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Design and thermo-mechanical analysis of sandwich structures with negative thermal expansion

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Abstract

In this study, an analytical model based on Classic Laminate Theory was developed for the prediction of effective thermal expansion coefficients (ETECs) of general angle-ply laminates (symmetrical and asymmetrical). Examples are given of the applications of the analytical solution to the prediction of the ETEC of sandwich structures with fiber reinforced composite (FRC) core for various ply angles. The proposed analytical solutions are applied to predict the ETEC of laminate structures with fiber reinforced composite core for various ply angles. Laminate structures with negative thermal expansion (NTE) are obtained and considered as special cases of interest. For an extreme case, a laying angle of [0Ti/(± 30)2S/0Ti] and [0Ti/(± 60)2S/0Ti] along with an NTE of -1.335 × 10–5/K has been achieved. Meanwhile, Finite Strip Method is extended to the framework of first order shear theory, and the corresponding governing equations are established. With the help of the Bolotin method, the dynamic instability region of the sandwich structures with NTE is obtained. Numerical results show that the thermal vibration, buckling and dynamic instability behaviors may be adjusted and controlled by changing the TEC and stacking configurations. The present analytical results are not only theoretical fundament for understanding the interrelationship between the mechanical and temperature dependent material properties and the shrinkage of the structures but also serve as guiding NTE design of structures.

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References

  • Akula, V.M.K., Garnich, M.R.: Effective ply and constituent elastic properties for cracked laminates. Compos. B Eng. 43, 2143–2151 (2012)

    Article  Google Scholar 

  • Bolotin, V.V.: The dynamic stability of elastic systems: San Francisco. Holden-day Inc, CA (1964)

    Google Scholar 

  • Castigliano CA. Elastic stresses in structures (Translated by E. S. Andrews). London: Scott, Greenwood, and Son,1919

  • Chen, X.H., Shen, H.S., Huang, X.H.: Thermo-mechanical postbuckling analysis of sandwich plates with functionally graded auxetic GRMMC core on elastic foundations. Compos. Struct. 279, 114796 (2022)

    Article  Google Scholar 

  • Dinh Dat, N., Quoc Quan, T., Dinh, D.N.: Vibration analysis of auxetic laminated plate with magneto-electro-elastic face sheets subjected to blast loading. Compos. Struct. 280, 114925 (2022)

    Article  Google Scholar 

  • Dong, C., Li, K., Jiang, Y., Arola, D., Zhang, D.: Evaluation of thermal expansion coefficient of carbon fiber reinforced composites using electronic speckle interferometry. Opt. Express 26, 531 (2018)

    Article  Google Scholar 

  • Dove, M.T., Fang, H.: Negative thermal expansion and associated anomalous physical properties: review of the lattice dynamics theoretical foundation. Rep. Prog. Phys. 79, 66503 (2016)

    Article  Google Scholar 

  • Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc Royal Soc London Ser A. Math. Phys. Sci. 241, 376-396 (1957)

    MathSciNet  MATH  Google Scholar 

  • Fan, Y., Xiang, Y., Shen, H.S.: Temperature-dependent negative Poisson’s ratio of monolayer graphene: prediction from molecular dynamics simulations. Nanotechnol. Rev. 8, 415–421 (2019)

    Article  Google Scholar 

  • Galiakhmetova, E.A., Korznikova, A.A., KudreykoDmitriev, S.V.: Negative thermal expansion of carbon nanotube bundles. Phys Status Solidi (RRL) – Rapid Res. Lett. 16(3), 2100415 (2021). https://doi.org/10.1002/pssr.202100415

    Article  Google Scholar 

  • Kim, N., Shin, D.K., Park, Y.: Dynamic stiffness matrix of thin-walled composite I-beam with symmetric and arbitrary laminations. J. Sound Vib. 318, 364–388 (2008)

    Article  Google Scholar 

  • Lee, D., Song, Y.S.: Modeling the effects of elastic modulus and thermal expansion coefficient on the shrinkage of glass fiber reinforced composites. Compos. B Eng. 146, 98–105 (2018)

    Article  Google Scholar 

  • Li, Y., Chen, Y., Li, T., Cao, S., Wang, L.: Hoberman-sphere-inspired lattice metamaterials with tunable negative thermal expansion. Compos. Struct. 189, 586–597 (2018)

    Article  Google Scholar 

  • Li, C., Shen, H.S., Wang, H.: Nonlinear bending of sandwich beams with functionally graded negative Poisson’s ratio honeycomb core. Compos. Struct. 212, 317–325 (2019a)

    Article  Google Scholar 

  • Li, C., Shen, H.S., Wang, H.: Nonlinear dynamic response of sandwich beams with functionally graded negative Poisson’s ratio honeycomb core. Europ Phys J plus (2019b). https://doi.org/10.1140/epjp/i2019-12572-7

    Article  Google Scholar 

  • Li, C., Shen, H.S., Wang, H.: Nonlinear dynamic response of sandwich plates with functionally graded auxetic 3D lattice core. Nonlinear Dyn. 100, 3235–3252 (2020)

    Article  Google Scholar 

  • Lim, T.C.: Coefficient of thermal expansion of stacked auxetic and negative thermal expansion laminates. Phys Status Solidi (b) 248(1), 140–147 (2011). https://doi.org/10.1002/pssb.200983970

    Article  Google Scholar 

  • Liu, T.Q., Vieira, J.D., Harries, K.A.: Predicting Flange Local Buckling Capacity of Pultruded GFRP I-Sections Subject to Flexure. J. Compos. Constr. 24, 4020025 (2020)

    Article  Google Scholar 

  • McCartney, L.N., Kelly, A.: Effective thermal and elastic properties of [+θ/−θ]s laminates. Compos. Sci. Technol. 67, 646–661 (2007)

    Article  Google Scholar 

  • Patel, S.N., Datta, P.K., Sheikh, A.H.: Buckling and dynamic instability analysis of stiffened shell panels. Thin-Walled Structures. 44, 321–333 (2006)

    Article  Google Scholar 

  • Peng, X., Bargmann, S.: A novel hybrid-honeycomb structure: Enhanced stiffness, tunable auxeticity and negative thermal expansion. Int. J. Mech. Sci. 190, 106021 (2021)

    Article  Google Scholar 

  • Quang, V.D., Quan, T.Q., Tran, P.: Static buckling analysis and geometrical optimization of magneto-electro-elastic sandwich plate with auxetic honeycomb core. Thin-Walled Struct. 173, 108935 (2022)

    Article  Google Scholar 

  • Raminhos, J.S., Borges, J.P., Velhinho, A.: Development of polymeric anepectic meshes: auxetic metamaterials with negative thermal expansion. Smart Mater. Struct. 28, 45010 (2019)

    Article  Google Scholar 

  • Reddy JN. Mechanics of Laminated Composite Plates: Theory and Analysis: CRC Press, Boca Raton,FL, 1997

  • Romanowicz, M.: Prediction of elastic moduli of angle-ply laminates from various rhombohedral unit cells. Mech. Adv. Mater. Struct. 26, 307–313 (2019)

    Article  Google Scholar 

  • Shen, H.S.: Hygrothermal effects on the postbuckling of shear deformable laminated plates. Int. J. Mech. Sci. 43, 1259–1281 (2001)

    Article  MATH  Google Scholar 

  • Shen, H.S.: Functionally Graded Materials Nonlinear Analysis of Plates and Shells. Boca Raton, CRC Press (2009)

    Google Scholar 

  • Scheel, K.: Versuche ueber die ausdehnung fester koerper, insbesondere von quarz in richtung der hauptachse, platin, palladium und quarzglas bei der temperatur der fluessigen Luft. Verh. Deutsch. Phys. Ges. 9, 3–23 (1907)

    Google Scholar 

  • Vo, T.P., Lee, J.: Flexural–torsional coupled vibration and buckling of thin-walled open section composite beams using shear-deformable beam theory. Int. J. Mech. Sci. 51, 631–641 (2009)

    Article  Google Scholar 

  • Wei, K., Peng, Y., Wang, K., Duan, S., Yang, X., Wen, W.: Three dimensional lightweight lattice structures with large positive, zero and negative thermal expansion. Compos. Struct. 188, 287–296 (2018)

    Article  Google Scholar 

  • Yoon, K.J., Kim, J.S.: Prediction of thermal expansion properties of carbon/epoxy laminates for temperature variation. J. Compos. Mater. 34, 90–100 (2000)

    Article  Google Scholar 

  • Yu, Y., Shen, H.S.: A Comparison of nonlinear bending and vibration of hybrid metal/CNTRC laminated beams with positive and negative poisson’s ratios. Int. J Struct Stabil Dynam 20(14), 2043007 (2020a). https://doi.org/10.1142/S0219455420430075

    Article  MathSciNet  Google Scholar 

  • Yu, Y., Shen, H.S.: A comparison of nonlinear vibration and bending of hybrid CNTRC/metal laminated plates with positive and negative Poisson’s ratios. Int. J. Mech. Sci. 183, 105790 (2020b)

    Article  Google Scholar 

  • Zhang, C.L., Shen, H.S.: Temperature-dependent elastic properties of single-walled carbon nanotubes: Prediction from molecular dynamics simulation. Appl. Phys. Lett. 89, 81904 (2006)

    Article  Google Scholar 

  • Zhao, S., Zhang, Y., Chen, D., Yang, J., Kitipornchai, S.: Enhanced thermal buckling resistance of folded graphene reinforced nanocomposites with negative thermal expansion: From atomistic study to continuum mechanics modelling. Compos. Struct. 279, 114872 (2022)

    Article  Google Scholar 

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Acknowledgements

The authors acknowledge the financial support received from National Natural Science Foundation of China (No. 12102214, 11972203). The second author also wishes to acknowledge the project of the Program of Scientific and Technological Innovation (Xinmiao Program) of Zhejiang Province (No. 2022R405A017). The fifth author wishes to acknowledge the project of Key Laboratory of Urban Rail Transit Intelligent Operation and Maintenance Technology & Equipment of Zhejiang Province (No. ZSDRTKF2021006). The fourth author wishes to acknowledge the Ningbo Municipal Natural Science Foundation (No. 202003N4152).

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Authors and Affiliations

  1. Zhejiang Provincial Engineering Research Center for the Safety of Pressure Vessel and Pipeline, Key Laboratory of Impact and Safety Engineering, Ministry of Education, Faculty of Mechanical Engineering and Mechanics, Ningbo University, Ningbo, 315211, People’s Republic of China

    Meng-Jing Wu, Si-Yu Zhao, Jue Zhu & Xu-Hao Huang

  2. Key Laboratory of Urban Rail Transit Intelligent Operation and Maintenance Technology & Equipment of Zhejiang Province, Zhejiang Normal University, Zhejiang, 321004, China

    Meng-Jing Wu & Xu-Hao Huang

  3. Public Health Engineering Department, Government of KPK, Peshawar, 25000, Pakistan

    Iftikhar Azim

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  1. Meng-Jing Wu
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  2. Si-Yu Zhao
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  3. Iftikhar Azim
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  4. Jue Zhu
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  5. Xu-Hao Huang
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Correspondence to Meng-Jing Wu or Xu-Hao Huang.

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Wu, MJ., Zhao, SY., Azim, I. et al. Design and thermo-mechanical analysis of sandwich structures with negative thermal expansion. Int J Mech Mater Des 18, 807–822 (2022). https://doi.org/10.1007/s10999-022-09609-6

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  • DOI: https://doi.org/10.1007/s10999-022-09609-6

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