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Acta Mechanica

, Volume 230, Issue 5, pp 1641–1662 | Cite as

Coupling magneto-electro-elastic cell-based smoothed radial point interpolation method for static and dynamic characterization of MEE structures

  • Liming Zhou
  • Bin Nie
  • Shuhui Ren
  • Ruiyao Liu
  • Xiaolin Li
  • Bing XueEmail author
Original Paper
  • 74 Downloads

Abstract

To increase the computational precision of the finite element method (FEM) for multi-field coupling problems, we proposed a coupling magneto-electro-elastic (MEE) cell-based smoothed radial point interpolation method (CM-CS-RPIM) with the coupling MEE Wilson-\(\theta \) scheme for MEE structures. Generalized approximation field functions were established by using the linearly independent and consistent RPIM shape functions. The basic equations of CM-CS-RPIM were deduced by applying G space theory and the weakened weak formulation to the MEE multi-physics coupling field. Meanwhile, the coupling MEE Wilson-\(\theta \) scheme was proposed. Several numerical examples were modeled, and the behavior of MEE structures was studied under static and dynamic loads. The CM-CS-RPIM outperformed FEM with higher accuracy, convergence, and stability in static and dynamic analysis of MEE structures, even if the meshes were distorted extremely. And it worked well with simplex meshes (triangles or tetrahedrons) that can be automatically generated for complex structures. Therefore, the effectiveness and potential of CM-CS-RPIM were demonstrated for the design of smart devices, such as MEE sensors and energy harvesters.

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Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11502092); Jilin Provincial Science Foundation for Youths (Grant No. 20160520064JH); Foundation Sciences Jilin Provincial (Grant No. 20170101043JC); Educational Commission of Jilin Province of China (Grant Nos. JJKH20180084KJ and JJKH20190131KJ); Graduate Innovation Fund of Jilin University (Grant No. 101832018C184); Fundamental Research Funds for the Central Universities.

Author’s contribution

LZ and BX contributed to the research concept and design. BN and SR contributed to the writing the article. RL and XL contributed to collection of data. BX contributed to the research concept, design and data analysis.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest.

Data availability

All data included in this study are available upon request by contact with the corresponding author.

References

  1. 1.
    Sadovnikov, A.V., Grachev, A.A., Beginin, E.N., Sheshukova, S.E., Sharaevskii, Y.P., Nikitov, S.A.: Voltage-controlled spin-wave coupling in adjacent ferromagnetic-ferroelectric heterostructures. Phys. Rev. Appl. (2017).  https://doi.org/10.1103/PhysRevApplied.7.014013
  2. 2.
    Wu, L., Salehi, M., Koirala, N., Moon, J., Oh, S., Armitage, N.P.: Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator. Science 354(6316), 1124–1127 (2016)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Serpilli, M.: Asymptotic interface models in magneto-electro-thermo-elastic composites. Meccanica 52(6), 1407–1424 (2017).  https://doi.org/10.1007/s11012-016-0481-4 MathSciNetzbMATHGoogle Scholar
  4. 4.
    Sarkar, N., Lahiri, A.: The effect of fractional parameter on a perfect conducting elastic half-space in generalized magneto-thermoelasticity. Meccanica 48(1), 231–245 (2013).  https://doi.org/10.1007/s11012-012-9597-3 MathSciNetzbMATHGoogle Scholar
  5. 5.
    Jamalpoor, A., Ahmadi-Savadkoohi, A., Hosseini, M., Hosseini-Hashemi, S.: Free vibration and biaxial buckling analysis of double magneto-electro-elastic nanoplate-systems coupled by a visco-Pasternak medium via nonlocal elasticity theory. Eur. J. Mech. A Solids 63, 84–98 (2017).  https://doi.org/10.1016/j.euromechsol.2016.12.002 MathSciNetzbMATHGoogle Scholar
  6. 6.
    Mundy, J.A., Brooks, C.M., Holtz, M.E., Moyer, J.A., Das, H., Rebola, A.F., Heron, J.T., Clarkson, J.D., Disseler, S.M., Liu, Z.Q., Farhan, A., Held, R., Hovden, R., Padgett, E., Mao, Q.Y., Paik, H., Misra, R., Kourkoutis, L.F., Arenholz, E., Scholl, A., Borchers, J.A., Ratcliff, W.D., Ramesh, R., Fennie, C.J., Schiffer, P., Muller, D.A., Schlom, D.G.: Atomically engineered ferroic layers yield a room-temperature magnetoelectric multiferroic. Nature 537(7621), 523 (2016).  https://doi.org/10.1038/nature19343 Google Scholar
  7. 7.
    Pan, E.: Exact solution for simply supported and multilayered magneto-electro-elastic plates. J. Appl. Mech. Trans. ASME 68(4), 608–618 (2001).  https://doi.org/10.1115/1.1380385 zbMATHGoogle Scholar
  8. 8.
    Pan, E., Heyliger, P.R.: Free vibrations of simply supported and multilayered magneto-electro-elastic plates. J. Sound Vib. 252(3), 429–442 (2002).  https://doi.org/10.1006/jsvi.2001.3693 Google Scholar
  9. 9.
    Pan, E.: Three-dimensional Green’s functions in anisotropic magneto-electro-elastic bimaterials. Z. Angew. Math. Phys. 53(5), 815–838 (2002).  https://doi.org/10.1007/s00033-002-8184-1 MathSciNetzbMATHGoogle Scholar
  10. 10.
    Pan, E., Han, F.: Exact solution for functionally graded and layered magneto-electro-elastic plates. Int. J. Eng. Sci. 43(3–4), 321–339 (2005)Google Scholar
  11. 11.
    Du, J., Jin, X., Wang, J.: Love wave propagation in layered magneto-electro-elastic structures with initial stress. Acta Mech. 192(1–4), 169–189 (2007).  https://doi.org/10.1007/s00707-006-0435-3 zbMATHGoogle Scholar
  12. 12.
    Arefi, M., Zenkour, A.M.: Wave propagation analysis of a functionally graded magneto-electro-elastic nanobeam rest on Visco-Pasternak foundation. Mech. Res. Commun. 79, 51–62 (2017)Google Scholar
  13. 13.
    Arefi, M., Zenkour, A.M.: Influence of magnetoelectric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory. J. Sandw. Struct. Mater. (2017).  https://doi.org/10.1177/1099636217723186
  14. 14.
    Arefi, M., Zenkour, A.M.: Transient sinusoidal shear deformation formulation of a size-dependent three-layer piezo-magnetic curved nanobeam. Acta Mech. 228(10), 3657–3674 (2017)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Arefi, M., Zenkour, A.M.: Size-dependent free vibration and dynamic analyses of piezo-electromagnetic sandwich nanoplates resting on viscoelastic foundation. Phys. B Condens. Matter 521, 188–197 (2017).  https://doi.org/10.1016/j.physb.2017.06.066 Google Scholar
  16. 16.
    Wang, H.M., Ding, H.J.: Transient responses of a special non-homogeneous magneto-electro-elastic hollow cylinder for a fully coupled axisymmetric plane strain problem. Acta Mech. 184(1–4), 137–157 (2006).  https://doi.org/10.1007/s00707-006-0338-3 zbMATHGoogle Scholar
  17. 17.
    Chen, J.Y., Ding, H.J., Hou, P.F.: Analytical solutions of simply supported magnetoelectroelastic circular plate under uniform loads. J. Zhejiang Univ. Sci. A 4(5), 560–564 (2003).  https://doi.org/10.1631/jzus.2003.0560 Google Scholar
  18. 18.
    Jiang, A.M., Ding, H.J.: Analytical solutions to magneto-electro-elastic beams. Struct. Eng. Mech. 18(2), 195–209 (2004)Google Scholar
  19. 19.
    Huang, D.J., Ding, H.J., Chen, W.Q.: Analytical solution for functionally graded magneto-electro-elastic plane beams. Int. J. Eng. Sci. 45(2–8), 467–485 (2007)Google Scholar
  20. 20.
    Li, X.Y., Ding, H.J., Chen, W.Q.: Three-dimensional analytical solution for functionally graded magneto-electro-elastic circular plates subjected to uniform load. Compos. Struct. 83(4), 381–390 (2008)Google Scholar
  21. 21.
    Liu, M.F., Chang, T.P.: Closed form expression for the vibration problem of a transversely isotropic magneto-electro-elastic plate. J. Appl. Mech. Trans. ASME 77(2), 024502 (2010).  https://doi.org/10.1115/1.3176996 Google Scholar
  22. 22.
    Pakam, N., Arockiarajan, A.: An analytical model for predicting the effective properties of magneto-electro-elastic (MEE) composites. Comput. Mater. Sci. 65, 19–28 (2012).  https://doi.org/10.1016/j.commatsci.2012.07.003 Google Scholar
  23. 23.
    Elloumi, R., El-Borgi, S., Guler, M.A., Kallel-Kamoun, I.: The contact problem of a rigid stamp with friction on a functionally graded magneto-electro-elastic half-plane. Acta Mech. 227(4), 1123–1156 (2016).  https://doi.org/10.1007/s00707-015-1504-2 MathSciNetzbMATHGoogle Scholar
  24. 24.
    Makvandi, H., Moradi, S., Poorveis, D., Shirazi, K.H.: A new approach for nonlinear vibration analysis of thin and moderately thick rectangular plates under inplane compressive load. J. Comput. Appl. Mech. 48(2), 185–198 (2017).  https://doi.org/10.22059/jcamech.2017.240726.181 Google Scholar
  25. 25.
    Waksmanski, N., Pan, E.: An analytical three-dimensional solution for free vibration of a magneto-electro-elastic plate considering the nonlocal effect. J. Intell. Mater. Syst. Struct. 28(11), 1501–1513 (2016).  https://doi.org/10.1177/1045389x16672734 Google Scholar
  26. 26.
    Lezgy-Nazargah, M., Cheraghi, N.: An exact Peano Series solution for bending analysis of imperfect layered functionally graded neutral magneto-electro-elastic plates resting on elastic foundations. Mech. Adv. Mater. Struct. 24(3), 183–199 (2017)Google Scholar
  27. 27.
    Shishesaz, M., Shirbani, M.M., Sedighi, H.M., Hajnayeb, A.: Design and analytical modeling of magneto-electro-mechanical characteristics of a novel magneto-electro-elastic vibration-based energy harvesting system. J. Sound Vib. 425, 149–169 (2018).  https://doi.org/10.1016/j.jsv.2018.03.030 Google Scholar
  28. 28.
    Arefi, M.: Analysis of wave in a functionally graded magneto-electro-elastic nano-rod using nonlocal elasticity model subjected to electric and magnetic potentials. Acta Mech. 227(9), 2529–2542 (2016).  https://doi.org/10.1007/s00707-016-1584-7 MathSciNetzbMATHGoogle Scholar
  29. 29.
    Arefi, M., Zenkour, A.M.: Effect of thermo-magneto-electro-mechanical fields on the bending behaviors of a three-layered nanoplate based on sinusoidal shear-deformation plate theory. J. Sandw. Struct. Mater. (2017).  https://doi.org/10.1177/1099636217697497
  30. 30.
    Arefi, M., Zenkour, A.M.: Thermo-electro-magneto-mechanical bending behavior of size-dependent sandwich piezomagnetic nanoplates. Mech. Res. Commun. 84, 27–42 (2017)Google Scholar
  31. 31.
    Xu, X.J., Deng, Z.C., Zhang, K., Meng, J.M.: Surface effects on the bending, buckling and free vibration analysis of magneto-electro-elastic beams. Acta Mech. 227(6), 1557–1573 (2016).  https://doi.org/10.1007/s00707-016-1568-7 MathSciNetzbMATHGoogle Scholar
  32. 32.
    Buchanan, G.R.: Free vibration of an infinite magneto-electro-elastic cylinder. J. Sound Vib. 268(2), 413–426 (2003).  https://doi.org/10.1016/S0022-460x(03)00357-2 Google Scholar
  33. 33.
    Lage, R.G., Soares, C.M.M., Soares, C.A.M., Reddy, J.N.: Layerwise partial mixed finite element analysis of magneto-electro-elastic plates. Comput. Struct. 82(17–19), 1293–1301 (2004).  https://doi.org/10.1016/j.compstruc.2004.03.026 Google Scholar
  34. 34.
    Daga, A., Ganesan, N., Shankar, K.: Behaviour of magneto-electro-elastic sensors under transient mechanical loading. Sens. Actuators A Phys. 150(1), 46–55 (2009)Google Scholar
  35. 35.
    Moita, J.M.S., Soares, C.M.M., Soares, C.A.M.: Analyses of magneto-electro-elastic plates using a higher order finite element model. Compos. Struct. 91(4), 421–426 (2009).  https://doi.org/10.1016/j.compstruct.2009.04.007 Google Scholar
  36. 36.
    Carrera, E., Nali, P.: Multilayered plate elements for the analysis of multifield problems. Finite Elem. Anal. Des. 46(9), 732–742 (2010).  https://doi.org/10.1016/j.finel.2010.04.001 MathSciNetGoogle Scholar
  37. 37.
    Alaimo, A., Milazzo, A., Orlando, C.: A four-node MITC finite element for magneto-electro-elastic multilayered plates. Comput. Struct. 129, 120–133 (2013).  https://doi.org/10.1016/j.compstruc.2013.04.014 Google Scholar
  38. 38.
    Alaimo, A., Benedetti, L., Milazzo, A.: A finite element formulation for large deflection of multilayered magneto-electro-elastic plates. Compos. Struct. 107, 643–653 (2014).  https://doi.org/10.1016/j.compstruct.2013.08.032 Google Scholar
  39. 39.
    Rao, M.N., Schmidt, R., Schroder, K.U.: Finite rotation FE-simulation and active vibration control of smart composite laminated structures. Comput. Mech. 55(4), 719–735 (2015).  https://doi.org/10.1007/s00466-015-1132-7 MathSciNetzbMATHGoogle Scholar
  40. 40.
    Vinyas, M., Kattimani, S.C.: Static studies of stepped functionally graded magneto-electro-elastic beam subjected to different thermal loads. Compos. Struct. 163, 216–237 (2017).  https://doi.org/10.1016/j.compstruct.2016.12.040 Google Scholar
  41. 41.
    Vinyas, M., Kattimani, S.C.: Finite element evaluation of free vibration characteristics of magneto-electro-elastic rectangular plates in hygrothermal environment using higher-order shear deformation theory. Compos. Struct. (2018).  https://doi.org/10.1016/j.compstruct.2018.06.069
  42. 42.
    Gui, C.Y., Bai, J.T., Zuo, W.J.: Simplified crashworthiness method of automotive frame for conceptual design. Thin Walled Struct. 131, 324–335 (2018)Google Scholar
  43. 43.
    Liu, G.R., Nguyen, T.T., Dai, K.Y., Lam, K.Y.: Theoretical aspects of the smoothed finite element method (SFEM). Int. J. Numer. Methods Eng. 71(8), 902–930 (2007).  https://doi.org/10.1002/nme.1968 MathSciNetzbMATHGoogle Scholar
  44. 44.
    Nguyen-Xuan, H., Rabczuk, T., Bordas, S., Debongnie, J.F.: A smoothed finite element method for plate analysis. Comput. Methods Appl. Mech. Eng. 197(13–16), 1184–1203 (2008)zbMATHGoogle Scholar
  45. 45.
    Nguyen-Xuan, H., Bordas, S., Nguyen-Dang, H.: Smooth finite element methods: convergence, accuracy and properties. Int. J. Numer. Methods Eng. 74(2), 175–208 (2008).  https://doi.org/10.1002/nme.2146 MathSciNetzbMATHGoogle Scholar
  46. 46.
    Zeng, W., Liu, G.R.: Smoothed Finite element methods (S-FEM): an overview and recent developments. Arch. Comput. Methods Eng. 25(2), 397–435 (2018)MathSciNetzbMATHGoogle Scholar
  47. 47.
    Bie, Y.H., Cui, X.Y., Li, Z.C.: A coupling approach of state-based peridynamics with node-based smoothed finite element method. Comput. Methods Appl. Mech. Eng. 331, 675–700 (2018)MathSciNetGoogle Scholar
  48. 48.
    Cui, X.Y., Hu, X.B., Zeng, Y.: A Copula-based perturbation stochastic method for fiber-reinforced composite structures with correlations. Comput. Methods Appl. Mech. Eng. 322, 351–372 (2017)MathSciNetGoogle Scholar
  49. 49.
    Cui, X.Y., Li, S., Feng, H., Li, G.Y.: A triangular prism solid and shell interactive mapping element for electromagnetic sheet metal forming process. J. Comput. Phys. 336, 192–211 (2017)MathSciNetGoogle Scholar
  50. 50.
    Zuo, W.J., Saitou, K.: Multi-material topology optimization using ordered SIMP interpolation. Struct. Multidiscipl. Optim. 55(2), 477–491 (2017)MathSciNetGoogle Scholar
  51. 51.
    Wang, J.G., Liu, G.R.: A point interpolation meshless method based on radial basis functions. Int. J. Numer. Methods Eng. 54(11), 1623–1648 (2002).  https://doi.org/10.1002/nme.489 zbMATHGoogle Scholar
  52. 52.
    Wang, Y.G., Hu, D., Yang, G., Han, X., Gu, Y.T.: An effective sub-domain smoothed Galerkin method for free and forced vibration analysis. Meccanica 50(5), 1285–1301 (2015).  https://doi.org/10.1007/s11012-014-0088-6 MathSciNetzbMATHGoogle Scholar
  53. 53.
    Yang, G., Hu, D., Ma, G.W., Wan, D.T.: A novel integration scheme for solution of consistent mass matrix in free and forced vibration analysis. Meccanica 51(8), 1897–1911 (2016)MathSciNetzbMATHGoogle Scholar
  54. 54.
    Cui, X.Y., Liu, G.R., Li, G.Y.: A cell-based smoothed radial point interpolation method (CS-RPIM) for static and free vibration of solids. Eng. Anal. Bound. Elem. 34(2), 144–157 (2010)MathSciNetzbMATHGoogle Scholar
  55. 55.
    Liu, G.R., Nguyen-Thoi, T., Lam, K.Y.: An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids. J. Sound Vib. 320(4–5), 1100–1130 (2009).  https://doi.org/10.1016/j.jsv.2008.08.027 Google Scholar
  56. 56.
    Li, Y., Liu, G.R., Yue, J.H.: A novel node-based smoothed radial point interpolation method for 2D and 3D solid mechanics problems. Comput. Struct. 196, 157–172 (2018)Google Scholar
  57. 57.
    Feng, S.Z., Cui, X.Y., Chen, F., Liu, S.Z., Meng, D.Y.: An edge/face-based smoothed radial point interpolation method for static analysis of structures. Eng. Anal. Bound. Elem. 68, 1–10 (2016).  https://doi.org/10.1016/j.enganabound.2016.03.016 MathSciNetzbMATHGoogle Scholar
  58. 58.
    Cui, X.Y., Feng, H., Li, G.Y., Feng, S.Z.: A cell-based smoothed radial point interpolation method (CS-RPIM) for three-dimensional solids. Eng. Anal. Bound. Elem. 50, 474–485 (2015).  https://doi.org/10.1016/j.enganabound.2014.09.017 MathSciNetzbMATHGoogle Scholar
  59. 59.
    Cui, X.Y., Feng, S.Z., Li, G.Y.: A cell-based smoothed radial point interpolation method (CS-RPIM) for heat transfer analysis. Eng. Anal. Bound. Elem. 40, 147–153 (2014).  https://doi.org/10.1016/j.enganabound.2013.12.004 MathSciNetzbMATHGoogle Scholar
  60. 60.
    Feng, S.Z., Li, A.M.: Analysis of thermal and mechanical response in functionally graded cylinder using cell-based smoothed radial point interpolation method (vol 65, p 46, 2017). Aerosp. Sci. Technol. 66, 402–402 (2017).  https://doi.org/10.1016/j.ast.2017.05.019 Google Scholar
  61. 61.
    Wu, G., Zhang, J., Li, Y.L., Yin, L.R., Liu, Z.Q.: Analysis of transient thermo-elastic problems using a cell-based smoothed radial point interpolation method. Int. J. Comput. Methods (2016).  https://doi.org/10.1142/S0219876216500237
  62. 62.
    Tootoonchi, A., Khoshghalb, A., Liu, G.R., Khalili, N.: A cell-based smoothed point interpolation method for flow-deformation analysis of saturated porous media. Comput. Geotech. 75, 159–173 (2016).  https://doi.org/10.1016/j.compgeo.2016.01.027 Google Scholar
  63. 63.
    Yao, L.Y., Li, Y.W., Li, L.: A cell-based smoothed radial point interpolation-perfectly matched layer method for two-dimensional acoustic radiation problems. J. Press. Vessel Technol. Trans. ASME (2016).  https://doi.org/10.1115/1.4031720
  64. 64.
    Yao, L.Y., Yu, D.J., Zhou, J.W.: Numerical treatment of 2D acoustic problems with the cell-based smoothed radial point interpolation method. Appl. Acoust. 73(6–7), 557–574 (2012).  https://doi.org/10.1016/j.apacoust.2011.10.011 Google Scholar
  65. 65.
    Liu, G.R., Jiang, Y., Chen, L., Zhang, G.Y., Zhang, Y.W.: A singular cell-based smoothed radial point interpolation method for fracture problems. Comput. Struct. 89(13–14), 1378–1396 (2011)Google Scholar
  66. 66.
    Liu, G.R.: On G space theory. Int. J. Comput. Methods 6(2), 257–289 (2009)MathSciNetzbMATHGoogle Scholar
  67. 67.
    Liu, G.R., Zhang, G.Y.: Smoothed Point Interpolation Method: G Space Theory and Weakened Weak Forms. World Scientific, Singapore (2013)zbMATHGoogle Scholar
  68. 68.
    Zhou, L., Ren, S., Liu, C., Ma, Z.: A valid inhomogeneous cell-based smoothed finite element model for the transient characteristics of functionally graded magneto-electro-elastic structures. Compos. Struct. 208, 298–313 (2019)Google Scholar
  69. 69.
    Arefi, M., Zamani, M.H., Kiani, M.: Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak’s foundation. J. Intell. Mater. Syst. Struct. 29(5), 774–786 (2018)Google Scholar
  70. 70.
    Arefi, M., Kiani, M., Zenkour, A.M.: Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak’s foundation via MCST. J. Sandw. Struct. Mater. (2017).  https://doi.org/10.1177/1099636217734279
  71. 71.
    Zhu, X.Y., Huang, Z.Y., Jiang, A.M., Chen, W.Q., Nishimura, N.: Fast multipole boundary element analysis for 2D problems of magneto-electro-elastic media. Eng. Anal. Bound. Elem. 34(11), 927–933 (2010)MathSciNetzbMATHGoogle Scholar
  72. 72.
    Fu, P., Liu, H., Chu, X.H., Qu, W.Z.: Multiscale finite element method for a highly efficient coupling analysis of heterogeneous magneto-electro-elastic media. Int. J. Multiscale Comput. Eng. 16(1), 77–100 (2018)Google Scholar
  73. 73.
    Annigeri, A.R., Ganesan, N., Swarnamani, S.: Free vibration behaviour of multiphase and layered magneto-electro-elastic beam. J. Sound Vib. 299(1–2), 44–63 (2007)Google Scholar
  74. 74.
    Zhou, L., Li, M., Meng, G., Zhao, H.: An effective cell-based smoothed finite element model for the transient responses of magneto-electro-elastic structures. J. Intell. Mater. Syst. Struct. (2018).  https://doi.org/10.1177/1045389x18781258

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Liming Zhou
    • 1
  • Bin Nie
    • 1
  • Shuhui Ren
    • 1
  • Ruiyao Liu
    • 1
  • Xiaolin Li
    • 1
    • 2
  • Bing Xue
    • 1
    • 3
    Email author
  1. 1.School of Mechanical and Aerospace EngineeringJilin UniversityChangchunPeople’s Republic of China
  2. 2.College of Construction EngineeringJilin UniversityChangchunPeople’s Republic of China
  3. 3.Key Laboratory of Automobile Materials, Ministry of Education, Department of Materials Science and EngineeringJilin UniversityChangchunPeople’s Republic of China

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