Modal nudging and elastic tailoring for blade-stiffened wing structures

航空航天要求强调发展轻型结构，以帮助降低燃料消耗和相关成本。通常，航天工程中的设计者使用周期性地加筋、框架和龙骨的薄壁结构，即半整体结构，作为一种有效的解决方案。然而，细长和薄壁结构经常表现出不良的弹性非线性和不稳定性，需要以质量效率为代价进行补救。然而，已经证明，结合行为良好的弹性非线性提供了恢复基线效率甚至提高基线效率的手段。模态微调是最近引入的一种剪裁技术，该技术将屈曲后区域的振型作为初始摄动输入到完美结构的几何形状中。对结构几何形状的微小改变可以用于连接稳定的屈曲前响应和稳定的屈曲后响应。这一特性通过消除临界分叉和稳定后屈曲响应，消除了通常在屈曲后可能遇到的任何不期望的不稳定性，从而提高了结构的承载能力。作为一个额外的好处，在稳定屈曲后的响应时，模态轻推还可以改善缺陷敏感性。最终，屈曲后响应的稳定，承载能力的提高，缺陷敏感性的降低，都有利于航空航天半整体结构的进一步轻量化。初步工作表明，通过几何变换进行模态微调可以成功地提高叶片加筋机翼结构的承载能力和柔度。通过在原始几何形状上合理地选择后屈曲模式，可以严格控制和优化结构的非线性荷载-位移轨迹，以满足柔度、承载能力或附加功能的要求。几何方法的缺点是，对初始几何的微小扰动很难制造，成本也很高。此外，某些应用程序不允许几何更改。例如，在空气动力学结构中，任何几何变化都会扰乱流动和性能。然后，更合适的轻推方法可能是通过弹性剪裁来控制非线性行为。例如，这可以通过中性轴的局部移动、通过层压设计或通过使用复合丝束转向平滑地改变材料属性来实现。本项目将研究通过复合材料的弹性剪裁来取代几何缺陷播种作为模式轻推技术的有效性。第一个目标是通过数值原型的设计和分析，证明半整体结构可以通过剪裁刚度进行微调。该项目的第二个目标是通过设计、制造和测试原型叶片加筋飞机壁板，在实验测试中验证数值结果。挑战是设计和建造一个物理原型，它展示出所需的结构行为，并且对制造缺陷具有很强的抵抗力。为了实现这一目标，有必要了解制造缺陷对非线性结构的力学行为的影响。对微调原型结构的精确试验将使数值分析的验证成为可能，并将使良好的非线性结构响应的实际应用成为可能。

Aerospace requirements put an emphasis on developing lightweight structures to help reduce fuel consumption and related costs. Typically, designers in aerospace engineering use thin-walled structures which are periodically stiffened with ribs, frames and longerons, i.e. semi-monocoque structures, as an efficient solution. However, slender and thin-walled structures often exhibit undesirable elastic nonlinearities and instabilities that need to be remedied at the cost of mass efficiency. However, it has been demonstrated that incorporating well-behaved elastic nonlinearities offers the means to recuperate the baseline's efficiency or even improve upon it. Modal nudging is a recently introduced tailoring technique, whereby mode shapes from the post buckling regime are seeded as initial perturbations to the geometry of the perfect structure. The small alterations to the geometry of a structure can be used to connect stable pre-buckling responses to stable post-bucking ones. This characteristic increases the load carrying capability of the structure by removing critical bifurcations and stabilising the post-buckling response removing any of the undesirable instabilities which may typically be encountered post-bucking. As an additional benefit, in stabilising the post-buckling response, modal nudging also ameliorates imperfection sensitivity. Ultimately, the stabilisation of post-buckling responses, the increase in load-carrying capacity, and the reduction in imperfection sensitivity, are conducive to further lightweighting of aerospace, semi-monocoque structures. Preliminary work has shown that modal nudging via geometric alterations can successfully be used to increase the load carrying capacity and the compliance of blade-stiffened wing structures. With a judicious selection of the post-buckling modes seeded onto the original geometry, the nonlinear load-displacement trajectory of a structure can be closely controlled and optimised for compliance, load-carrying capacity, or additional functionality. The drawback of the geometric approach is that small perturbations to the initial geometry are difficult and costly to manufacture. Moreover, certain applications do not permit geometric changes. That is the case, for instance, in aerodynamic structures where any geometric alteration would disrupt flow and performance. A more suitable approach to nudging could then be controlling the nonlinear behaviour by elastic tailoring. This can, for example, be achieved by localised shifting of the neutral axis, by laminate design, or by smoothly varying the material properties using composite tow-steering. This project will investigate the efficacy of elastic tailoring through composite materials to replace geometric imperfection seeding for the modal nudging technique. The first objective is to demonstrate, by design and analysis of numerical prototypes, that semi-monocoque structures can be nudged through stiffness tailoring. The second objective of the project is to verify the numerical findings in experimental tests, by designing, building, and testing a prototype blade-stiffened aircraft panel. The challenge is to design and build a physical prototype that exhibits the desired structural behaviour, and which is robust to manufacturing imperfections. To achieve this objective, an understanding of the effect of manufacturing imperfections on the mechanical behaviour of the nonlinear structure is necessary. Accurate experimentation on the nudged prototype structures will enable the validation of the numerical analyses and will enable practical applications of well-behaved nonlinear structural responses.