Coupling magneto-electro-elastic cell-based smoothed radial point interpolation method for static and dynamic characterization of MEE structures
- 74 Downloads
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.
Unable to display preview. Download preview PDF.
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.
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.
All data included in this study are available upon request by contact with the corresponding author.
- 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
- 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.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
- 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
- 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.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
- 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.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.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
- 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.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
- 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.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
- 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
- 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.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
- 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
- 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
- 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
- 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
- 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.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.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
- 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.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.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