Large deflections of functionally graded sandwich beams with influence of homogenization schemes

Archive of Applied Mechanics - Tập 92 Số 6 - Trang 1757-1775 - 2022
Dinh Kien Nguyen1, Thi Thu Hoai Bui2, Thị Thu Hường Trần3, Sergei Alexandrov4
1Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam
2Graduate University of Science and Technology, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam
3Faculty of Vehicle and Energy Engineering, Phenikaa University, Yen Nghia, Ha Dong, Hanoi, 12116, Vietnam
4Faculty of Materials Science and Metallurgy Engineering, Federal State Autonomous Educational Institution of Higher Education "South Ural State University (National Research University)", 76 Lenin Prospekt, Chelyabinsk, Russia, 454080

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Koizumi, M.: FGM activities in Japan. Compos. Part B Eng. 28, 1–4 (1997). https://doi.org/10.1016/S1359-8368(96)00016-9

Paulino, G.H., Yin, H.M., Sun, L.Z.: Micromechanics-based interfacial debonding model for damage of functionally graded materials with particle interactions. Int. J. Damage Mech. 15, 267–288 (2006). https://doi.org/10.1177/1056789506060756

Jha, D.K., Kant, T., Singh, R.K.: A critical review of recent research on functionally graded plates. Compos. Struct. 96, 833–849 (2013). https://doi.org/10.1016/j.compstruct.2012.09.001

Praveen, G.N., Reddy, J.N.: Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. Int. J. Solids Struct. 35, 4457–4476 (1998). https://doi.org/10.1016/S0020-7683(97)00253-9

Agarwal, S., Chakraborty, A., Gopalakrishnan, S.: Large deformation analysis for anisotropic and inhomogeneous beams using exact linear static solutions. Compos. Struct. 72, 91–104 (2006). https://doi.org/10.1016/j.compstruct.2004.10.019

Doctor, S.L., Zhang, J., Zhao, Y.: Thermal post-buckling of functionally graded material Timoshenko beams. Appl. Math. Mech. 27, 803–810 (2006). https://doi.org/10.1007/s10483-006-0611-y

Kang, Y.-A., Li, X.-F.: Bending of functionally graded cantilever beam with power-law nonlinearity subjected to an end force. Int. J. Non-Linear Mech. 44, 696–703 (2009). https://doi.org/10.1016/j.ijnonlinmec.2009.02.016

Kang, Y.-A., Li, X.F.: Large deflection of a non-linear cantilever functionally graded beam. J. Reinf. Plast. Compos. 29, 1761–1774 (2010). https://doi.org/10.1177/0731684409103340

Lee, Y.Y., Zhao, X., Reddy, J.N.: Postbuckling analysis of functionally graded plates subjected to compressive and thermal loads. Comput. Methods Appl. Mech. Eng. 199, 1645–1653 (2010). https://doi.org/10.1016/j.cma.2010.01.008

Kocatürk, T., Şimşek, M.S., Akbaş, S.D.: Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded material. Sci. Eng. Compos. Mater. 18, 21–34 (2011). https://doi.org/10.1515/secm.2011.005

Almeida, C.A., Albino, J.C.R., Menezes, I.F.M., Paulino, G.H.: Geometric nonlinear analyses of functionally graded beams using a tailored Lagrangian formulation. Mech. Res. Commun. 38, 553–559 (2011). https://doi.org/10.1016/j.mechrescom.2011.07.006

Arbind, A., Reddy, J.N.: Nonlinear analysis of functionally graded microstructure-dependent beams. Compos. Struct. 98, 272–281 (2013). https://doi.org/10.1016/j.compstruct.2012.10.003

Arbind, A., Reddy, J.N., Srinivasa, A.R.: Modified couple stress-based third-order theory for nonlinear analysis of functionally graded beams. Lat. Am. J. Solids Struct. 11, 459–487 (2014). https://doi.org/10.1590/S1679-78252014000300006

Levyakov, S.V.: Elastica solution for thermal bending of a functionally graded beam. Acta Mech. 224, 1731–1740 (2013). https://doi.org/10.1007/s00707-013-0834-1

Levyakov, S.V.: Thermal elastica of shear-deformable beam fabricated of functionally graded material. Acta Mech. 226, 723–733 (2015). https://doi.org/10.1007/s00707-014-1218-x

Zhang, D.G.: Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory. Compos. Struct. 100, 121–126 (2013). https://doi.org/10.1016/j.compstruct.2012.12.024

Nguyen, D.K.: Large displacement response of tapered cantilever beams made of axially functionally graded material. Compos. Part B Eng. 55, 298–305 (2013). https://doi.org/10.1016/j.compositesb.2013.06.024

Nguyen, D.K.: Large displacement behaviour of tapered cantilever Euler-Bernoulli beams made of functionally graded material. Appl. Math. Comput. 237, 340–355 (2014). https://doi.org/10.1016/j.amc.2014.03.104

Nguyen, D.K., Gan, B.S.: Large deflections of tapered functionally graded beams subjected to end forces. Appl. Math. Model. 38, 3054–3066 (2014). https://doi.org/10.1016/j.apm.2013.11.032

Nguyen, D.K., Gan, B.S., Trinh, T.H.: Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material. Struct. Eng. Mech. 49, 727–743 (2014). https://doi.org/10.12989/sem.2014.49.6.727

Vosoughi, A.R.: Thermal postbuckling analysis of functionally graded beams. J. Therm. Stresses 37, 532–544 (2014). https://doi.org/10.1080/01495739.2013.872462

Trinh, T.H., Nguyen, D.K., Gan, B.S., Alexandrov, S.: Post-buckling responses of elasto-plastic FGM beams on nonlinear elastic foundation. Struct. Eng. Mech. 58, 515–532 (2016). https://doi.org/10.12989/sem.2016.58.3.515

Nguyen, D.K., Nguyen, K.V., Dinh, V.M., Gan, B.S., Alexandrov, S.: Nonlinear bending of elastoplastic functionally graded ceramic-metal beams subjected to nonuniform distributed loads. Appl. Math. Comput. 333, 443–459 (2018). https://doi.org/10.1016/j.amc.2018.03.100

Niknam, H., Fallah, A., Aghdam, M.M.: Nonlinear bending of functionally graded tapered beams subjected to thermal and mechanical loading. Int. J. Non-Linear Mech. 65, 141–147 (2014). https://doi.org/10.1016/j.ijnonlinmec.2014.05.011

Li, L., Li, X., Hu, Y.: Nonlinear bending of a two-dimensionally functionally graded beam. Compos. Struct. 184, 1049–1061 (2018). https://doi.org/10.1016/j.compstruct.2017.10.087

Masjedia, P.K., Maheri, A., Weaver, P.M.: Large deflection of functionally graded porous beams based on a geometrically exact theory with a fully intrinsic formulation. Appl. Math. Model. 76, 938–957 (2019). https://doi.org/10.1016/j.apm.2019.07.018

Pascon, J.P.: Finite element analysis of flexible functionally graded beams with variable Poisson’s ratio. Eng. Comput. 33, 2421–2447 (2016). https://doi.org/10.1108/EC-08-2015-0225

Pascon, J.P.: Finite element analysis of functionally graded hyperelastic beams under plane stress. Eng. Comput. 36, 1265–1288 (2020). https://doi.org/10.1007/s00366-019-00761-w

Fukui, Y.: Fundamental investigation of functionally graded materials manufacturing system using centrifugal force. JSME Int. J. Ser. III 34, 144–148 (1991). https://doi.org/10.1299/jsmec1988.34.144

Lambros, J., Santare, M.H., Li, H., Sapna, G.H.: A novel technique for the fabrication of laboratory scale model of FGM. Exp. Mech. 39, 184–190 (1999). https://doi.org/10.1007/BF02323551

Sayyad, A.S., Ghugal, Y.M.: Modeling and analysis of functionally graded sandwich beams: a review. Mech. Adv. Mater. Struct. 26, 1776–1795 (2018). https://doi.org/10.1080/15376494.2018.1447178

Chakraborty, A., Gopalakrishnan, S., Reddy, J.N.: A new beam finite element for the analysis of functionally graded materials. Int. J. Mech. Sci. 45, 519–539 (2003). https://doi.org/10.1016/S0020-7403(03)00058-4

Bhangale, R.K., Ganesan, N.: Thermoelastic buckling and vibration behavior of a functionally graded sandwich beam with constrained viscoelastic core. J. Sound Vib. 295, 294–316 (2006). https://doi.org/10.1016/j.jsv.2006.01.026

Bui, T.Q., Khosravifard, A., Zhang, C., Hematiyan, M., Golub, M.: Dynamic analysis of sandwich beams with functionally graded core using a truly meshfree radial point interpolation method. Eng. Struct. 47, 90–104 (2013). https://doi.org/10.1016/j.engstruct.2012.03.041

Vo, T.P., Thai, H.T., Nguyen, T.K., Maheri, A., Lee, J.: Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory. Eng. Struct. 64, 12–22 (2014). https://doi.org/10.1016/j.engstruct.2014.01.029

Vo, T.P., Thai, H.T., Nguyen, T.K., Inam, F., Lee, J.: A quasi-3D theory for vibration and buckling of functionally graded sandwich beams. Compos. Struct. 119, 1–12 (2015). https://doi.org/10.1016/j.compstruct.2014.08.006

Yarasca, J., Mantari, J., Arciniega, R.: Hermite–Lagrangian finite element formulation to study functionally graded sandwich beams. Compos. Struct. 140, 567–581 (2016). https://doi.org/10.1016/j.compstruct.2016.01.015

Nguyen, D.K., Tran, T.T.: A co-rotational formulation for large displacement analysis of functionally graded sandwich beam and frame structures. Math. Probl. Eng. (2016). https://doi.org/10.1155/2016/5698351

Le, C.I., Le, N.A.T., Nguyen, D.K.: Free vibration and buckling of bidirectional functionally graded sandwich beams using an enriched third-order shear deformation beam element. Compos. Struct. (2020). https://doi.org/10.1016/j.compstruct.2020.113309

Nguyen, D.K., Vu, A.N.T., Pham, V.N., Truong, T.T.: Vibration of a three-phase bidirectional functionally graded sandwich beam carrying a moving mass using an enriched beam element. Eng. Comput. (2021). https://doi.org/10.1007/s00366-021-01496-3

Vu, A.N.T., Le, N.A.T., Nguyen, D.K.: Dynamic behaviour of bidirectional functionally graded sandwich beams under a moving mass with partial foundation supporting effect. Acta Mech. 232, 2853–2875 (2021). https://doi.org/10.1007/s00707-021-02948-z

Zuiker, J.R.: Functionally graded materials: choice of micromechanics model and limitations in property variation. Compos. Eng. 5, 807–819 (1995). https://doi.org/10.1016/0961-9526(95)00031-H

Karami, B., Shahsavari, D., Janghorban, M., Li, L.: Influence of homogenization schemes on vibration of functionally graded curved microbeams. Compos. Struct. 216, 67–79 (2019). https://doi.org/10.1016/j.compstruct.2019.02.089

Loja, M.A.R., Barbosa, J.I., Mota Soares, C.M.: A study on the modeling of sandwich functionally graded particulate composites. Compos. Struct. 94, 2209–2217 (2012). https://doi.org/10.1016/j.compstruct.2012.02.015

Chen, Q., Wang, G., Pindera, M.-J.: Homogenization and localization of nanoporous composites—a critical review and new developments. Compos. Part B Eng. 155, 329–368 (2018). https://doi.org/10.1016/j.compositesb.2018.08.116

Chen, Q., Wang, G., Chen, X.: Three-dimensional parametric finite-volume homogenization of periodic materials with multi-scale structural applications. Int. J. Appl. Mech. 10(4), 1850045 (2018). https://doi.org/10.1142/S175882511850045X

Tu, W., Chen, Q.: Homogenization and localization of unidirectional fiber-reinforced composites with evolving damage by FVDAM and FEM approaches: a critical assessment. Eng. Fract. Mech. (2020). https://doi.org/10.1016/j.engfracmech.2020.107280

Christensen, R.M.: Mechanics of Composite Materials. Wiley, New York (1979)

Mori, T., Tanaka, K.: Average stress in the matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21, 571–574 (1973). https://doi.org/10.1016/0001-6160(73)90064-3

Hashin, Z., Shtrikman, S.: A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11, 127–140 (1963). https://doi.org/10.1016/0022-5096(63)90060-7

Tamura, I., Tomota, Y., Ozawa, M.: Strength and ductility of Fe–Ni–C alloys composed of austenite and martensite with various strength. In: Proceedings of 3rd International Conference on Strength and Metal Alloys, vol. 1, pp. 611-615, Cambridge (1973)

Jin, Z.H., Paulino, G.H., Dodds, R.H., Jr.: Cohesive fracture modeling of elastic plastic crack growth in functionally graded materials. Eng. Fract. Mech. 70, 1885–1912 (2003). https://doi.org/10.1016/S0013-7944(03)00130-9

Pacoste, C., Eriksson, A.: Beam elements in instability problems. Comput. Methods Appl. Mech. Eng. 144, 163–197 (1997). https://doi.org/10.1016/S0045-7825(96)01165-6

Antman, S.S.: Nonlinear Problems of Elasticity. Springer, New York (1995)

Cook, R.R., Malkus, D.S., Plesha, M.E., Witt, R.J.: Concepts and Applications of Finite Element Analysis, 4th edn. Wiley, New York (2002)

Crisfield, M.A.: Non-linear Finite Element Analysis of Solids and Structures, Volume 1: Essentials. Wiley, Chichester (1991)