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ORIGINAL ARTICLE

Buckling load optimization of laminated composite plates with elliptical hole under different non-uniform edge loads using bonobo optimizer algorithm

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Received 04 May 2024, Accepted 28 Jul 2024, Published online: 09 Aug 2024

References

  • Y. Wang, C. Pan, C. Zhang, W. Zhou, X. Liu, K. Xia, and J. Xu, Analyzing free vibration and buckling of heated laminated plate with cutouts: A Nitsche-based isogeometric approach, Compos. Struct., vol. 329, pp. 117812, 2024. DOI: 10.1016/j.compstruct.2023.117812.
  • B.S. Srivatsan, B.D. Karthik, P. Darshan, and B.R. Lokavarapu, Buckling analysis of laminated composite rectangular plates with diamond cut-outs, Mater. Today: Proc., 2023. DOI: 10.1016/j.matpr.2023.06.289.
  • M. Aydin Komur, F. Sen, A. Ataş, and N. Arslan, Buckling analysis of laminated composite plates with an elliptical/circular cutout using FEM, Adv. Eng. Softw., vol. 41, no. 2, pp. 161–164, 2010. DOI: 10.1016/j.advengsoft.2009.09.005.
  • A.L. Narayana, K. Rao, and R.V. Kumar, Buckling analysis of rectangular composite plates with rectangular cutout subjected to linearly varying in-plane loading using FEM, Sadhana, vol. 39, no. 3, pp. 583–596, 2014. DOI: 10.1007/s12046-014-0250-9.
  • Z. Junqing, Z. Hongjian, S. Xinyang, and J. Yuhang, Evaluation on compressive properties of composite laminates with a hole reinforced by metal plate, Compos. Struct., vol. 258, pp. 113423, 2021. DOI: 10.1016/j.compstruct.2020.113423.
  • N. Yidris, I.S. Osman, and E. Gires, Influence of shear direction on the buckling of CFRP composite perforated plate, Forces Mech., vol. 9, pp. 100146, 2022. DOI: 10.1016/j.finmec.2022.100146.
  • B. Devarajan, and R.K. Kapania, Thermal buckling of curvilinearly stiffened laminated composite plates with cutouts using isogeometric analysis, Compos. Struct., vol. 238, pp. 111881, 2020. DOI: 10.1016/j.compstruct.2020.111881.
  • Z. Cao, M. Dong, Q. Shi, Z. Han, and R. Qiu, Research on buckling characteristics and placement processability of variable stiffness open-hole laminates, Compos Part C: Open Access, vol. 7, pp. 100233, 2022. DOI: 10.1016/j.jcomc.2022.100233.
  • A. Milazzo, G. Guarino, and V. Gulizzi, Buckling and post-buckling of variable stiffness plates with cutouts by a single-domain Ritz method, Thin-Walled Struct., vol. 182, pp. 110282, 2023. DOI: 10.1016/j.tws.2022.110282.
  • D. Ouinas, and B. Achour, Buckling analysis of laminated composite plates [(θ/−θ)] containing an elliptical notch, Compos. B: Eng., vol. 55, pp. 575–579, 2013. DOI: 10.1016/j.compositesb.2013.07.011.
  • D.M. Li, C.A. Featherston, and Z. Wu, An element-free study of variable stiffness composite plates with cutouts for enhanced buckling and post-buckling performance, Comput. Methods Appl. Mech. Eng., vol. 371, pp. 113314, 2020. DOI: 10.1016/j.cma.2020.113314.
  • T. Yu, S. Yin, T.Q. Bui, S. Xia, S. Tanaka, and S. Hirose, NURBS-based isogeometric analysis of buckling and free vibration problems for laminated composites plates with complicated cutouts using a new simple FSDT theory and level set method, Thin-Walled Struct., vol. 101, pp. 141–156, 2016. DOI: 10.1016/j.tws.2015.12.008.
  • M. Damghani, R.A. Pir, A. Murphy, and M. Fotouhi, Experimental and numerical study of hybrid (CFRP-GFRP) composite laminates containing circular cut-outs under shear loading, Thin-Walled Struct., vol. 179, pp. 109752, 2022. DOI: 10.1016/j.tws.2022.109752.
  • A. Baltaci, M. Sarikanat, and H. Yildiz, Static stability of laminated composite circular plates with holes using shear deformation theory, Finite Elem. Anal. Des., vol. 43, no. 11-12, pp. 839–846, 2007. DOI: 10.1016/j.finel.2007.05.004.
  • X.B. Luo, D.M. Li, C.L. Liu, and J.H. Pan, Buckling analysis of variable stiffness composite plates with elliptical cutouts using an efficient RPIM based on naturally stabilized nodal integration scheme, Compos. Struct., vol. 302, pp. 116243, 2022. DOI: 10.1016/j.compstruct.2022.116243.
  • T. Shojaee, B. Mohammadi, R. Madoliat, and D. Salimi-Majd, Development of a finite strip method for efficient prediction of buckling and post-buckling in composite laminates containing a cutout with/without stiffener, Compos. Struct., vol. 210, pp. 538–552, 2019. DOI: 10.1016/j.compstruct.2018.11.007.
  • A. Kalhori, M.J. Bayat, and K. Asem, Buckling analysis of stiffened functionally graded multilayer graphene platelet reinforced composite plate with circular cutout embedded on elastic support subjected to in-plane normal and shear loads, Results Eng., vol. 20, pp. 101563, 2023. DOI: 10.1016/j.rineng.2023.101563.
  • S.A.M. Ghannadpour, and F. Rashidi, Efficient and accurate semi-analytical simulation of nonlinear behavior of imperfect variable stiffness plates containing rectangular holes, Thin-Walled Struct., vol. 171, pp. 108830, 2022. DOI: 10.1016/j.tws.2021.108830.
  • S.A.M. Ghannadpour, A. Najafi, and B. Mohammadi, On the buckling behavior of cross-ply laminated composite plates due to circular/elliptical cutouts, Compos. Struct., vol. 75, no. 1-4, pp. 3–6, 2006. DOI: 10.1016/j.compstruct.2006.04.071.
  • M. Tercan, and M. Aktaş, Buckling behavior of 1x1 rib knitting laminated plates with cutouts, Compos. Struct., vol. 89, no. 2, pp. 245–252, 2009. DOI: 10.1016/j.compstruct.2008.07.030.
  • D. Kumar, and S.B. Singh, Effects of boundary conditions on buckling and postbuckling responses of composite laminate with various shaped cutouts, Compos. Struct., vol. 92, no. 3, pp. 769–779, 2010. DOI: 10.1016/j.compstruct.2009.08.049.
  • T. Rajanna, K.S.S. Chandra, and K.V. Rao, Influence of local stiffeners and cutout shapes on the vibration and stability characteristics of quasi-isotropic laminates under hygrothermo-mechanical loadings, Def. Technol., vol. 18, no. 12, pp. 2107–2124, 2022. DOI: 10.1016/j.dt.2021.10.002.
  • J. Awrejcewicz, L. Kurpa, and O. Mazur, Dynamical instability of laminated plates with external cutout, Int. J. Non-Linear Mech., vol. 81, pp. 103–114, 2016. DOI: 10.1016/j.ijnonlinmec.2016.01.002.
  • V. Anil, C.S. Upadhyay, and N.G.R. Iyengar, Stability analysis of composite laminate with and without rectangular cutout under biaxial loading, Compos. Struct., vol. 80, no. 1, pp. 92–104, 2007. DOI: 10.1016/j.compstruct.2006.04.088.
  • T. Kremer, and H. Schürmann, Buckling of tension-loaded thin-walled composite plates with cut-outs, Compos. Sci. Technol., vol. 68, no. 1, pp. 90–97, 2008. DOI: 10.1016/j.compscitech.2007.05.035.
  • P. Jain, and A. Kumar, Postbuckling response of square laminates with a central circular/elliptical cutout, Compos. Struct., vol. 65, no. 2, pp. 179–185, 2004. DOI: 10.1016/j.compstruct.2003.10.014.
  • D. Kumar, and S.B. Singh, Stability and failure of composite laminates with various shaped cutouts under combined in-plane loads, Compos. B: Eng., vol. 43, no. 2, pp. 142–149, 2012. DOI: 10.1016/j.compositesb.2011.09.005.
  • R. Kumar, A. Lal, and B.M. Sutaria, Buckling of laminated composite plate with various shapes of holes underuniform/nonuniform mechanical and thermal loading, Plast. Rubber Compos., vol. 52, no. 7, pp. 387–401, 2023. DOI: 10.1080/14658011.2023.2207061.
  • B. Chhorn, and W.Y. Jung, A parametric study on the elliptical hole effects of laminated composite plates under thermal buckling load, Sci. Eng. Compos. Mater., vol. 27, no. 1, pp. 196–203, 2020. DOI: 10.1515/secm-2020-0019.
  • A.R. Shaterzadeh, S. Abolghasemi, and R. Rezaei, Finite element analysis of thermal buckling of rectangular laminated composite plates with circular cut-out, J. Therm. Stress., vol. 37, no. 5, pp. 604–623, 2014. DOI: 10.1080/01495739.2014.885322.
  • A. Avci, S. Kaya, and B. Daghan, Thermal buckling of rectangular laminated plates with a hole, J. Reinf. Plast. Compos., vol. 24, no. 3, pp. 259–272, 2005. DOI: 10.1177/1731684405043554.
  • A. Erkliğ, and E. Yeter, On the thermal buckling behavior oflaminated hybrid composite plates owing to square/circular cut-outs, MCA, vol. 18, no. 3, pp. 548–557, 2013. DOI: 10.3390/mca18030548.
  • O.S. Sahin, Thermal buckling of hybrid angle-ply lami-nated composite plates with a hole, Compos. Sci. Technol., vol. 65, pp. 1780–1790, 2005. DOI: 10.1016/j.compscitech.2005.03.007.
  • Y.P.P. Muddappa, T. Rajanna, and G. Giridhara, Effect of nonlinear edge loads and hybridization of FMLs on buckling performance of interlaminar composites with/without cutouts, Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., vol. 236, no. 6, pp. 3027–3040, 2022. DOI: 10.1177/09544062211037367.
  • T. Rajanna, S. Banerjee, Y.M. Desai, and D.L. Prabhakara, Vibration and buckling analyses of laminated panels with and without cutouts under compressive and tensile edge loads, Steel Compos. Struct., vol. 21, no. 1, pp. 37–55, 2016. DOI: 10.12989/scs.2016.21.1.037.
  • T. Rajanna, S. Banerjee, Y.M. Desai, and D.L. Prabhakara, Effect of reinforced cutouts and ply-orientations on buckling behavior of composite panels subjected to non-uniform edge loads, Int. J. Str. Stab. Dyn., vol. 18, no. 04, pp. 1850058, 2018. DOI: 10.1142/S021945541850058X.
  • K.S.S. Chandra, T. Rajanna, and K.V. Rao, A parametric study on the effect of elliptical cutouts for buckling behavior of composite plates under non-uniform edge loads, Lat. Am. J. Solids Struct., vol. 17, no. 8, pp. e328, 2020. DOI: 10.1590/1679-78256225.
  • A.P. Kalgutkar, S. Banerjee, and T. Rajanna, Effect of elliptical cutouts on buckling and vibration characteristics of stiffened composite panels under non-uniform edge loads, Mech. Based Des. Struct. Mach., vol. 51, no. 9, pp. 5340–5354, 2023. DOI: 10.1080/15397734.2021.1999266.
  • P.P.Y. Muddappa, T. Rajanna, and G. Giridhara, Effects of different interlaminar hybridization and localized edge loads on the vibration and buckling behavior of fiber metal composite laminates, Compos. Part C: Open Access, vol. 4, pp. 100084, 2021. DOI: 10.1016/j.jcomc.2020.100084.
  • P.P.Y. Muddappa, T. Rajanna, and G. Giridhara, Effect of reinforced cutouts on the buckling and vibration performance of hybrid fiber metal laminates, Mech. Based Des. Struct. Mach., vol. 51, no. 7, pp. 3986–4006, 2023. DOI: 10.1080/15397734.2021.1948862.
  • S. Hirannaiah, K. Swaminathan, and T. Rajanna, Thermo-mechanical vibration and buckling analysis of porous FG sandwich plates with geometric discontinuity based on physical neutral surface, Mech. Based Des. Struct. Mach., pp. 1–25, 2023. DOI: 10.1080/15376494.2023.2220493.
  • Maharudra, T. Rajanna, and B. Arya, Influence of trapezoidal shapes and cutout sizes on the buckling behaviour of composite laminates under thermally induced loads, Lat. Am. J. Solids Struct., 3, vol. 18, pp. e360, 2021. DOI: 10.1590/1679-78256331.
  • Maharudra, B. Arya, and T. Rajanna, Buckling behaviour of composite laminates of trapezoidal panel with cutout subjected to non-uniform in-plane edge loads, Mater. Today Proc., vol. 45, pp. 21–26, 2021. DOI: 10.1016/j.matpr.2020.09.224.
  • P.P.Y. Muddappa, T. Rajanna, and G. Giridhara, Effects of different interlaminar hybridization and cutout sizes on the vibration and buckling characteristics of fiber metal composite laminates under partial edge loads, Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., vol. 236, no. 2, pp. 1083–1098, 2022. DOI: 10.1177/09544062211002876.
  • P.P.Y. Muddappa, T. Rajanna, and G. Giridhara, Effect of tensile and compressive nonlinear edge loads on the buckling performance of hybrid metal composite laminates with cutouts, Mech. Based Des. Struct. Mach., vol. 51, no. 8, pp. 4294–4312, 2023. DOI: 10.1080/15397734.2021.1956331.
  • M. Ranjere, T. Rajanna, and B. Arya, Influence of trapezoidal shapes and linearly varying edge loads on the buckling characteristics of plates with cutouts, J. Inst. Eng. India. Ser. C., vol. 102, no. 5, pp. 1231–1249, 2021. DOI: 10.1007/s40032-021-00735-2.
  • C.V. Srinivasa, W.P.P. Kumar, M.T.P. Kumar, A.R. Bangar, P. Kumar, and M.S. Rudresh, Experimental and numerical studies on buckling of laminated composite skew plates with circular holes under uniaxial compression, Mech. Adv. Mater. Struct., vol. 24, no. 4, pp. 304–317, 2017. DOI: 10.1080/15376494.2016.1142023.
  • M.H.G. Rad, and S.M. Hosseini, Application of the CUF–EFG method for buckling analysis of the multilayer GPLs–CNTs-reinforced FG plates with cutout, Mech. Adv. Mater. Struct., vol. 31, no. 3, pp. 533–549, 2024. DOI: 10.1080/15376494.2022.2116664.
  • S. Khan, M.A. Nik, K. Fayazbakhsh, and Z. Fawaz, Continuous curvilinear variable stiffness design for improved strength of a panel with a cutout, Mech. Adv. Mater. Struct., vol. 29, no. 7, pp. 975–983, 2022. DOI: 10.1080/15376494.2020.1801914.
  • S. Samukham, G. Raju, Z. Wu, and C.P. Vyasarayani, Dynamic instability analysis of variable angle tow composite plate with delamination around a cut-out, Mech. Adv. Mater. Struct., vol. 26, no. 1, pp. 62–70, 2019. DOI: 10.1080/15376494.2018.1534166.
  • K. Sharma, and D. Kumar, Nonlinear stability analysis of a perforated FGM plate under thermal load, Mech. Adv. Mater. Struct., vol. 25, no. 2, pp. 100–114, 2018. DOI: 10.1080/15376494.2016.1255817.
  • H.R. Ovesy, M. Kharazi, and M. Taghizadeh, Semi-analytical buckling analysis of clamped composite plates containing embedded rectangular and circular delaminations, Mech. Adv. Mater. Struct., vol. 17, no. 5, pp. 343–352, 2010. DOI: 10.1080/15376494.2010.488605.
  • P. Jiao, Z. Chen, H. Ma, Z. Cheng, Y. Gu, and W. Tao, Post-buckling behavior of rectangular multilayer FG-GPLRC plate with initial geometric defects subjected to non-uniform in-plane compression loads in thermal environment, Mech. Adv. Mater. Struct., vol. 31, no. 3, pp. 693–712, 2024. DOI: 10.1080/15376494.2022.2119313.
  • T. Dey, and L.S. Ramachandra, Linear and nonlinear parametric instability behavior of cylindrical sandwich panels subjected to various mechanical edge loadings, Mech. Adv. Mater. Struct., vol. 23, no. 1, pp. 8–21, 2016. DOI: 10.1080/15376494.2014.918222.
  • O.E. Oluwabusi, and E.A. Toubia, Effect of central circular cut-out and low velocity impact damage on shear buckling and post-buckling of composite laminated plates, Compos. Struct., vol. 245, pp. 112304, 2020. DOI: 10.1016/j.compstruct.2020.112304.
  • S. Mondal, and L.S. Ramachandra, Nonlinear dynamic pulse buckling of imperfect laminated composite plate with delamination, Int. J. Solids Struct., vol. 198, pp. 170–182, 2020. DOI: 10.1016/j.ijsolstr.2020.04.010.
  • C. Zhao, J. Niu, Q. Zhang, C. Zhao, and J. Xie, Buckling behavior of a thin-walled cylinder shell with the cutout imperfections, Mech. Adv. Mater. Struct., vol. 26, no. 18, pp. 1536–1542, 2019. DOI: 10.1080/15376494.2018.1444225.
  • M. Kathiresan, K. Manisekar, V. Rajamohan, and M.A. Güler, Investigations on crush behavior and energy absorption characteristics of GFRP composite conical frusta with a cutout under axial compression loading, Mech. Adv. Mater. Struct., vol. 29, no. 26, pp. 5360–5377, 2022. DOI: 10.1080/15376494.2021.1955168.
  • M.A. Nik, K. Fayazbakhsh, S. Khan, and Z. Fawaz, Strength evaluation of continuous curvilinear variable stiffness panels with circular cutouts under biaxial normal loading and off-design conditions, Mech. Adv. Mater. Struct., vol. 29, no. 25, pp. 3860–3870, 2022. DOI: 10.1080/15376494.2021.1912441.
  • S.K. Chaudhary, V.R. Kar, and K.K. Shukla, Geometrically nonlinear large-deflection analysis of heated functionally graded composite panels with single and multiple perforations, Mech. Adv. Mater. Struct., vol. 30, no. 21, pp. 4329–4346, 2023. DOI: 10.1080/15376494.2022.2092798.
  • P.A. Shirbhate, and M.D. Goel, Investigation of effect of perforations in honeycomb sandwich structure for enhanced blast load mitigation, Mech. Adv. Mater. Struct., vol. 30, no. 17, pp. 3463–3478, 2023. DOI: 10.1080/15376494.2022.2076958.
  • H. Zhang, P. Zhu, Z. Liu, S. Qi, and Y. Zhu, Research on prediction method of mechanical properties of open-hole laminated plain woven CFRP composites considering drilling-induced delamination damage, Mech. Adv. Mater. Struct., vol. 28, no. 24, pp. 2515–2530, 2021. DOI: 10.1080/15376494.2020.1745969.
  • K. Khatri, and A. Lal, Stochastic XFEM fracture and crack propagation behavior of an isotropic plate with hole emanating radial cracks subjected to various in-plane loadings, Mech. Adv. Mater. Struct., vol. 25, no. 9, pp. 732–755, 2018. DOI: 10.1080/15376494.2017.1308599.
  • J.J. Fesharaki, and S. Golabi, Effect of stiffness ratio of piezoelectric patches and plate on stress concentration reduction in a plate with a hole, Mech. Adv. Mater. Struct., vol. 24, no. 3, pp. 253–259, 2017. DOI: 10.1080/15376494.2016.1139214.
  • U. Topal, and Ü. Uzman, Maximization of buckling load of laminated composite plates with central circular holes using MFD method, Struct. Multidisc. Optim., vol. 35, no. 2, pp. 131–139, 2008. DOI: 10.1007/s00158-007-0119-1.
  • A. Alhajahmad, and C. Mittelstedt, Buckling and postbuckling performance of composite fuselage panels with cutouts using continuous streamline fibres, Int. J. Mech. Sci., vol. 212, pp. 106841, 2021. DOI: 10.1016/j.ijmecsci.2021.106841.
  • M. Walker, Optimal design of symmetric laminates with cut-outs for maximum buckling load, Comput. Struct., vol. 70, pp. 337–343, 1999.
  • H. Ding, B. Xu, L. Song, W. Li, and X. Huang, Buckling optimization of variable-stiffness composites with multiple cutouts considering manufacturing constraints, Adv. Eng. Softw., vol. 174, pp. 103303, 2022. DOI: 10.1016/j.advengsoft.2022.103303.
  • W. Zhao, and R.K. Kapania, Buckling analysis and optimization of stiffened variable angle tow laminates with a cutout considering manufacturing constraints, J. Compos. Sci., vol. 6, no. 3, pp. 80, 2022. DOI: 10.3390/jcs6030080.
  • Z. Cao, G. Lin, Q. Shi, and Q. Cao, Optimization analysis of NURBS curved variable stiffness laminates with a hole, Mater. Today Commun., vol. 31, pp. 103364, 2022. DOI: 10.1016/j.mtcomm.2022.103364.
  • A.P. Kalgutkar, S. Banerjee, and T. Rajanna, Optimum arrangement of stiffener on the buckling behaviour of stiffened composite panels with reinforced elliptical cutouts subjected to non-uniform edge load, Steel Compos. Struct., vol. 42, pp. 427–446, 2022. DOI: 10.12989/scs.2022.42.4.427.
  • M. Zeinali, G. Rahimi, and S. Hosseini, Buckling load optimization of sandwich plates with trapezoidal corrugated core and elliptical cutout using vibration correlation techniques and artificial neural network; experimental and numerical analysis, Thin-Walled Struct., vol. 200, pp. 111957, 2024. DOI: 10.1016/j.tws.2024.111957.
  • Z. Jing, L. Duan, and S. Wang, Buckling optimization of variable-stiffness composite plates with two circular holes using discrete Ritz method and potential flow, Int. J. Solids Struct., vol. 297, pp. 112845, 2024. DOI: 10.1016/j.ijsolstr.2024.112845.
  • J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed., Taylor & Francis, Boca Raton, 2004.
  • R. Lal, and R. Saini, Buckling and vibration of non-homogeneous rectangular plates subjected to linearly varying in-plane force, Shock Vib., vol. 20, no. 5, pp. 879–894, 2013. DOI: 10.3233/SAV-130791.
  • P. Aiah, Global College of Engineering and Technology, Deriving shape functions for 9-noded rectangular element by using lagrange functions in natural coordinate system and verified, IJMTT, vol. 51, no. 6, pp. 429–433, 2017. DOI: 10.14445/22315373/IJMTT-V51P560.
  • V. Goodarzimehr, U. Topal, A.K. Das, and T. Vo-Duy, Bonobo optimizer algorithm for optimum design of truss structures with static constraints, Structures, vol. 50, pp. 400–417, 2023. DOI: 10.1016/j.istruc.2023.02.023.
  • B. Adhikari, P. Dash, and B. Singh, Buckling analysis of porous FGM sandwich plates under various types nonuniform edge compression based on higher order shear deformation theory, Compos. Struct., vol. 251, pp. 112597, 2020. DOI: 10.1016/j.compstruct.2020.112597.
  • S.K. Panda, and L.S. Ramachandra, Buckling of rectangular plates with various boundary conditions loaded by non-uniform inplane loads, Int. J. Mech. Sci., vol. 52, no. 6, pp. 819–828, 2010. DOI: 10.1016/j.ijmecsci.2010.01.009.
  • X. Wang, X. Wang, and X. Shi, Accurate buckling loads of thin rectangular plates under parabolic edge compressions by the differential quadrature method, Int. J. Mech. Sci., vol. 49, no. 4, pp. 447–453, 2007. DOI: 10.1016/j.ijmecsci.2006.09.004.
  • B. Adhikari, and B.N. Singh, Buckling characteristics of laminated functionally-graded CNT-reinforced composite plate under nonuniform uniaxial and biaxial in-plane edge loads, Int. J. Str. Stab. Dyn., vol. 20, no. 02, pp. 2050022, 2019. DOI: 10.1142/S0219455420500224.
  • S. Verma, A. Gupta, B.R. Thakur, D. Oguamana, and B.N. Singh, A unified buckling formulation for linear and nonlinear analysis of laminated plates using penalty based Co FEM-HSDT model, Int. J. Non–Linear Mech., vol. 159, pp. 104619, 2024. DOI: 10.1016/j.ijnonlinmec.2023.104619.

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