Abstract
This manuscript proposes an iterative scheme for geometrically large deflection analysis of corrugated structures using the nonlinear shooting method. The corrugated structure is modeled by discretizing it in several corrugated units. The solution of each unit is obtained assuming it to be consistering of several beam elements. Finally, the deflection of a corrugated structure is calculated assembling the deflection of each of the corrugated units. The formulation has been extended to various boundary conditions (fixed–fixed and fixed–hinged) and loading conditions (point loads and uniformly distributed load). This shows the versatility of the methods in solving various problems. Furthermore, two prototypes of the corrugated structure are fabricated using aluminum and carbon fiber reinforced polymer (CFRP) laminate, and a moment actuation test is performed. The deflections of these prototypes obtained using the proposed iterative scheme are compared with the numerical model and validated with experiments, and results are found to be in good agreement.
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References
Dayyani, I., Shaw, A.D., Flores, E.I.S., Friswell, M.I.: The mechanics of composite corrugated structures: a review with applications in morphing aircraft. Compos. Struct. 133, 358–380 (2015)
Yokozeki, T., Sugiura, A., Hirano, Y.: Development of variable camber morphing airfoil using corrugated structure. J. Aircr. 51, 1–7 (2014)
Liang, C.-C., Yang, M.-F., Wu, P.-W.: Optimum design of metallic corrugated core sandwich panels subjected to blast loads. Ocean Eng. 28, 825–861 (2001)
Queheillalt, D.T., Murty, Y., Wadley, H.N.G.: Mechanical properties of an extruded pyramidal lattice truss sandwich structure. Scr. Mater. 58, 76–79 (2008)
Bowen, C.R., Butler, R., Jervis, R., Kim, H.A., Salo, A.I.T.: Morphing and shape control using unsymmetrical composites. J. Intell. Mater. Syst. Struct. 18, 89–98 (2007)
Phani, A.S., Richard, B., Stephen, H., Bowen, C.R.: Analysis of wing morphing via frame buckling,In: 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials, Schaumburg, IL (2008)
Fusi, F., Congedo, P.M., Guardone, A., Quaranta, G.: Shape optimization under uncertainty of morphing airfoils. Acta Mech. 229, 1229–1250 (2018)
Kumar, D., Ali, S.F., Arockiarajan, A.: Structural and aerodynamics studies on various wing configurations for morphing. IFAC-PapersOnLine 51, 498–503 (2018)
Mukherjee, A., Kumar, D., Ali, S.F., Arockiarajan, A.: Design and conception of a trailing edge morphing wing concept with bistable composite skin. Act. Passiv. Smart Struct. Integr. Syst. XIV, Int. Soc. Opt. Photonics 11376, 497–506 (2020)
Dhileep, K., Kumar, D., Ghosh, S., Ali, S. F., Arockiarajan, A.: Numerical Study of Camber Morphing in NACA0012 Airfoil, In: AIAA AVIATION 2020 FORUM, 2781, June 15-19, 2020, VIRTUAL EVENT (2020)
Yokozeki, T., Takeda, S.-I., Ogasawara, T., Ishikawa, T.: Mechanical properties of corrugated composites for candidate materials of flexible wing structures. Comp. Part A: Appl. Sci. Manuf. 37, 1578–1586 (2006)
Xia, Y., Friswell, M.I., Flores, E.I.S.: Equivalent models of corrugated panels. Int. J. Solids Struct. 49, 1453–1462 (2012)
Mohammadi, H., Ziaei-Rad, S., Dayyani, I.: An equivalent model for trapezoidal corrugated cores based on homogenization method. Comp. Struct. 131, 160–170 (2015)
Wang, C., Khodaparast, H.H., Friswell, M.I., Shaw, A.D.: An equivalent model of corrugated panels with axial and bending coupling. Comput. Struct. 183, 61–72 (2017)
Samanta, A., Mukhopadhyay, M.: Finite element static and dynamic analyses of folded plates. Eng. Struct. 21, 277–287 (1999)
Thill, C., Etches, J.A., Bond, I.P., Potter, K.D., Weaver, P.M., Wisnom, M.R.: Investigation of trapezoidal corrugated aramid/epoxy laminates under large tensile displacements transverse to the corrugation direction. Comp. Part A: Appl. Sci. Manuf. 41, 168–176 (2010)
Dayyani, I., Ziaei-Rad, S., Salehi, H.: Numerical and experimental investigations on mechanical behavior of composite corrugated core. Appl. Comp. Mater. 19, 705–721 (2012)
Liew, K.M., Peng, L.X., Kitipornchai, S.: Nonlinear analysis of corrugated plates using a FSDT and a meshfree method. Comput. Methods Appl. Mech. Eng. 196, 2358–2376 (2007)
Talebi, H., Zakerzadeh, M.R., Salehi, H., Golestanian, H.: Nonlinear analysis of a corrugate composite panel actuated by shape memory alloy wire, In: 22nd Annual International Conference on Mechanical Engineering, ISME2014-2185, Ahvaz, Iran (2014)
Wang, N., Liang, X., Zhang, X.: Pseudo-rigid-body model for corrugated cantilever beam used in compliant mechanisms. Chinese J. Mech. Eng. 27, 122–129 (2014)
Zheng, Y., Qiu, Z.: Analysis of the critical buckling loads of composite corrugated plates under nonlinearly distributed compressive loads accounting for flexural-twist coupling. Acta Mech. 227, 3407–3428 (2016)
Thurnherr, C., Ruppen, L., Kress, G., Ermanni, P.: Non-linear stiffness response of corrugated laminates in tensile loading. Comp. Struct. 157, 244–255 (2016)
Thurnherr, C., Ruppen, L., Brändli, S., Franceschi, C.M., Kress, G., Ermanni, P.: Stiffness analysis of corrugated laminates under large deformation. Comp. Struct. 160, 457–467 (2017)
Karakoti, A., Kar, V.R.: Deformation characteristics of sinusoidally-corrugated laminated composite panel- A higher-order finite element approach. Comp. Struct. 216, 151–158 (2019)
Tsushima, N., Yokozeki, T., Su, W., Arizono, H.: Geometrically nonlinear static aeroelastic analysis of composite morphing wing with corrugated structures. Aerosp. Sci. Technol. 88, 244–257 (2019)
Kress, G.R., Filipovic, D.T.: An analytical nonlinear morphing model for corrugated laminates. Curved Layer. Struct. 6, 57–67 (2019)
Filipovic, D., Kress, G.R.: Manufacturing method for high-amplitude corrugated thin-walled laminates. Comp. Struct. 222, 110925 (2019)
Wang, C., Xia, Y., Friswell, M.I., Flores, E.I.S.: Predicting global strain limits for corrugated panels. Comp. Struct. 231, 111472 (2020)
Howell, L.L.: Compliant Mechanisms, Composite Structures. Wiley, New York, NY (2001)
Bona, F.D., Zelenika, S.: A generalized elastica-type approach to the analysis of large displacements of spring-strips. J. Mech. Eng. Sci. 211, 509–517 (1997)
Mukherjee, A., Ali, S.F., Arockiarajan, A.: Compliant structure under follower forces and any combined loading: Theoretical and experimental studies. Int. J. Mech. Sci. 153–154, 75–82 (2019)
Howell, L.L., Midha, A.: Parametric deflection approximations for end-loaded, large-deflection beams in compliant mechanisms. J. Mech. Des. 117, 156–165 (1995)
González, C., Llorca, J.: Stiffness of a curved beam subjected to axial load and large displacements. Int. J. Solids Struct. 42, 1537–1545 (2005)
Stanoyevitch, A.: Introduction to Numerical Ordinary and Partial Differential Equations using MATLAB, vol. 72. Wiley, New Jersey (2011)
Banerjee, A., Bhattacharya, B., Mallik, A.K.: Large deflection of cantilever beams with geometric non-linearity: Analytical and numerical approaches. Int. J. Non-linear Mech. 43, 366–376 (2008)
ASTM D3039 / D3039M-17: Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials, ASTM International, PA, 15.03, pp. 1-13 (2017)
ASTM D3518 / D3518M-18: Standard Test Method for In-Plane Shear Response of Polymer Matrix Composite Materials by Tensile Test of a \(\pm 45^{\circ }\) Laminate, ASTM International, PA, 15.03, pp. 1-13 (2018)
Ge, R., Wang, B., Mou, C., Zhou, Y.: Deformation characteristics of corrugated composites for morphing wings. J. Mech. Des. 117, 156–165 (1995)
ASTM D3171-15: Standard Test Method for Constituent Content of Composite Materials, ASTM International, PA, 15.03, 1-11 (2015)
Simulia and S, Dassault: ABAQUS 6.13 Documentation, Dassault Systemes (2013)
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The authors hereby acknowledge the funding obtained from DRDO (DRDO/DFTM/04/3304/PC/02/776/D (R&D)) through CoPT and ARDB (ARDB/01/1051810/M/I) projects.
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Kumar, D., Ali, S.F. & Arockiarajan, A. Studies on large deflection of geometrically nonlinear corrugated structures. Acta Mech 232, 461–482 (2021). https://doi.org/10.1007/s00707-020-02861-x
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DOI: https://doi.org/10.1007/s00707-020-02861-x