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BY 4.0 license Open Access Published by De Gruyter Open Access September 18, 2020

Free-edge effects of corrugated laminates

  • Daniel T. Filipovic EMAIL logo and Gerald R. Kress

Abstract

Due to their high numerical efficiency, homogenization models are often employed in the analysis of corrugated laminates. They are usually derived assuming periodic behavior in the corrugated direction and generalized plane strain in the out-of-plane direction, which corresponds to the assumption of infinite dimensions of the structure. As a consequence, any influences of edge effects are not mapped, although they can have a significant impact on the mechanical behavior of a given structure. The objective of this manuscript is to investigate the influence of boundary conditions - a combination of free-edges and clamping - on the structural stiffness of corrugated laminates. A total of six load cases are investigated which correspond to the line loads considered in the classical theory of laminated plates. The results of this parameter study allow the identification of several critical loading situations, where free edges can significantly alter structural stiffness. The given investigations hence contribute to the investigation of the validity range of homogenization models.

References

[1] Junkers H., Flying-machine supporting surface, 1923, US Patent No.14627.Search in Google Scholar

[2] Junkers H., Corrugated sheet metal, 1924, US Patent No. 1517633.Search in Google Scholar

[3] Junkers H., Flying-machine covering, 1925, US Patent No. 1553695.Search in Google Scholar

[4] Junkers H., Corrugated sheet-metal shape, 1929, US Patent No. 704326.Search in Google Scholar

[5] Mornement A., Holloway, S., Corrugated Iron - Builing on the Frontier, 2007, Francis Lincoln Limited, London, UK.Search in Google Scholar

[6] Thurnherr C., Ruppen L., Kress G., Ermanni, P., Interlaminar Stresses in Corrugated Laminates, Compos. Struct., 2016, 140, 296-308.10.1016/j.compstruct.2015.11.038Search in Google Scholar

[7] Thurnherr C.N., Ruppen L., Kress G., Ermanni P., Non-linear Stiffness Response of Corrugated Laminates in Tensile Loading, Compos. Struct., 2016, 157, 244-255.10.1016/j.compstruct.2016.08.038Search in Google Scholar

[8] Thurnherr C.N., Ruppen L., Brändli S., Franceschi C., Kress G., Ermanni P., Stiffness Analysis of Corrugated Laminates under Large Deformation, Compos. Struct., 2017, 160, 457-467.10.1016/j.compstruct.2016.10.079Search in Google Scholar

[9] Bai J. B., Chen D., Xiong J.J., Dong C.H., A semi-analytical model for predicting nonlinear tensile behaviour of corrugated flexible composite skin, Compos. Part B: Eng., 2019, 168, 312-319.10.1016/j.compositesb.2019.01.053Search in Google Scholar

[10] Kress G.R., Filipovic D.T., An analytical nonlinear morphing model for corrugated laminates, Curved and Layer. Struct., 2019, 6, 57-67.10.1515/cls-2019-0005Search in Google Scholar

[11] Soltani Z., Kordkheili S.A., Kress G., Experimental and numerical study of geometrically nonlinear behavior of corrugated laminated composite shells using a nonlinear layer-wise shell fe formulation, Eng. Struct. 184, 2019, 61-73.10.1016/j.engstruct.2019.01.077Search in Google Scholar

[12] Thurnherr C.N., Pedergnana T., Kress G, Ermanni P., Non-Classical Vibration Behavior of Highly Anisotropic Corrugated Laminates, Compos. Struct. 168, 2017, 84-91.10.1016/j.compstruct.2017.02.001Search in Google Scholar

[13] Malikan M., Dimitri R., Tornabene F., Effect of sinusoidal corrugated geometries on the vibrational response of viscoelastic nanoplates, Appl. Sci., 2018, 8(9), 1432.10.3390/app8091432Search in Google Scholar

[14] Nguyen-Minh N., Tran-Van N., Bui-Xuan T., Nguyen-Thoi T., Free Vibration Analysis of Corrugated Panels Using Homogenization Methods and a Cell-Based Smoothed Mindlin Plate Element, CSMIN3), Thin. Wall. Struct., 2018, 124, 184-201.10.1016/j.tws.2017.12.003Search in Google Scholar

[15] Filipovic D.T., Kress G.R., A planar finite-element formulation for corrugated laminates under transverse shear load, Compos. Struct., 2018, 201, 958-967.10.1016/j.compstruct.2018.06.048Search in Google Scholar

[16] Filipovic D., Kress G., Manufacturing method for high-amplitude corrugated thin-walled laminates, Compos. Struct., 2019, 222, 110925.10.1016/j.compstruct.2019.110925Search in Google Scholar

[17] Dayyani I., Shaw A.D., Saavedra Flores E., Friswell M. I., The mechanics of composite corrugated structures: a review with applications in morphing aircraft, Compos. Struct. 2015, 133, 358-380.10.1016/j.compstruct.2015.07.099Search in Google Scholar

[18] Friswell M.I., Morphing aircraft: An improbable dream?, in: Proc. ASME Conf. Smart Mater., Adaptive Structures and Intelligent Systems SMASIS2014, Newport, Rhode Island, USA, 2014, V001T08A001.Search in Google Scholar

[19] Ajaj R.M., Beaverstock C.S., Friswell M.I., Morphing aircraft: The need for a new design philosophy, Aerosp. Sci. Technol., 2016, 49, 154-166.10.1016/j.ast.2015.11.039Search in Google Scholar

[20] Li D., Zhao S., Da Ronch A., Xiang J., Drofelnik J., Li Y., Zhang L., Wu Y., Kintscher M., Monner H.P., Rudenko A., Guo S., YinW., Kirn J., Storm S., De Breuker R., A review of modelling and analysis of morphing wings, Prog. Aerosp. Sci., 2018, 100, 46-62.10.1016/j.paerosci.2018.06.002Search in Google Scholar

[21] Thill C., Etches J., Bond I., Potter K., Morphing skins, Aeronaut. J., 2008, 112(1129), 117-139.10.1017/S0001924000002062Search in Google Scholar

[22] Thill C., Etches J.A., Bond I.P., Potter K.D., Weaver P.M., Corrugated composite structures for aircraft morphing skin applications, in:, Ed. 18th Int. Conf. of Adaptive Structures and Technologies, Ottawa, Ontario, Canada, 2007, 134, 507-514.Search in Google Scholar

[23] Gandhi F., Anusonthi P., Skin design studies for variable camber morphing airfoils, Smart. Mater. Struct., 2008, 17, 1-8.10.1088/0964-1726/17/01/015025Search in Google Scholar

[24] Airoldi A., Sala G., Di Landro L.A., Bettini P., Gilardelli A., Composite Corrugated Laminates for Morphing Applications, in: Antonio Concilio, Ignazio Dimino, Leonardo Lecce, Rosario Pecora, Ed., Morphing Wing Technologies, Butterworth and Heinemann, Oxford, 2018, 9, 247-276.10.1016/B978-0-08-100964-2.00009-5Search in Google Scholar

[25] Previtali F., Molinari G., Arrieta A.F., Guillaume M., Ermanni P., Design and Experimental Characterization of a Morphing Wing with Enhanced Corrugated Skin, J. Intell. Mat. Syst. Str., 2016, 27(2), 278-292.10.1177/1045389X15595296Search in Google Scholar

[26] Takahashi H., Yokozeki T., Hirano Y., Development of Variable Camber Wing with Morphing Leading and Trailing Sections Using Corrugated Structures, J. Intell. Mat. Syst. Str., 2016, 27(20), 2827-2836.10.1177/1045389X16642298Search in Google Scholar

[27] Bai J.B., Chen D., Xiong J.J., Shenoi R.A., A Corrugated Flexible Composite Skin for Morphing Applications, Compos. Part B: Eng., 2017, 131, 134-143.10.1016/j.compositesb.2017.07.056Search in Google Scholar

[28] Henry A.C., Molinari G., Rives-Padilla J.R., Arrieta A.F., Smart morphing wing: Optimization of distributed piezoelectric actuation, AIAA J., 2019, 254.10.2514/1.J057254Search in Google Scholar

[29] Gong X., Liu L., Scarpa F., Leng J., Liu Y., Variable stiffness corrugated composite structure with shape memory polymer for morphing skin applications, Smart Mater. Struct., 2017, 26, 035052.10.1088/1361-665X/aa516dSearch in Google Scholar

[30] Thurnherr C., Mirabito Y., Kress G., Ermanni P., Highly Anisotropic Corrugated Laminates Deflection under Uniform Pressure, Compos. Struct., 2016, 154, 31-38.10.1016/j.compstruct.2016.07.017Search in Google Scholar

[31] Ermakova A., Dayyani I., Shape optimisation of composite corrugated morphing skins, Compos. Part B: Eng., 2017, 115, 87-101.10.1016/j.compositesb.2016.10.029Search in Google Scholar

[32] Shaw A.D., Dayyani I., Friswell M.I., Optimisation of Composite Corrugated Skins for Buckling in Morphing Aircraft, Compos. Struct., 2015, 119, 227-237.10.1016/j.compstruct.2014.09.001Search in Google Scholar

[33] Thill C., Downsborough J.D., Lai S.J., Bond I.P., Jones D.P., Aerodynamic study of corrugated skins for morphing wing applications, Aeronaut. J., 2010, 3407, 237-244.10.1017/S0001924000003687Search in Google Scholar

[34] Xia Y., Bilgen O., Friswell M.I., The effect of corrugated skins on aerodynamic performance, J. Intell. Mat. Syst. Str. 2012, 25(7), 786-794.10.1177/1045389X14521874Search in Google Scholar

[35] Dayyani I., Ziaei-Rad S., Friswell M.I., The mechanical behavior of composite corrugated core coated with elastomer for morphing skins, J. Compos. Mater., 2014, 48(13), 1623-1636.10.1177/0021998313488807Search in Google Scholar

[36] Dayyani I., Friswell M.I., Multi-objective optimization for the geometry of trapezoidal corrugated morphing skins, Struct. Multi-discip. O. 2017, 55(1), 331-345.10.1007/s00158-016-1476-4Search in Google Scholar

[37] Ren Y., Jiang H., Ji W., Zhang H., Xiang J., Yuan F.-G., Improvement of progressive damage model to predicting crashworthy composite corrugated plate, Appl. Compos. Mater., 2018, 25(1), 45-66.10.1007/s10443-017-9610-zSearch in Google Scholar

[38] Ren Y., Jiang H., Gao B., Xiang J., A progressive intraply material deterioration and delamination based failure model for the crashworthiness of fabric composite corrugated beam: Parameter sensitivity analysis, Compos. Part B: Eng., 2018, 135, 49-71.10.1016/j.compositesb.2017.09.072Search in Google Scholar

[39] Ren Y., Zhang H., Xiang J., A novel aircraft energy absorption strut system with corrugated composite plate to improve crashworthiness, Int. J. Crashworthines, 2018, 23(1), 1-10.10.1080/13588265.2017.1301082Search in Google Scholar

[40] Buannic N., Cartraud P., Quesnel T., Homogenization of corrugated core sandwich panels, Compos. Struct., 2003, 59, 299-312.10.1016/S0263-8223(02)00246-5Search in Google Scholar

[41] Aboura Z., Talbi N., Allaoui S., Benzeggagh M.L., Elastic behavior of corrugated cardboard: experiments and modeling, Compos. Struct., 2004, 63(1), 53-62.10.1016/S0263-8223(03)00131-4Search in Google Scholar

[42] Biancolini M.E., Evaluation of equivalent stiffness properties of corrugated board, Compos. Struct., 2005, 69(3), 322-328.10.1016/j.compstruct.2004.07.014Search in Google Scholar

[43] Talbi N., Batti A., Ayad R., Guo Y.Q., An analytical homogenization model for finite element modelling of corrugated cardboard, Compos. Struct., 2009, 88(2), 280-289.10.1016/j.compstruct.2008.04.008Search in Google Scholar

[44] Kazemahvazi S., Zenkert D., Corrugated all-composite sandwich structures. part 1: Modeling, Compos. Sci. Technol., 2009, 69(7-8), 913-919.10.1016/j.compscitech.2008.11.030Search in Google Scholar

[45] Kazemahvazi S., Tanner D., Zenkert D., Corrugated all-composite sandwich structures. part 2: Failure mechanisms and experimental programme, Compos. Sci., Technol., 2009, 69(7-8), 920-925.10.1016/j.compscitech.2008.11.035Search in Google Scholar

[46] Abbčs B., Guo Y.Q., Analytic homogenization for torsion of orthotropic sandwich plates: Application to corrugated cardboard, Compos. Struct., 2010, 92(3), 699-706.10.1016/j.compstruct.2009.09.020Search in Google Scholar

[47] Dayyani I., Friswell M.I., Ziaei-Rad S., Equivalent models of composite corrugated cores with elastomeric coatings for morphing structures, Compos. Struct., 2013, 104, 281-292.10.1016/j.compstruct.2013.04.034Search in Google Scholar

[48] Bartolozzi G., Pierini M., Orrenius U., Baldanzini N., An equivalent material formulation for sinusoidal corrugated cores of structural sandwich panels, Compos. Struct., 2013, 100, 173-185.10.1016/j.compstruct.2012.12.042Search in Google Scholar

[49] Bartolozzi G., Baldanzini N., Pierini M., Equivalent properties for corrugated cores of sandwich structures: A general analytical method, Compos. Struct., 2014, 108, 736-746.10.1016/j.compstruct.2013.10.012Search in Google Scholar

[50] Cheon Y.-J., Kim H.-G., An Equivalent Model for Corrugated Sandwich Panels, J. Mech. Sci. Technol. 29, 3„ 2015, 1217-1223.10.1007/s12206-015-0235-6Search in Google Scholar

[51] Isaksson P., Carlson L.A., Analysis of the Out-Of-Plane Compression and Shear Response of Paper-based Web-Core Sandwiches Subject to Large Deformation, Compos. Struct., 2017, 159, 96-109.10.1016/j.compstruct.2016.09.060Search in Google Scholar

[52] Briassoulis D., Equivalent Orthotropic Properties of Corrugated Sheets, Comput. Struct., 1986, 23(2), 129–138.10.1016/0045-7949(86)90207-5Search in Google Scholar

[53] Shimansky R.A., Lele M.M., Transverse Stiffness of a sinusoidally corrugated plate, Mech. Struct. Mech., 1995, 23(3), 439-451.10.1080/08905459508905246Search in Google Scholar

[54] Yokozeki T., Takeda S.-T., Ogasawara T., Ishikawa T., Mechanical properties of corrugated composites for candidate materials of flexible wing structures, Compos. Part A: Appl. S., 2006, 37, 1578-1586.10.1016/j.compositesa.2005.10.015Search in Google Scholar

[55] Kress G., Winkler M., Corrugated Laminate Homogenization Model, Compos. Struct., 2010, 92,(3), 795-810.10.1016/j.compstruct.2009.08.027Search in Google Scholar

[56] Xia Y., Friswell M.I., Equivalent models of corrugated laminates for morphing skins, in: Active and Passive Smart Structures and Integrated Systems 2011, Proc. Vol. 7977 of SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, SPIE, San Diego, California, USA, 2011, 79771I10.1117/12.880433Search in Google Scholar

[57] Xia Y., Flores E.I.S., Friswell M.I., Equivalent Models of Corrugated Panels, Int. J. Solids. Struct., 2012, 49(13), 1453-1462.10.1016/j.ijsolstr.2012.02.023Search in Google Scholar

[58] Mohammadi H., Ziaei-Rad S., Dayyani I., An Equivalent Model for Trapezoidal Corrugated Cores Based on Homogenization Method, Compos. Struct., 2015, 131, 160-170.10.1016/j.compstruct.2015.04.048Search in Google Scholar

[59] Wang C., Khodaparast H.H., Friswell M.I., Shaw A.D., An equivalent model of corrugated panels with axial and bending coupling, Comput. Struct., 2017, 183, 61-72.10.1016/j.compstruc.2017.01.008Search in Google Scholar

[60] Nguyen-Minh N., Tran-Van N., Bui-Xuan T., Nguyen-Thoi T., Static Analysis of Corrugated Panels Using Homogenization Models and a Cell-Based Smoothed Mindlin Plate Element (CS-MIN3), Front. Struct. Civil Eng., 2018, https://doi.org/10.1007/s11709-017-0456-0).10.1016/j.tws.2017.12.003Search in Google Scholar

[61] Moro A., Filipovic D., Kress G., Winkler M., Thin-shell-theory solutions for the static structural response of circular-sections shaped corrugated laminates, Compos. Struct., 2020, 236, 111730.10.1016/j.compstruct.2019.111730Search in Google Scholar

[62] Kress G., Winkler M., Corrugated Laminate Analysis: A Generalized Plane-Strain Problem, Compos. Struct., 2011, 93, 1493-1504.10.1016/j.compstruct.2010.12.004Search in Google Scholar

[63] Park K.-J., Jung K., Kim Y.-W., Evaluation of Homogenized Effective Properties for Corrugated Composite Panels, Compos. Struct., 2016, 140, 644-654.10.1016/j.compstruct.2016.01.002Search in Google Scholar

[64] Aoki Y., Maysenhölder W., Experimental and Numerical Assessment of the Equivalent-Orthotropic-Thin-Plate model for Bending of Corrugated Panels, Int. J. Solid. Struct. 2017, 108, 11-23.10.1016/j.ijsolstr.2016.07.042Search in Google Scholar

[65] Pipes R.B., Pagano N.J., Interlaminar stresses in composite laminates under uniform axial extension, J. Compos. Mater., 1970, 4, 538.10.1177/002199837000400409Search in Google Scholar

[66] Hsu P.W., Herakovich C.T., Edge effects in angle-ply composite laminates, J. Compos. Mater., 1977, 11(4), 422-428.10.1177/002199837701100405Search in Google Scholar

[67] O’Brien T.K., Characterization of delamination onset and growth in a composite laminate, in: K. Reifsnider, Ed.), Damage in Composite Materials: Basic Mechanisms, Accumulation, Tolerance, and Characterization, West Conshohocken, PA: ASTM Int., 1982, 140-167.10.1520/STP34325SSearch in Google Scholar

[68] Wang S.S., Choi I., Boundary-layer effects in composite laminates: Part 2 - free-edge stress solutions and basic characteristics, J. Appl. Mech., 1982, 49(3), 549-560.10.1115/1.3162521Search in Google Scholar

[69] Whitcomb J., Raju I.S., Superposition method for analysis of free-edge stresses, J. Compos. Mater., 1983, 17(6), 492-507.10.1177/002199838301700602Search in Google Scholar

[70] Kress G., Width influence on stiffness measurements of multi-directional CFRP laminates under uniaxial load, Compos. Eng., 1992, 2(2), 83-90.10.1016/0961-9526(92)90047-ASearch in Google Scholar

[71] Kress G., Free-edge influence on CFRP-laminate strength, Int. J. Damage Mech., 1994, 3, 194-211.10.1177/105678959400300205Search in Google Scholar

[72] Becker W., Closed-form solution for the free-edge effect in crossply laminates, Compos. Struct., 1993, 26(1-2), 39-45.10.1016/0263-8223(93)90042-OSearch in Google Scholar

[73] Becker W., Kress G., Stiffness reduction in laminate coupons due to free-edge effect, Compos. Sci. Technol., 1994, 52, 109-115.10.1016/0266-3538(94)90013-2Search in Google Scholar

[74] Mittelstedt C., Becker W., Free-edge effects in composite laminates, Appl. Mech. Rev., 2007, 60(5), 217-245.10.1115/1.2777169Search in Google Scholar

[75] Dhanesh N., Kapuria S., Achary G.G.S., Accurate prediction of three-dimensional free edge stress field in composite laminates using mixed-field multiterm extended kantorovich method, Acta Mech., 2016, 228(8), 2895-2919.10.1007/s00707-015-1522-0Search in Google Scholar

[76] Hajikazemi M., Paepegem W.V., A variational model for free-edge interlaminar stress analysis in general symmetric and thin-ply composite laminates, Compos. Struct., 2018, 184, 443-451.10.1016/j.compstruct.2017.10.012Search in Google Scholar

[77] Seydel E., Über das Ausbeulen von rechteckigen, isotropen oder orthogonal-anisotropen Platten bei Schubbeanspruchung, Ingenieur-Archiv, 1933, 4(2), 169-191.10.1007/BF02079856Search in Google Scholar

[78] ANSYS®Academic Research, Release 19.2.Search in Google Scholar

[79] MATLAB®, Release 2019a.Search in Google Scholar

[80] Winkler M., Analysis of Corrugated Laminates, 3407, ETH Zürich, diss. ETH No. 20130, 2012.Search in Google Scholar

[81] Whitney J.M., Analysis of anisotropic laminated plates subjected to torsional loading, Compos. Eng., 1993, 3(6), 567-582.10.1016/0961-9526(93)90053-MSearch in Google Scholar

[82] Honickman H., Johrendt J., Frise P., On the torsional stiffness of thick laminated plates, J. Compos. Mater. 2014, 48(21), 2639-2655.10.1177/0021998313501919Search in Google Scholar

Received: 2020-05-27
Accepted: 2020-07-16
Published Online: 2020-09-18

© 2020 Daniel T. Filipovic et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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