# Structural Enablers for Advanced Metal Wing (StEAM)

Name | Affiliation | Phone Number | Email Address |
---|---|---|---|

David Standingford | CFMS | 0117 906 1100 | david.standingford@cfms.org.uk |

Aerospace

The Airbus StEAM project aims first to produce a software application able to perform optimisation of metallic structures (in particular, the wing box). These structures are made of various components that need to be sized taking into account static constraints (obtained through either analytical methods or detailed FE analyses) as well as Fatigue and Damage Tolerance (F&DT) results. StEAM benefits from the experience of the Advanced Composite Optimized Wing project. It also aims to ease the exploitation of optimisation results by providing refined representations of the sized structure, suitable for the next stages of structure design and stress check. StEAM includes research and development work spanning several fields, from stress analysis and Computer Aided Engineering (CAE) to software integration and high-performance computing. As such, the project inputs and deliverables are subject to certain levels of uncertainty. Our intention is to augment the existing and developing design process with robust UQ&M technology in order to capture and manage these uncertainties.
Metal wing component work for Airbus wings was ramped up significantly at start of 2014. This was a consequence of metal / composite trade-analysis work completed in 2012. Insights from putting A350 into production, plus research activities on composite wings have prompted interest in hybrid solutions. The current Airbus strategy is focused on derivatives, building on the success of the A320.
*Fig 1: Advanced Composite / Metallic Optimiser Architecture. [Airbus, 2015]. *
The focus for activity is to meet the structural performance characteristics for a given concept design while optimizing the weight and cost metrics. The material and (if metal) alloy selection for each part is tailored to local stress regime (including static stress versus Fatigue and & Damage Tolerance (F&DT) requirements). The main focus is on weight reduction by improving the static (buckling, strength) structural response while simultaneously satisfying fatigue and damage tolerance criteria.
Key stages include:
First, estimation of external loads applied to the structure and identification of key structural features such as material allowable, location of key loads introduction points, etc.
Second, structural sizing is performed using optimisation techniques and numerical algorithms to identify with good confidence the structure’s dimensions (e.g. sheet thickness, stiffening elements cross-sectional geometry) leading to minimum weight and cost. This step simultaneously takes into account static strength and stability criteria, F&DT criteria and, likely, other design and manufacturing criteria. A variety of analytical, semi-analytical and fully numerical approaches (e.g. FEA) can be used for computing the structural criteria.
Third, a design interpretation step is often performed to take into account complex additional design and manufacturing criteria, as well as likely more complex strength criteria.
In early and preliminary stages of the design key structural parameters will necessarily contain a significant amount of uncertainty due to either incomplete testing data and incomplete structural definition or other immature design specifics. In turn, the uncertain sizing will necessarily introduce, via a feedback mechanism, uncertainty in the loading applied to the wings.
The sizing of components and material selection must be robust to likely variations in both material properties (e.g. allowables) and in applied external loading, either in terms of magnitude of position of points of introduction. UQ&M will be used to provide performance confidence levels for the intermediate and ultimate designs with respect to the identified intervals of uncertainty for the material allowables and applied external loading.
The end-to-end process is embodied in a workflow being created during the project. The architecture of this solution can expose information to the UQ&M framework whenever a sub-module executes or when files are exchanged. These points can be used to control the flow of the system logic and this can be informed by UQ&M output.
The design space is highly constrained, and a variety of high-dimensional optimizers are being applied to establish and maintain design point feasibility. The challenge of maintaining feasibility is likely to be best addressed with a penalty scheme including confidence.
The viability if the next hybrid metal / composite wing critically depends upon the confidence in the structural performance of a lightweight and flexible wing structure.

The basic inputs to the AC/MO are
**Global design description variables**
The structural optimisation model employed by AC/MO references typical geometric dimensions of representative structural elements – e.g. stiffening elements between supports (e.g. ribs), skin sheets between supports (e.g. stiffeners and ribs). These parameters are used as design variables for the structural sizing optimisation problem. Potentially such design parameters can be linked or grouped via mathematical formulations such that they can be driven by a reduced number of global design variables.
**Uncertain inputs**
*Material properties. *In early aircraft design stages material properties – in particular allowable stress or strain for different failure modes – are uncertain due to either the potential selection of slightly different materials (e.g. variations due to suppliers) or due to incomplete test/analysis data. In the first case, the intervals of uncertainty are relatively well understood, with likely uniform pdf. In the latter, the uncertainty is not fully well understood. Likely Gaussian pdfs are appropriate for idealization, while initial magnitudes and standard mean deviations can be inferred from available test data or via a Knowledge Based Engineering approach.
*Applied loading. *Uncertainty of the applied loading can likely be considered on various specific applied loads, dependent on the loading nature in the considered sizing problem. Specifically, loading uncertainty of point loads may potentially be treated as Gaussian in nature, with appropriate levels of the mean and the standard deviation to be assessed via knowledge based engineering (KBE) and expert knowledge.
**Numerical and computational parameters**
A target for full-wing sizing using AC/MO optimisation processes is to provide robust sizing assessments in a maximum 24hr interval.
The optimisation problem size often involves well over 10^3 variables and 10^6 constraints. Intense usage of efficient parallel (distributed) computing is required to meet such timescales, often requiring usage of 50-100 CPUs.
A target of approximately 7 days (168 hr.) is considered for generating a design robust to uncertainties.
Due to the complexity of the sizing problems, representative use cases can be considered, with appropriate dimensionality reduction of the structural sizing problem.

The software framework for AC/MO is under development and a decision would need to be made as to whether to include invasive UQ&M into the current phase of development, or else use non-invasive methods for the initial stage, and then take a view on further development for StEAM 2. As optimisation technology including MMA/SCP; SQP; SQP-QLB; MISQP (mixed-integer SQP); IPOPT are being applied for the primary system, then adding UQ&M might be marginal in terms of cost. Moderately invasive methods may potentially be used, exploiting intermediate results available in the code. In the short term it will be difficult to include highly invasive methods. The design space is likely to include a large linear component, and is highly constrained. Some of the more sophisticated analysis modules may introduce strong nonlinearity (e.g. fracture propagation). We expect modules in the system to be generally tightly coupled, with the exception of physics models separated by time and / or scale or by logical construct. Examples are fatigue versus maximum strength, or the (binary) decision to use a specific class of fastener or joint.

UQ&M for aerospace components is a crucial element to allowing migration from existing platform variants to new concepts. The visual functionality is secondary, though of course clarity and aesthetics are desirable.

The use case is the basis for a £6.4m collaborative project sponsored by the Aerospace Technology Institute, including partners Airbus Group, Constellium UK, Magellan Aerospace, Testia and CFMS. UQ&M would be a valuable and additional element to the project.

Sayan Ghosh, David Rancourt, Dimitri N. Mavris, and Simon Coggon. "Principal Component Analysis Assisted Surrogate Modeling (PCA-SM) of Correlated Loads for Uncertainty Analysis of Design Load Envelopes", 16th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Aviation. http://arc.aiaa.org/doi/abs/10.2514/6.2015-3092 .