bi-stable regions, and the snap-divergence concept was introduced. The strong structural nonlinearities have demonstrated to be dominant also for small angles of attack and attached flow, which can be considered linear.…”