Abstract
This paper contributes an analytical nonlinear morphing model for high-amplitude corrugated thinwalled laminates of arbitrary stack-up with a corrugation shape composed of circular sections. The model describes large deformations, the nonlinear relation between line force and global stretch, and the distribution of local line loads. The quarter-unit-cell approach together with assuming small material strains and a plane strain situation contribute to the model’s simplicity. It is explained how the solution procedure minimizes the force and moment residual of the equilibrium of cutting and reaction line loads by using Newton’s optimization method. Deformation results are verified by comparison with FEM simulation. The effects of laminate design and corrugation amplitude on deformations, line-force-stretch diagrams, and bending-curvature-stretch diagrams are presented and discussed.
References
[1] Mornement, A., and Holloway S., Corrugated Iron - Builing on the Frontier, Francis Lincoln Limited, London, UK, 2007.Search in Google Scholar
[2] H. Junkers, Flying-machine supporting surface, US Patent No. 14627, 1923.Search in Google Scholar
[3] H. Junkers, Corrugated sheet metal, US Patent No. 1517633, 1924.Search in Google Scholar
[4] H. Junkers, Flying-machine covering, US Patent No. 1553695, 1925.Search in Google Scholar
[5] H. Junkers, Corrugated sheet-metal shape, US Patent No. 1704326, 1929.Search in Google Scholar
[6] M.I. Friswell, Morphing aircraft: An improbable dream? in: Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems SMASIS2014, Newport, Rhode Island, USA, 2014.10.1115/SMASIS2014-7754Search in Google Scholar
[7] Thill, C., J.A. Etches, I.P. Bond, K.D. Potter, and P.M. Weaver, Corrugated composite structures for aircraft morphing skin applications, in: (Ed.), 18th Int. Conf. of Adaptive Structures and Technologies, Vol. 134, Ottawa, Ontario, Canada, 2007, pp. 507–14.Search in Google Scholar
[8] Barbarino, S.,O. Bilgen, R.M. Ajaj, M.I. Friswell, D.J. Inman, A Review of Morphing Aircraft, J. IntellMater Syst Struct 22 (9) (2011) 823–77.10.1177/1045389X11414084Search in Google Scholar
[9] Dayyani, I., A.D. Shaw, E. Saavedra Flores, M.I. Friswell, The Mechanics of Composite Corrugated Structures: A Review with Applications in Morphing Aircraft, Composite Structures 133 (2015) 358–80.10.1016/j.compstruct.2015.07.099Search in Google Scholar
[10] Airoldi, A., G. Sala, L.A. Di Landro, P. Bettini, A. Gilardelli, Composite Corrugated Laminates for Morphing Applications, in: Antonio Concilio, Ignazio Dimino, Leonardo Lecce, Rosario Pecora (Ed.), Morphing Wing Technologies, Butterworth and Heinemann, Oxford, 2018, Ch. 9, pp. 247–276.10.1016/B978-0-08-100964-2.00009-5Search in Google Scholar
[11] Gandhi, F., Anusonthi, P., Skin design studies for variable camber morphing airfoils, SmartMaterials and Structures 17 (2008) 1–8.10.1088/0964-1726/17/01/015025Search in Google Scholar
[12] Yokozeki T., S.-I. Takeda, T. Ogasawara, T. Ishikawa, Mechanical properties of corrugated composites for candidate materials of flexible wing structures, Composites: Part A 37 (2006) 1578?1586.10.1016/j.compositesa.2005.10.015Search in Google Scholar
[13] Shaw, A.D., I. Dayyani, M.I. Friswell, Optimisation of Composite Corrugated Skins for Buckling in Morphing Aircraft, Composite Structures 119 (2015) 227–237.10.1016/j.compstruct.2014.09.001Search in Google Scholar
[14] Takahashi, H., T. Yokozeki and Y. Hirano, Development of Variable Camber Wing with Morphing Leading and Trailing Sections Using Corrugated Structures, Journal of Intelligent Material Systems 27 (20) (2016) 2827–2836.10.1177/1045389X16642298Search in Google Scholar
[15] Previtali, F., G. Molinari, A. F. Arrieta, M. Guillaume and P. Ermanni, Design and Experimental Characterization of a Morphing Wing with Enhanced Corrugated Skin, Journal of Intelligent Material Systems 27 (2) (2016) 278–292.10.1177/1045389X15595296Search in Google Scholar
[16] Zheng, Y., Z. Qiu, Analysis of the Critical Buckling Loads of Composite Corrugated Plates Under Nonlinearly Distributed Compressive Loads Accounting for Flexural Twist Coupling, Acta Mechanica 227 (2016) 3407–3428.10.1007/s00707-016-1668-4Search in Google Scholar
[17] Kress, G., C. Thurnherr, Bending Stiffness of Transversal Isotropic Materials, Composite Structures 176 (2017) 692–701.10.1016/j.compstruct.2017.05.065Search in Google Scholar
[18] Bai, J.B., D. Chen, J.J. Xiong, R.A. Shenoi, A Corrugated Flexible Composite Skin for Morphing Applications, Composites Part B 131 (2017) 134–143.10.1016/j.compositesb.2017.07.056Search in Google Scholar
[19] Briassoulis, D., Equivalent Orthotropic Properties of Corrugated Sheets, Computers and Structures 23 (2) (1986) 129–138.10.1016/0045-7949(86)90207-5Search in Google Scholar
[20] Kress, G., M. Winkler, Corrugated Laminate Homogenization Model, Composite Structures 92 (3) (2010) 795–810.10.1016/j.compstruct.2009.08.027Search in Google Scholar
[21] Kress, G., M. Winkler, Corrugated Laminate Analysis: A Generalized Plane-Strain Problem, Composite Structures 93 (2011) 1493–1504.10.1016/j.compstruct.2010.12.004Search in Google Scholar
[22] Xia, Y., M.I. Friswell, Equivalent Models of Corrugated Laminates for Morphing Skins, Active Passive Smart Struct Integr Syst 7977 (797711-79711-0).Search in Google Scholar
[23] Xia, Y., Flores, E.I.S., M.I. Friswell, Equivalent Models of Corrugated Panels, Int J Solids Struct 49 (13) (2012) 1453–62.10.1016/j.ijsolstr.2012.02.023Search in Google Scholar
[24] Park, K.-J., K. Jung, Y.-W. Kim, Evaluation of Homogenized Effective Properties for Corrugated Composite Panels, Composite Structures 140 (2016) 644–654.10.1016/j.compstruct.2016.01.002Search in Google Scholar
[25] Nguyen-Minh, N., N. Tran-Van, T. Bui-Xuan, T. Nguyen-Thoi, Static Analysis of Corrugated Panels Using Homogenization Models and a Cell-Based Smoothed Mindlin Plate Element (CSMIN3), Frontiers of Structural Civil Engineering https://doi.org/10.1007/s11709-017-0456-0.10.1007/s11709-017-0456-0Search in Google Scholar
[26] Nguyen-Minh, N., N. Tran-Van, T. Bui-Xuan, T. Nguyen-Thoi, Free Vibration Analysis of Corrugated Panels Using Homogenization Methods and a Cell-Based Smoothed Mindlin Plate Element (CSMIN3), Thin-Walled Structures 124 (2018) 184–201.10.1016/j.tws.2017.12.003Search in Google Scholar
[27] Thurnherr, C., L. Ruppen, G. Kress, P. Ermanni, Interlaminar Stresses in Corrigated Laminates, Composite Structures 140 (2016) 296–308.10.1016/j.compstruct.2015.11.038Search in Google Scholar
[28] Winkler, M., G. Kress, Deformations limits for Corrugated Cross-Ply Laminates, Composite Structures 92 (6) (2010) 1458–68.10.1016/j.compstruct.2009.11.015Search in Google Scholar
[29] A. Schmitz, P. Horst, Bending deformation limits of corrugated unidirectionally reinforced laminates, Composite Structures 107 (2014) 103–111.10.1016/j.compstruct.2013.07.048Search in Google Scholar
[30] Thurnherr, C.N., L. Ruppen, G. Kress, P. Ermanni, Non-linear Striffness Response of Corrugated Laminates in Tensile Loading, Composites structures 157 (2016) 244–255.10.1016/j.compstruct.2016.08.038Search in Google Scholar
[31] Ren, H., W.D. Zhu, W. Fan, A nonlinear planar beam formulation with stretch and shear deformations under end forces and moments, International Journal of Non-Linear Mechanics 85 (2016) 126–142.10.1016/j.ijnonlinmec.2016.05.008Search in Google Scholar
[32] Kress, G.R., Winkler, M., Honeycomb Sandwich Residual Stress Deformation Pattern, Composite Structures 89 (2009) 294–302.10.1016/j.compstruct.2008.08.009Search in Google Scholar
[33] Jones, R.M., Mechanics of Composite Materials, Hemisphere Publishing Corporation, New York, 1975.Search in Google Scholar
[34] ANSYS® Academic Research, Release 18.2.Search in Google Scholar
[35] C. Thill, J.D. Downsborough, S.J. Lai, I.P. Bond, D.P. Jones, Aerodynamic study of corrugated skins for morphing wing applications, Awronautical Journal 3407 (2010) 237–244.10.1017/S0001924000003687Search in Google Scholar
© 2019 G.R. Kress et al., published by De Gruyter
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