A Computational Method for Structurally Nonlinear Joined Wings Based on Modal Derivatives

Abstract

Past studies showed that the overconstrained nature of Joined Wings and the strong structural geometric nonlinearities make difficult the use of standard packages of aeroelastic solvers (usually modally reduced and frequency domain based) which have been effectively adopted by the industry for decades. We present here a study on the reduction of the computational cost in presence structural nonlinear effects that cannot be neglected in Joined Wings, even at small angles of attack and attached flow. In particular, a reduced order model is achieved with a basis constituted by vibration modes augmented with the corresponding modal derivatives. The results can be considered excellent when compared to the full order reference solution. However, a convergence test showed that the required number of vectors is relatively high and the basis needs to be often updated to achieve the best performance. More investigations will be necessary for an effective use in the industry and complicate dynamic problems involving the unsteadiness of the aerodynamics.

Challenges, Ideas, and Innovations of Joined-Wing Configurations: A Concept from the Past, an Opportunity for the Future

“…In fact, matching "just" the first buckling eigenvalue can be considered a kind of reduced order model. Thus, all the problems and difficulties of reduced order modeling for Joined Wings apply here [91,100,342]. This is also implicitly recognized in reference [37], in which matching of more buckling modes was suggested to improve the accuracy in the case of relatively large applied loads.…”

“…This could be assessed if one attempts to use a reduced order model (for example with a basis of vibration modes) and tracks the nonlinear response. As shown in references [342,343], adding modal derivatives in a reduced order model greatly improves the quality of the approximation since the very beginning of the load-displacement curve. In other words, nonlinearities in Joined Wings may be important and have relevant effects long before they are actually "evident" (i.e, when significant displacements occur).…”

“…Third, even for "small" deformations, nonlinearities may be important for Joined Wings (see references [212,270,342]).…”

“…The procedure was not satisfactory for loading conditions relatively far from the range in which the POD basis was obtained. Additional studies in the direction of implementing an efficient ROM were presented in references [270,342,343]. Several strategies were investigated (see Figure 72).…”