Groh, Rainer

Kim, Byung Chul (Eric)

Mcinnes, Calum J

Pirrera, Alberto

English

In the development of next-generation air and space vehicles mass efficiency is a key design driver [1]. As aerostructures become thinner, their stability becomes an increasing concern. Traditionally, industrial design has followed a linearized approach where instabilities are viewed as a ‘failure’ mode. If instead methodologies can embrace nonlinearity, postbuckling can be safely exploited for enabling additional structural capability [2]. In this work we utilize the postbuckling regime to design mass-efficient thin laminated plates for aerospace applications. This work optimizes the stacking sequences (fiber orientation and number of layers) of both conventional straight fiber and novel fiber-steered laminates to minimize for a target axial compression and load-carrying capacity. Fiber-steered structures [3], those in which the fiber orientations follow curvilinear reference paths, have been identified as a route towards improved structural lightweighting by engineering stiffness variations to redistribute prebuckling stresses [4]. This work investigates the design of a simply supported plate under uniaxial compression whilst applying nonlinear design constraints: load carrying capacity, static strength and manufacturability in response to a prescribed end-shortening strain. Genetic algorithms in MATLAB are used to determine the optimal layups for minimum mass problems using the Finite Element Method (FEM). Three optimizations are conducted to demonstrate the increasing tailor-ability achievable by fiber-reinforced materials. A Quasi-Isotropic structure is first presented that serves as the baseline for angle-ply and fiber-steered optimizations to outperform. Overall, the proposed work aims to progress towards the safe and controlled use of instabilities in future design methodologies and further the application of structural nonlinearity in aerospace applications.REFERENCES:[1] L. Zhu, N. Li and P. Childs, Prop. Pow. Res., vol. 7, no. 2, pp. 103-119, 2018. [2] A. Champneys, T. Dodwell, R. Groh, G. Hunt, R. Neville, A. Pirrera, A. Sakhaei, M. Schenk and M. Wadee, Front. Appl. Math. Stat., vol. 5, 2019. [3] M. W. Hyer and R. F. Charette, AIAA 30th Structures, Structural Dynamics, and Materials Conference, Mobile, 1990. [4] C. McInnes, A. Pirrera, B. Kim and R. Groh, AIAA SciTech 2023, National Harbor, 2023. <br/

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                          Mcinnes, C. J., Pirrera, A., Kim, B. C., & Groh, R. (2023). FiberSteering for Mass-Efficient Thin Plate Structures. Abstract fromSociety of Engineering Science Annual Technical Meeting 2023,Minneapolis, Minnesota, United States.Publisher's PDF, also known as Version of recordLink to publication record in Explore Bristol ResearchPDF-documentUniversity of Bristol - Explore Bristol ResearchGeneral rightsThis document is made available in accordance with publisher policies. Please cite only thepublished version using the reference above. Full terms of use are available:http://www.bristol.ac.uk/red/research-policy/pure/user-guides/ebr-terms/Fiber Steering for Mass-Efficient Thin Plate StructuresCalum J. McInnes, Alberto Pirrera, Byung Chul Kim, Rainer M.J. GrohSociety of Engineering Science Annual Technical Meeting 202311th October 2023Motivation: Lightweight Structures211th October 2023Fiber Steering for Mass-Efficient Thin Plate Structures• Increasing use of advanced composites in aerospace structures• Mass efficiency is a key design driver • Larger payload capacity• Lower fuel burn• New economic opportunities [1][1]𝑥𝑦𝑙𝑥𝑙𝑦𝐿∆𝑢[1]  R. Wanhill, Carbon Fibre Polymer Matrix Structural Composites, Springer, 2016[2] Tiwari et al., Automated inspection using database technology within the aerospace industry, Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture, 2008[2]Context: Fiber-Steered Composites3• Steering of composite material tapes produces non-constant fiber angle across a ply • In-plane shearing of material tows by Continuous Tow Shearing (CTS) processalong curvilinear reference eliminates potential defects and allows tessellation• CTS process exhibits nonlinear orientation-thickness coupling (𝑡 = 𝑡0 sec 𝜃) and allows periodic fiber steering [2]Fiber Steering for Mass-Efficient Thin Plate Structures11th October 2023[2] European Space Agency. (2022, May 31). Rapid tow shearing. Retrieved from https://www.esa.int/ESA_Multimedia/Images/2022/06/Rapid_tow_shearingReference PathThicknessIncreaseFiber AnglesThicknessesMethod: Finite Element Model4Lower (tool) surfaceUpper surfaceMid-planeFiber Steering for Mass-Efficient Thin Plate Structures11th October 2023• Finite Element Method employed in commercial solver (ABAQUS)• Element-wise angle and thickness algorithm for computation of unique composite sections• Continuum shell elements (SC8R) necessary for application of simple support conditions to curved mid-plane• Example discretization of ±90 0|70 1 𝑠,𝑥∅𝑇1 = 70°𝑥′∅𝑥′∅𝑥′𝑇1 = 70°𝑇0 = 0°Objective: Design Problem5• Application• Simply supported square aspect ratio panel 𝒍𝒙 = 𝒍𝒚 = 𝟎. 𝟐𝟓𝒎 under uniaxial compression• Hypothesis• Constraints• Design load• Minimum load-carrying capacity• Tsai-Wu failure criterion• Solution stability assurance• Balanced and symmetric layupsApplied loading as uniform end-shortening Measured reaction forceFiber Steering for Mass-Efficient Thin Plate Structures11th October 2023𝑚𝐶𝑇𝑆 𝑚𝑆𝑇<Method: Elastic Tailoring Potential by Orthotropic Materials6Traditional Angles Angle Ply Thickness-Tailored Angle Ply Fiber-Steered𝑧Tailoring Method Ply Angles 𝜃𝑘 Ply Thickness 𝑡𝑘Traditional Angles 0°, ±45°, 90° 𝑡0Angle Ply 0°, 1°, 2°, … , 90° 𝑡0Thickness-Tailored Angle Ply 0°, 1°, 2°, … , 90° 𝑡0sec(𝜗𝑘)Fiber-Steered 𝑓(𝑥, 𝑦) 𝑡0sec(𝜃𝑘(𝑥, 𝑦))Fiber Steering for Mass-Efficient Thin Plate Structures11th October 2023Method: Nonlinear Performance Evaluation7Linear Buckling StepLinear Static StepNonlinear Riks StepLoad Carrying Capacity EstimationStiffness EvaluationFitness Evaluation𝐹, 𝑢, 𝐼𝐹(𝑥, 𝑦)𝑃𝑐𝑟𝑚, 𝜆𝑢, Φ(𝑥, 𝑦)𝐹3600𝜇𝜀𝑘𝑥𝑝𝑟𝑒, 𝑘𝑥𝑝𝑜𝑠𝑡Structural Stability 𝑛−𝜆Fiber Steering for Mass-Efficient Thin Plate Structures11th October 2023min𝛼𝑚(𝛼) ∙ max 1, ൗ𝐹𝑅𝐹3600𝜇𝜀1∙ max 1,  max 𝐼𝐹 𝑥, 𝑦1∙ max 1,  1 + 𝑛−𝜆1Method: Optimization Process8Random Initial PopulationGA OptimizerOptimum ConfigurationTop 2 from Final GenMass ComparisonTA Tailoring GA OptimizerOptimum ConfigurationTop 2 from Final Gen AP Tailoring GA OptimizerOptimum ConfigurationTop 2 from Final Gen AP-TT Tailoring GA OptimizerOptimum ConfigurationTop 2 from Final Gen CTS Tailoring Fiber Steering for Mass-Efficient Thin Plate Structures11th October 2023Random Initial PopulationRandom Initial PopulationRandom Initial PopulationResults: Key Findings91. Mass efficiency achievable by elastic tailoring with orthotropic materials2. Mass penalty when fiber steering by CTS process is high (up to ~3 ×)3. Fiber steering can result in structural mass efficiency but is not a catch-all design method4. Significant potential for programmable ply thicknesses by CTS processFiber Steering for Mass-Efficient Thin Plate Structures11th October 2023−6%Results: Square Aspect Ratio, 𝑭𝑹 = 𝟎. 𝟓𝒌𝑵/𝒎𝒎10Fiber Steering for Mass-Efficient Thin Plate Structures11th October 2023Optimization Mass 𝐠TA 360AP 360AP-TT 345CTS 339902/012 𝑠902/010/±45 𝑠902/010/±72 𝑠±15 63|35 2/∓7 −37| − 2 2/∓72 −48| − 63 1/∓7 −17| − 21 1/∓28 −26| − 29 2 𝑠• Dataset extreme value identification as 𝐼𝐹 max(𝐹𝑅) , max(𝐹𝑅) and min 𝐼𝐹 , 𝐹𝑅(min 𝐼𝐹 )• Several coincident extreme values due to layered optimization methodology Results: Square Aspect Ratio, 𝑭𝑹 = 𝟎. 𝟓𝒌𝑵/𝒎𝒎11𝐎𝐩𝐭𝐢𝐦𝐢𝐳𝐚𝐭𝐢𝐨𝐧 𝐎𝐩𝐭𝐢𝐦𝐢𝐳𝐞𝐝 𝐋𝐚𝐲𝐮𝐩TA 902/012 𝑠AP 902/012 𝑠AP_TT ±69/±5/±19/±3 𝑠, 𝑡0 sec 44 2/ 𝑡0 sec 70 2/ 𝑡0 sec 10 2/ 𝑡0 sec 44 2 𝑠CTS ±15 63|35 2/∓7 −37| − 2 2/∓72 −48| − 63 1/∓7 −17| − 21 1/∓28 −26| − 29 2 𝑠Fiber Steering for Mass-Efficient Thin Plate Structures11th October 2023Ply 1Ply 3Ply 5Ply 7Ply 11Results: Square Aspect Ratio, 𝑭𝑹 = 𝟎. 𝟓𝒌𝑵/𝒎𝒎12𝐎𝐩𝐭𝐢𝐦𝐢𝐳𝐚𝐭𝐢𝐨𝐧 𝐦 (𝒈) 𝑵𝒑𝒍𝒚𝒔 𝒌𝒙𝒑𝒓𝒆 𝑮𝑵𝒎𝒌𝒙𝒑𝒐𝒔𝒕 𝑮𝑵𝒎𝑷𝒄𝒓(𝒌𝑵) 𝐦𝐚𝐱 𝑰𝑭𝟑𝟔𝟎𝟎𝝁𝜺𝒙, 𝒚 𝑭𝟑𝟔𝟎𝟎𝝁𝜺/𝑭𝑹TA 360 28 0.97 0.26 32.4 0.99 1.13AP 360 28 0.97 0.26 32.4 0.99 1.13AP_TT 345 16 0.83 0.23 33.4 0.96 1.02CTS 339 20 0.72 0.23 36.0 0.89 1.01𝐎𝐩𝐭𝐢𝐦𝐢𝐳𝐚𝐭𝐢𝐨𝐧 𝐎𝐩𝐭𝐢𝐦𝐢𝐳𝐞𝐝 𝐋𝐚𝐲𝐮𝐩TA 902/012 𝑠AP 902/012 𝑠AP_TT ±69/±5/±19/±3 𝑠, 𝑡0 sec 44 2/ 𝑡0 sec 70 2/ 𝑡0 sec 10 2/ 𝑡0 sec 44 2 𝑠CTS ±15 63|35 2/∓7 −37| − 2 2/∓72 −48| − 63 1/∓7 −17| − 21 1/∓28 −26| − 29 2 𝑠Fiber Steering for Mass-Efficient Thin Plate Structures11th October 2023Results: Square Aspect Ratio, 𝑭𝑹 = 𝟎. 𝟓𝒌𝑵/𝒎𝒎13Fiber Steering for Mass-Efficient Thin Plate Structures11th October 2023• Load-displacement history (L) and equilibrium curve (R) of optimized structural configurationsConclusions & Future Work14• Mass efficiency achievable by elastic tailoring with orthotropic materials• Mass penalty when fiber steering by CTS process is high (up to 3x)• Fiber steering can result in structural mass efficiency • Significant potential for programmable ply thicknesses by CTS process• Aspect ratio change• Increased minimum load carrying capacity Fiber Steering for Mass-Efficient Thin Plate Structures11th October 2023Acknowledgements15• This work was supported by the Engineering and Physical Sciences Research Council through the EPSRC Centre for Doctoral Training in Composites Science, Engineering and Manufacturing [grant number EP/S021728/1]• This work was carried out using the computational facilities of the Advanced Computing Research Centre, University of Bristol – http://www.bris.ac.uk/acrc/Fiber Steering for Mass-Efficient Thin Plate Structures11th October 2023Questions?calum.mcinnes@bristol.ac.uk

Fiber Steering for Mass-Efficient Thin Plate Structures

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