Groh, Rainer

Lincoln, Reece L

Pirrera, Alberto

Weaver, Paul M

English

The sensitivity to geometric imperfections limits the performance of thin-walled cylinders in compression buckling. The presentwork focuses on reducing the imperfection sensitivity of cylinders by using a novel manufacturing technique for composite materials knownas Continuous Tow Shearing (CTS). CTS allows curvilinear steering of carbon fibre tows by shearing the carbon fibre tape, a 50 mm-widestrip of carbon fibre, that is placed via a robot arm. Steering of the carbon fibre tapes by shearing induces a smooth increase in the thicknessof the tape and these localised thickness build-ups are used as a symmetry-breaking device to limit the impact of imperfections. The localisedthickness build-ups are used to create embedded-stringers and -hoops that tailor the load path within the CTS cylinder. To maximise theeffectiveness of the CTS cylinders, an optimisation framework that accounts for uncertainty is used. The results of the optimisation arecorroborated with a Monte-Carlo analysis. The first optimisation goal is to maximise the thickness-normalised, mass-normalised bucklingload of a CTS cylinder. The second optimisation goal is to minimise mass of a CTS cylinder under a specific load

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                          Lincoln, R. L., Weaver, P. M., Pirrera, A., & Groh, R. (2021).Optimisation of continuous tow-sheared cylinders under uncertainty.Peer reviewed versionLink 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/  XXV ICTAM, 23-28 August 2020, Milano, ItalyOPTIMISATION OF CONTINUOUS TOW-SHEARED CYLINDERS UNDER UNCERTAINTY   Reece Lincoln*1, Paul Weaver1, 2, Alberto Pirrera1, and Rainer Groh1 1Bristol Composites Institute (ACCIS), Department of Aerospace Engineering, University of Bristol, Bristol, BS8 1TR, UK 2 Bernal Institute, School of Engineering, University of Limerick, Castletroy, V94 T9PX, Ireland  Summary The sensitivity to geometric imperfections limits the performance of thin-walled cylinders in compression buckling. The present work focuses on reducing the imperfection sensitivity of cylinders by using a novel manufacturing technique for composite materials known as Continuous Tow Shearing (CTS). CTS allows curvilinear steering of carbon fibre tows by shearing the carbon fibre tape, a 50 mm-wide strip of carbon fibre, that is placed via a robot arm. Steering of the carbon fibre tapes by shearing induces a smooth increase in the thickness of the tape and these localised thickness build-ups are used as a symmetry-breaking device to limit the impact of imperfections. The localised thickness build-ups are used to create embedded-stringers and -hoops that tailor the load path within the CTS cylinder. To maximise the effectiveness of the CTS cylinders, an optimisation framework that accounts for uncertainty is used. The results of the optimisation are corroborated with a Monte-Carlo analysis. The first optimisation goal is to maximise the thickness-normalised, mass-normalised buckling load of a CTS cylinder. The second optimisation goal is to minimise mass of a CTS cylinder under a specific load.  INTRODUCTION     The fuel and oxidizer cylindrical tanks of heavy launch vehicles are a large percentage of their total dry mass (60–70%). Using composite materials instead of current generation Li-Al fuel tanks is estimated to save up to 30% in mass and 25% in recurring manufacturing costs [1]. Several research programs have aimed to use composite materials to capitalise on these savings [2, 3] but have used blade-stiffened shells or foam/honeycomb sandwich structures. Few programmes have considered novel monocoque shell architectures due in part to their well-documented geometric imperfection sensitivity when loaded in compression—the design load case of heavy launch vehicles. Typically, the imperfection sensitivity is captured in the design phase using knockdown factors (KDFs), that are applied to the theoretical critical buckling load derived from a linear eigenvalue analysis. The classical KDFs of the NASA SP-8007 [4] guideline are still industry-standard but have been acknowledged to be too conservative for modern materials and manufacturing tolerances. Contemporary knockdown factors have been created that are less conservative [2, 5], but still show the imperfection sensitivity of cylindrical shells.    This paper looks at designing monocoque cylinders that are imperfection insensitive by tailoring load paths by using a novel variable-angle composite manufacturing technique, Continuous Tow Shearing (CTS) [6]. Preliminary work has found that CTS cylinders are less imperfection sensitive than straight-fibre cylinders [7, 8, 9]. It has also been shown that the imperfection sensitivity of composite cylinders can be decreased with Automated Fibre Placement (AFP) [10]. However, CTS has several benefits over AFP as a result of shearing the tows instead of bending the tows, e.g., no in-plane bending; no fibre buckling or wrinkling; perfect tessellation of tows; smaller steering radii. In addition to these benefits, the shearing process couples the fibre angle change to the local thickness of the tow, enabling the formation of embedded stringers and hoops perpendicular to the fibre steering direction. Fibre paths are described using the notation 𝜙⟨𝑇 |𝑇 ⟩ , where 𝜙 is the clockwise angle from the global x-axis that defines the refence axis for shearing; 𝑇  is the initial angle of shearing relative to 𝜙; 𝑇  is shearing angle in the middle of the ‘period’ relative to 𝜙; and 𝑛 is the periodicity—the frequency of a 𝑇 → 𝑇 → 𝑇  cycle. For the sake of illustration, Figure 1 shows how a  0⟨20|70⟩  layer and a 90⟨0|30⟩  layer is defined.    *Corresponding author. E-mail: reece.lincoln@bristol.ac.uk. Figure 1 CTS lamina sheared where left is 0⟨20|70⟩  and right figure is a 90⟨0|30⟩  lamina.   XXV ICTAM, 23-28 August 2020, Milano, ItalyFUTURE WORK     Two optimisations and a Monte-Carlo analysis will be carried out. The first optimisation will be to maximise the thickness-normalised and mass-normalised buckling load of a CTS cylinder. A by-product of the CTS process (where the local thickness of the tow is increased due to the shearing process) is that the average thickness of a CTS cylinder with shearing is greater than a straight-fibre cylinder. As the buckling load of a cylinder is proportional to 𝑡  and the mass of a cylinder proportional to 𝑡, the mass-normalised specific buckling load of a cylinder is proportional to 𝑡. Therefore, to ensure a fair comparison between CTS cylinders and straight-fibre cylinders, a thickness-normalised, mass-normalised buckling load is appropriate if the maximum load carrying capability of a structure is essential. The optimisation will use a reliability-based definition of buckling load. A forward-difference First-Order Second-Moment (FOSM) analysis will be used to calculate a conservative estimate of the buckling load. A realistic data bank of imperfections [11] will be spectrally decomposed into a five principal components that describe the data set. From the principal components, six FEA analyses of the CTS cylinder with different imperfections can approximate a distribution of buckling loads. A buckling load approximately equal to the mean buckling load minus three standard deviations will constitute 𝑃 , the buckling load calculated from the FOSM methodology. A Genetic Algorithm (GA) will be the framework in which the FOSM methodology is used to optimise towards maximising the thickness-normalised, mass-normalised 𝑃 . To test the robustness of the final result and the assumed distribution, a Monte-Carlo analysis of the converged value will be performed to ensure the assumptions are valid and the result is statistically significant.    As a secondary optimisation, the mass of a CTS cylinder will be optimised. The target function will be to minimise the mass of a CTS cylinder given certain loading criteria. A GA will be used as the optimisation framework. The buckling load will be calculated from the FOSM methodology previously described.   References [1] D. A. McCarville, J. C. Guzman, A. K. Dillon, J. R. Jackson, and J. O. Birkland, “Design, manufacture and test of cryotank components,” Compr. Compos. Mater. II, vol. 3, pp. 153–179, 2018. [2] M. W. Hilburger, “On the development of shell buckling knockdown factors for stiffened metallic launch vehicle cylinders,” in AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2018, pp. 1–17. [3] National Aeronautics and Space Administration, “Composite Cryotank Technologies and Demonstration,” 2013. [4] National Aeronautics and Space Administration, “Space Vehicle Design: Buckling Thin-Walled Circular (SP-8007),” 1968. [5]  R. M. Groh, A. Pirrera, “On the role of localizations in buckling of axially compressed cylinders”, Proc. Math. Phys. Eng. Sci. 475 (2224). [6] B. C. Kim, K. Potter, and P. M. Weaver, “Continuous tow shearing for manufacturing variable angle tow composites,” Compos. Part A Appl. Sci. Manuf., vol. 43, no. 8, pp. 1347–1356, 2012. [7] R. L. Lincoln, P. M. Weaver, A. Pirrera, and R. M. J. Groh, “Imperfection-Insensitive Continuous Tow-Sheared Cylinders,” Compos. Struct., vol. 260, no. March, p. 113445, 2021. [8] R. Lincoln, P. Weaver, A. Pirrera, and R. M. Groh, “Optimisation of Imperfection-Insensitive Continuous Tow Sheared Rocket Launch Structures,” AIAA SciTech 2021 Forum, no. January, pp. 1–19, 2021. [9] S. C. White and P. M. Weaver, “Towards imperfection insensitive buckling response of shell structures-shells with plate-like post-buckled responses,” Aeronaut. J., vol. 120, no. 1224, pp. 233–253, Feb. 2016. [10] K. C. Wu, B. Farrokh, B. Stanford, and P. Weaver, “Imperfection Insensitivity Analyses of Advanced Composite Tow-Steered Shells,” in 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2016, no. January, pp. 1–16. [11] H. N. R. Wagner, C. Hühne, and I. Elishakoff, “Probabilistic and deterministic lower-bound design benchmarks for cylindrical shells under axial compression,” Thin-Walled Struct., vol. 146, no. January, p. 106451, Jan. 2020.  

Optimisation of continuous tow-sheared cylinders under uncertainty

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Optimisation of continuous tow-sheared cylinders under uncertainty

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