Acta Mechanica

, Volume 230, Issue 10, pp 3645–3666 | Cite as

Magneto-electro-elastic node-based smoothed point interpolation method for micromechanical analysis of natural frequencies of nanobeams

  • Liming Zhou
  • Shuhui Ren
  • Bin Nie
  • Hongrong Yang
  • Peng LiuEmail author
Original Paper


As an addition to the traditional finite element method (FEM), the magneto-electro-elastic node-based smoothed point interpolation method (MEE-NS-PIM) with asymptotic homogenization method (AHM) is presented to solve the micromechanical problems of MEE nanobeams, which overcomes the deficiency of FEM and improves the accuracy of the calculation results. Firstly, the basic equations of MEE medium are derived. Secondly, AHM is adopted to calculate the property parameters of MEE materials under microcosmic situations, and the AHM model is illustrated. Then, the relative formulations of the discretized system used to calculate the frequency of MEE nanostructures are deduced based on MEE-NS-PIM. Moreover, several numerical examples are calculated, and the results of MEE-NS-PIM are compared with those of FEM, which proves the convergence, precision, and effectiveness of MEE-NS-PIM. Therefore, MEE-NS-PIM combined with AHM can be used to analyze the microcosmic MEE coupling problems and obtain a more accurate and reliable solution for MEE micromechanics.



This work was supported by the National Natural Science Foundation of China [Grant Number 11502092]; Jilin Provincial Science Foundation for Youths [Grant Number 20160520064JH]; Supported by Graduate Innovation Fund of Jilin University [Grant Number 101832018C184]; Foundation Sciences Jilin Provincial [Grant Number 20170101043JC]; Educational Commission of Jilin Province of China [Grant Numbers JJKH20180084KJ and JJKH20190131KJ].

Author contributions LZ and PL contributed to the research concept and design. SR, BN and HY contributed to the writing of the article and collection of data. PL 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.


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Authors and Affiliations

  1. 1.School of Mechanical and Aerospace EngineeringJilin UniversityChangchunPeople’s Republic of China

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