Journal of Applied Science and Engineering

Published by Tamkang University Press


Impact Factor



Kuan-Chung LinThis email address is being protected from spambots. You need JavaScript enabled to view it., Wei-Lun Chen, and Yi Yang

Department of Civil Engineering, National Cheng Kung University, Tainan, 70101, Taiwan



Received: January 3, 2024
Accepted: March 4, 2024
Publication Date: April 13, 2024

 Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||  

This research utilizes a meshfree nodal integration technique to analyze the static loading of Magneto-ElectroElastic (MEE) beams, a type of intelligent material. The shape function is constructed using the Reproducing Kernel Particle Method (RKPM), and numerical integration is carried out using Stabilized Conforming Node Integration (SCNI). If oscillations or errors occur, corrections are made with Naturally Stabilized Nodal Integration (NSNI). The study focuses on electromagnetic elastomers, intelligent materials characterized by physical field conversion coupling characteristics. Numerical example tests demonstrate that the NSNI correction method effectively improves the computational results of the SCNI method. The corrections bring the results closer to those produced by the Finite Element Method and enhance oscillation control, particularly under conditions of fixed beam and concentrated loading. This study demonstrates the effective application of the meshfree method of nodal discretization for the efficient analysis of physical multiple coupling problems within MEE materials, introducing a novel approach to the field.

Keywords: Meshfree methods, Reproducing Kernel Particle Method (RKPM); Stable Conforming Nodal Integration (SCNI); Naturally Stabilized Nodal Integration (NSNI); Mgneto-electro-elastic material

  1. [1] J.-W. Sohn and S.-B. Choi, (2017) “Various robots made from piezoelectric materials and electroactive polymers: a review" International Journal of Mechanical Systems Engineering 3(1): 122. DOI: 10.15344/2455-7412/2017/122.
  2. [2] Y. Wang, X. Xu, and L. Li, (2023) “Advances in Tunable Bandgaps of Piezoelectric Phononic Crystals" Materials 16(18): 6285. DOI: 10.3390/ma16186285.
  3. [3] Z. Han, P. Jiao, and Z. Zhu, (2021) “Combination of piezoelectric and triboelectric devices for robotic selfpowered sensors" Micromachines 12(7): 813. DOI: 10.3390/mi12070813.
  4. 4] M. Ju, Z. Dou, J.-W. Li, X. Qiu, B. Shen, D. Zhang, F.-Z. Yao, W. Gong, and K. Wang, (2023) “Piezoelectric Materials and Sensors for Structural Health Monitoring: Fundamental Aspects, Current Status, and Future Perspectives" Sensors 23(1): 543. DOI: 10.3390/s23010543.
  5. [5] S. Aimmanee and C. Phongsitthisak, (2022) “Analysis of electrical energy harvesting from piezoelectric integrated shallow conical composite shells in metastable configurations using mixed formulation" Composite Structures 282: 115031. DOI: 10.1016/j.compstruct.2021.115031.
  6. [6] C. Bazilo, A. Zagorskis, O. Petrishchev, Y. Bondarenko, V. Zaika, and Y. Petrushko. “Modelling of piezoelectric transducers for environmental monitoring”. In: Proceedings of 10th International Conference “Environmental Engineering”, Vilnius Gediminas Technical University, Lithuania. 2017. DOI: 10.3846/enviro.2017.008.
  7. [7] J. Van Suchtelen, (1972) “Product properties: a new application of composite materials" Phillips Research Reports 27: 28–37. DOI: 10.1299/jsmea.48.151.
  8. [8] A. Van Run, D. Terrell, and J. Scholing, (1974) “An in situ grown eutectic magnetoelectric composite material: part 2 physical properties" Journal of Materials Science 9: 1710–1714.
  9. [9] A.-M. Jiang and H.-J. Ding, (2004) “Analytical solutions to magneto-electro-elastic beams" Structural Engineering and Mechanics, An Int’l Journal 18(2): 195–209.
  10. [10] A.-M. Jiang, H.-J. Ding, and G.-Q. Wu, (2006) “Green’s Functions for a Two-Phase Infinite Magneto-ElectroElastic Plane" Multidiscipline Modeling in Materials and Structures 2(1): 67–82. DOI: 10.1163/157361106775249934.
  11. [11] F. C. Buroni and A. Sáez, (2010) “Three-dimensional Green’s function and its derivative for materials with general anisotropic magneto-electro-elastic coupling" Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466(2114): 515–537. DOI: 10.1098/rspa.2009.0389.
  12. [12] J. Sládek, V. Sladék, S. Krahulec, and E. Pan, (2013) “The MLPG analyses of large deflections of magnetoelectroelastic plates" Engineering Analysis with Boundary Elements 37(4): 673–682. DOI: 10.1016/j.enganabound.2013.02.001.
  13. [13] J. Sládek, V. Sladék, S. Krahulec, C.-S. Chen, and D.-L. Young, (2015) “Analyses of circular magnetoelectroelastic plates with functionally graded material properties" Mechanics of Advanced Materials and Structures 22(6): 479–489. DOI: 10.1080/15376494.2013.807448.
  14. [14] J. Liu, P.-C. Zhang, G. Lin, W.-Y. Wang, and S. Lu, (2016) “Solutions for the magneto-electro-elastic plate using the scaled boundary finite element method" Engineering Analysis with Boundary Elements 68: 103– 114. DOI: 10.1016/j.enganabound.2016.04.005.
  15. [15] V. Mahesh and S. Kattimani, (2017) “A 3D finite element static and free vibration analysis of magneto-electroelastic beam" Coupled Systems Mechanics 6: 465–485.
  16. [16] P.-C. Zhang, C.-Z. Qi, H.-Y. Fang, and X. Sun, (2021) “Free vibration analysis of functionally graded magneto-electro-elastic plates with in-plane material heterogeneity" Journal of Intelligent Material Systems and Structures 32(11): 1234–1255. DOI: 10.1177/1045389X20975487.
  17. [17] W.-K. Liu, S. Jun, and Y.-F. Zhang, (1995) “Reproducing kernel particle methods" International Journal for Numerical Methods in Fluids 20(8-9): 1081–1106. DOI: 10.1002/fld.1650200824.
  18. [18] L. B. Lucy, (1977) “A numerical approach to the testing of the fission hypothesis" Astronomical Journal 82: 1013–1024.
  19. [19] M. Hillman, J.-S. Chen, and Y. Bazilevs, (2015) “Variationally consistent domain integration for isogeometric analysis" Computer Methods in Applied Mechanics and Engineering 284: 521–540. DOI: 10.1016/j.cma.2014.10.004.
  20. [20] J.-S. Chen, C.-T. Wu, S. Yoon, and Y. You, (2001) “A stabilized conforming nodal integration for Galerkin meshfree methods" International journal for numerical methods in engineering 50(2): 435–466.
  21. [21] M. Hillman and J.-S. Chen, (2016) “An accelerated, convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics" International Journal for Numerical Methods in Engineering 107(7): 603–630. DOI: 10.1002/nme.5183.
  22. [22] D. Wang and J. Wu, (2019) “An inherently consistent reproducing kernel gradient smoothing framework toward efficient Galerkin meshfree formulation with explicit quadrature" Computer Methods in Applied Mechanics and Engineering 349: 628–672. DOI: 10.1016/j.cma.2019. 02.029.
  23. [23] J. Wu and D. Wang, (2021) “An accuracy analysis of Galerkin meshfree methods accounting for numerical integration" Computer Methods in Applied Mechanics and Engineering 375: 113631. DOI: 10.1016/j.cma.2020.113631.
  24. [24] H. Du, J. Wu, D. Wang, and J. Chen, (2022) “A unified reproducing kernel gradient smoothing Galerkin meshfree approach to strain gradient elasticity" Computational Mechanics 70(1): 73–100. DOI: 10.1007/s00466-022-02156-z.
  25. [25] W. K. Liu, S. Jun, and Y. F. Zhang, (1995) “Reproducing kernel particle methods" International Journal for Numerical Methods in Fluids 20(8-9): 1081–1106.
  26. [26] J.-S. Chen, C. Pan, C.-T. Wu, and W. K. Liu, (1996) “Reproducing Kernel Particle Methods for large deformation analysis of non-linear structures" Computer Methods in Applied Mechanics and Engineering 139(1-4): 195–227. DOI: 10.1016/S0045-7825(96)01083-3.
  27. [27] S. A. Kah and J.-X. Liu, (2005) “On the constitutive equations of magnetoelectroelastic solids" Journal of Intelligent Material Systems and Structures 16(7-8): 597–602. DOI: 10.1177/1045389X050516.
  28. [28] K.-J. Bathe. Finite element procedures. Klaus-Jurgen Bathe, 2006.
  29. [29] T.-H. Huang, H. Wei, J.-S. Chen, and M. Hillman, (2020) “RKPM2D: an open-source implementation of nodally integrated reproducing kernel particle method for solving partial differential equations" Computational particle mechanics 7: 393–433. DOI: 10.1007/s40571-019-00272-x.
  30. [30] J.-S. Chen, C.-H. Pan, C.-T. Wu, and W.-K. Liu, (1996) “Reproducing kernel particle methods for large deformation analysis of non-linear structures" Computer methods in applied mechanics and engineering 139(1-4): 195–227. DOI: 10.1016/S0045-7825(96)01083-3.
  31. [31] J.-S. Chen, M. Hillman, and M. Rüter, (2013) “An arbitrary order variationally consistent integration for Galerkin meshfree methods" International Journal for Numerical Methods in Engineering 95(5): 387–418. DOI: 10.1002/nme.4512.
  32. [32] A. Annigeri, N. Ganesan, and S. Seetharaman. “Static studies on magneto-electro-elastic beam”. In: Proceedings of the ISSS 2005 International Conference on Smart Materials Structures and Systems, Bangalore. 2005.



60th percentile
Powered by  Scopus

SCImago Journal & Country Rank

Enter your name and email below to receive latest published articles in Journal of Applied Science and Engineering.