This paper presents a coupled thermoelastic finite element formulation for static and dynamic analysis of composite laminated plates with embedded active shape memory alloy (SMA) wires, which accounts for both the phase transformation and the nonlinearity effects of SMA wires. The equations of motion are obtained by using Hamilton's principle and first-order shear deformation theory (FSDT). Furthermore, based on Brinson's one-dimensional phase transformation constitutive law, a novel coupled thermoelastic finite element model that enables analysis of the SMA hybrid composite (SMAHC) plate is developed. The accuracy and efficiency of the developed computational model for analysis of SMAHC plates are reinforced by comparing theoretical predictions with data available from the literature. The results of the numerical examples also show the ability of the proposed model to predict the thermal-mechanical behavior of SMAHC plates in accordance with SMA's hysteresis behavior. In addition, based on the proposed model, the influence of temperature as well as SMA volume fraction, pre-strain value, boundary condition and layup sequence on the static bending and free vibration behavior of the SMAHC plates is investigated in detail. The results of parametric analysis show that the variations of both static deflection and natural frequency of the SMAHC plate over temperature exhibit a nonmonotonic behavior.

Institute of Physics Czech Academy of Sciences Na Slovance 2 18200 Prague Czech Republic

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Jani J.M., Leary M., Subic A., Gibson M.A. A review of shape memory alloy research, applications and opportunities. Mater. Des. 2014;56:1078–1113. doi: 10.1016/j.matdes.2013.11.084. DOI

Jani J.M., Leary M., Subic A. Applied Mechanics and Materials. Volume 663. Trans Tech Publications Ltd.; Bach, Switzerland: 2014. Shape memory alloys in automotive applications; pp. 248–253.

Abavisani I., Rezaifar O., Kheyroddin A. Multifunctional properties of shape memory materials in civil engineering applications: A state-of-the-art review. J. Build Eng. 2021;44:102657. doi: 10.1016/j.jobe.2021.102657. DOI

Rogers C., Liang C., Jia J. Behavior of shape memory alloy reinforced composite plates. I-Model formulations and control concepts; Proceedings of the 30th Structures, Structural Dynamics and Materials Conference; Mobile, AL, USA. 3–5 April 1989; p. 1389. DOI

Rogers C., Barker D. Experimental studies of active strain energy tuning of adaptive composites; Proceedings of the 31st Structures, Structural Dynamics and Materials Conference; Long Beach, CA, USA. 2–4 April 1990; p. 1086. DOI

Epps J., Chandra R. Shape memory alloy actuation for active tuning of composite beams. Smart Mater. Struc. 1997;6:251. doi: 10.1088/0964-1726/6/3/004. DOI

Song G., Kelly B., Agrawal B.N. Active position control of a shape memory alloy wire actuated composite beam. Smart Mater. Struct. 2000;9:711. doi: 10.1088/0964-1726/9/5/316. DOI

Rogers C.A., Liang C., Jia J. Structural modification of simply-supported laminated plates using embedded shape memory alloy fibers. Comput. Struct. 1991;38:569–580. doi: 10.1016/0045-7949(91)90008-A. DOI

Yang Z., Deng T., Li J., Xu C. Experimental Study on Self-Centering Performance of the SMA Fiber Reinforced ECC Composite Beam. Materials. 2022;15:3062. doi: 10.3390/ma15093062. PubMed DOI PMC

Thompson S.P., Loughlan J. Adaptive post-buckling response of carbon fiber composite plates employing SMA actuators. Compos. Struct. 1997;38:667–678. doi: 10.1016/S0263-8223(97)00104-9. DOI

Kim E.H., Lee I., Roh J.H., Bae J.S., Choi I.H., Koo K.N. Effects of shape memory alloys on low velocity impact characteristics of composite plate. Compos. Struct. 2011;93:2903–2909. doi: 10.1016/j.compstruct.2011.05.013. DOI

Kuang K.S.C., Quek S.T., Cantwell W.J. Active control of a smart composite with shape memory alloy sheet using a plastic optical fiber sensor. Sens. Act. A Phys. 2013;201:182–187. doi: 10.1016/j.sna.2013.06.024. DOI

Abdullah E.J., Majid D.L., Romli F.I., Gaikwad P.S., Yuan L.G., Harun N.F. Active control of strain in a composite plate using shape memory alloy actuators. Int. J. Mech. Mater. Des. 2015;11:25–39. doi: 10.1007/s10999-014-9277-7. DOI

Wang E., Tian Y., Wang Z., Jiao F., Guo C., Jiang F. A study of shape memory alloy NiTi fiber/plate reinforced (SMAFR/SMAPR) Ti-Al laminated composites. J. Alloys Compd. 2017;696:1059–1066. doi: 10.1016/j.jallcom.2016.12.062. DOI

Liu Y., Wang Z., Li H., Sun M., Wang F., Chen B. Influence of embedding SMA fibres and SMA fibre surface modification on the mechanical performance of BFRP composite laminates. Materials. 2018;11:70. doi: 10.3390/ma11010070. PubMed DOI PMC

Thompson S.P., Loughlan J. Enhancing the post-buckling response of a composite panel structure utilising shape memory alloy actuators–a smart structural concept. Compos. Struct. 2001;51:21–36. doi: 10.1016/S0263-8223(00)00097-0. DOI

Birman V. Stability of functionally graded shape memory alloy sandwich panels. Smart Mater. Struct. 1997;6:278. doi: 10.1088/0964-1726/6/3/006. DOI

Li H., Wang Z., Yu Z., Sun M., Liu Y. The low velocity impact response of foam core sandwich panels with a shape memory alloy hybrid face-sheet. Materials. 2018;11:2076. doi: 10.3390/ma11112076. PubMed DOI PMC

Lu P., Cui F.S., Tan M.J. A theoretical model for the bending of a laminated beam with SMA fiber embedded layer. Compos. Struct. 2009;90:458–464. doi: 10.1016/j.compstruct.2009.04.018. DOI

Asadi H., Bodaghi M., Shakeri M., Aghdam M.M. An analytical approach for nonlinear vibration and thermal stability of shape memory alloy hybrid laminated composite beams. Eur. J. Mech. A Solids. 2013;42:454–468. doi: 10.1016/j.euromechsol.2013.07.011. DOI

Asadi H., Eynbeygi M., Wang Q. Nonlinear thermal stability of geometrically imperfect shape memory alloy hybrid laminated composite plates. Smart Mater. Struct. 2014;23:075012. doi: 10.1088/0964-1726/23/7/075012. DOI

Kabir M.Z., Tehrani B.T. Closed-form solution for thermal, mechanical, and thermo-mechanical buckling and post-buckling of SMA composite plates. Compos. Struct. 2017;168:535–548. doi: 10.1016/j.compstruct.2017.02.046. DOI

Bayat Y., EkhteraeiToussi H. Exact solution of thermal buckling and post buckling of composite and SMA hybrid composite beam by layerwise theory. Aerosp. Sci. Technol. 2017;67:484–494. doi: 10.1016/j.ast.2017.04.029. DOI

Fahimi P., Eskandari A.H., Baghani M., Taheri A. A semi-analytical solution for bending response of SMA composite beams considering SMA asymmetric behavior. Compos. Part B. 2019;163:622–633. doi: 10.1016/j.compositesb.2019.01.019. DOI

Khalili S.M.R., Dehkordi M.B., Carrera E., Shariyat M. Non-linear dynamic analysis of a sandwich beam with pseudoelastic SMA hybrid composite faces based on higher order finite element theory. Compos. Struct. 2013;96:243–255. doi: 10.1016/j.compstruct.2012.08.020. DOI

Tawfik M., Ro J.J., Mei C. Thermal post-buckling and aeroelastic behaviour of shape memory alloy reinforced plates. Smart Mater. Struct. 2002;11:297. doi: 10.1088/0964-1726/11/2/313. DOI

Kumar C.N., Singh B.N. Thermal buckling and post-buckling of laminated composite plates with SMA fibers using layerwise theory. Int. J. Comput. Methods Eng. Sci. Mech. 2009;10:423–429. doi: 10.1080/15502280903108024. DOI

Ibrahim H.H., Tawfik M., Negm H.M. Thermal buckling and nonlinear flutter behavior of shape memory alloy hybrid composite plates. J. Vib. Control. 2011;17:321–333. doi: 10.1177/1077546309353368. DOI

Lee H.J., Lee J.J. A numerical analysis of the buckling and postbuckling behavior of laminated composite shells with embedded shape memory alloy wire actuators. Smart Mater. Struct. 2000;9:780. doi: 10.1088/0964-1726/9/6/307. DOI

Roh J.H., Oh I.K., Yang S.M., Han J.H., Lee I. Thermal post-buckling analysis of shape memory alloy hybrid composite shell panels. Smart Mater. Struct. 2004;13:1337. doi: 10.1088/0964-1726/13/6/006. DOI

Karimiasl M., Ebrahimi F., Akgöz B. Buckling and post-buckling responses of smart doubly curved composite shallow shells embedded in SMA fiber under hygro-thermal loading. Compos. Struct. 2019;223:110988. doi: 10.1016/j.compstruct.2019.110988. DOI

Nejati M., Ghasemi-Ghalebahman A., Soltanimaleki A., Dimitri R., Tornabene F. Thermal vibration analysis of SMA hybrid composite double curved sandwich panels. Compos. Struct. 2019;224:111035. doi: 10.1016/j.compstruct.2019.111035. DOI

Panda S.K., Singh B.N. Nonlinear finite element analysis of thermal post-buckling vibration of laminated composite shell panel embedded with SMA fibre. Aerosp. Sci. Technol. 2013;29:47–57. doi: 10.1016/j.ast.2013.01.007. DOI

Ghomshei M.M., Tabandeh N., Ghazavi A., Gordaninejad F. Nonlinear transient response of a thick composite beam with shape memory alloy layers. Compos. Part B. 2005;36:9–24. doi: 10.1016/j.compositesb.2004.04.004. DOI

Cho H.K., Rhee J. Nonlinear finite element analysis of shape memory alloy (SMA) wire reinforced hybrid laminate composite shells. Int. J. Non-Linear Mech. 2012;47:672–678. doi: 10.1016/j.ijnonlinmec.2011.11.002. DOI

Zhang H., Zhu R., Shi D., Wang Q. A simplified plate theory for vibration analysis of composite laminated sector, annular and circular plate. Thin-Walled Struct. 2019;143:106252. doi: 10.1016/j.tws.2019.106252. DOI

Belardi V.G., Fanelli P., Vivio F. On the radial bending of shear-deformable composite circular plates with rectilinear orthotropy. Eur. J. Mech. A/Solids. 2021;86:104157. doi: 10.1016/j.euromechsol.2020.104157. DOI

Gao C., Pang F., Li H., Jia D., Tang Y. Steady and transient vibration analysis of uniform and stepped annular/circular plates based on FSDT. Acta Mech. 2022;233:1061–1082. doi: 10.1007/s00707-022-03157-y. DOI

Tabrizikahou A., Kuczma M., Łasecka-Plura M. Out-of-Plane Behavior of Masonry Prisms Retrofitted with Shape Memory Alloy Stripes: Numerical and Parametric Analysis. Sensors. 2022;22:8004. doi: 10.3390/s22208004. PubMed DOI PMC

Brinson L.C. One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variable. J. Intell. Mater. Syst. Struct. 1993;4:229–242. doi: 10.1177/1045389X9300400213. DOI

Reddy J.N. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press; New York, NY, USA: 2003. pp. 132–133.

Roodgar Saffari P., Sher W., Thongchom C. Size Dependent Buckling Analysis of a FG-CNTRC Microplate of Variable Thickness under Non-Uniform Biaxial Compression. Buildings. 2022;12:2238. doi: 10.3390/buildings12122238. DOI

Ebrahimi-Mamaghani A., Forooghi A., Sarparast H., Alibeigloo A., Friswell M.I. Vibration of viscoelastic axially graded beams with simultaneous axial and spinning motions under an axial load. Appl. Math. Model. 2021;90:131–150. doi: 10.1016/j.apm.2020.08.041. DOI

Newmark N.M. A method of computation for structural dynamics. J. Eng. Mech. Div. 1959;85:67–94. doi: 10.1061/JMCEA3.0000098. DOI