Modal Nudging and Elastic Tailoring for Blade-Stiffened Wing Structures

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. In order 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.

There are seven principal groups of beneficiaries for our new EPSRC Centre for Doctoral Training in Composites Science, Engineering, and Manufacturing.

1. Collaborating companies and organisations, who will gain privileged access to the unique concentration of research training and skills available within the CDT, through active participation in doctoral research projects. In the Centre we will explore innovative ideas, in conjunction with industrial partners, international partners, and other associated groups (CLF, Catapults). Showcase events, such as our annual conference, will offer opportunities to a much broader spectrum of potentially collaborating companies and other organisations. The supporting companies will benefit from cross-sector learning opportunities and

- specific innovations within their sponsored project that make a significant impact on the company;
- increased collaboration with academia;
- the development of blue-skies and long-term research at a lowered risk.

2. Early-stage investors, who will gain access to commercial opportunities that have been validated through proof-of-concept, through our NCC-led technology pull-through programme.

3. Academics within Bristol, across a diverse range of disciplines, and at other universities associated with Bristol through the Manufacturing Hub, will benefit from collaborative research and exploitation opportunities in our CDT. International visits made possible by the Centre will undoubtedly lead to a wider spectrum of research training and exploitation collaborations.

4. Research students will establish their reputations as part of the CDT. Training and experiences within the Centre will increase their awareness of wider and contextually important issues, such as IP identification, commercialisation opportunities, and engagement with the public.

5. Students at the partner universities (SFI - Limerick) and other institutions, who will benefit from the collaborative training environment through the technologically relevant feedback from commercial stakeholder organisations.

6. The University of Bristol will enhance their international profile in composites. In addition to the immediate gains such as high quality academic publications and conference presentations during the course of the Centre, the University gains from the collaboration with industry that will continue long after the participants graduate. This is shown by the

a) Follow-on research activities in related areas.
b) Willingness of past graduates to:

i) Act as advocates for the CDT through our alumni association;
ii) Participate in the Advisory Board of our proposed CDT;
iii) Act as mentors to current doctoral students.

7. Citizens of the UK. We have identified key fields in composites science, engineering and manufacturing technology which are of current strategic importance to the country and will demonstrate the route by which these fields will impact our lives. Our current CDTs have shown considerable impact on industry (e.g. Rolls Royce). Our proposed centre will continue to give this benefit. We have built activities into the CDT programme to develop wider competences of the students in:

a) Communication - presentations, videos, journal paper, workshops;
b) Exploitation - business plans and exploitation routes for research;
c) Public Understanding - science ambassador, schools events, website.