The MLPG in gradient theory for size-dependent magnetoelectroelasticity
Jan Sladek1, Vladimir Sladek1
, Slavomir Hrcek2
1Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia.
2Faculty of Mechanical Engineering, University of Zilina, 01026 Zilina, Slovakia.
DOI:
https://doi.org/10.7494/cmms.2017.1.0578
Abstract:
The strain gradient magnetoelectroelasticity is applied to solve two-dimensional boundary value problems. The electric and magnetic field-strain gradient coupling is considered in constitutive equations. The meshless local Petrov-Galerkin (MLPG) is developed to solve general problems. All field quantities are approximated by the moving least-squares (MLS) scheme. Effective material properties for a piezomagnetic matrix with regularly distributed piezoelectric fibres of a circular cross section and coating layer are presented.
Cite as:
Sladek, J., Sladek, V., Hrcek, S. (2017). The MLPG in gradient theory for size-dependent magnetoelectroelasticity. Computer Methods in Materials Science, 17(1), 76 – 82. https://doi.org/10.7494/cmms.2017.1.0578
Article (PDF):
![](https://www.cmms.agh.edu.pl/wp-content/uploads/2020/04/pdf_small.png)
Keywords:
Meshless approximation, Local integral equations, MLS approximation, Effective material properties
References:
Atluri, S.N., 2004, The Meshless Method (MLPG) for Domainand BIE Discretizations, Tech Science Press, Forsyth.
Bishay, P.L., Sladek, J., Sladek, V., Atluri, S.N. 2012, Analysisof functionally graded multiferroic composites using hybrid/mixed finite elements and node-wise material properties,CMC: Computers, Materials & Continua, 29,213-262.
Cross, L.E. 2006, Flexoelectric effects: charge separation ininsulating solids subjected to elastic strain gradients, J.Mater. Sci., 41, 53-63.
Hu, S.L., Shen, S.P. 2009, Electric field gradient theory withsurface effect for nano-dielectrics, CMC: Computers,Materials & Continua, 13, 63-87.
Ke, L. L., Wang, Y.S., Wang, Z.D. 2012, Nonlinear vibration ofthe piezoelectric nanobeams based on the nonlocal theory,Comp. Struct., 94, 2038-2047.
Kuo, H.Y., Wang, Y.L. 2012, Optimization of magnetoelectricityin multiferroic fibrous composites. Mechanics of Materials,50, 88-99.
Liang, X., Shen, S.P. 2013, Size-dependent piezoelectricity andelasticity due to the electric field-strain gradient couplingand strain gradient elasticity, Int. J. Appl. Mech., 5,1350015.
Liang, X., Hu, S., Shen, S. 2013, Bernoulli-Euler dielectricbeam model based on strain-gradient effect, J. Appl.Mech., 80, 044502-6.
Murmu, T., Pradhan, S.C. 2009, Thermo-mechanical vibrationof a single-walled carbon nanotube embedded in an elasticmedium based on nonlocal elasticity theory, Comput.Mater. Sci., 46, 854-859.
Pan, E., Chen, W. 2015, Static Green’s Functions in AnisotropicMedia, Cambridge University Press, New York.
Ryu, J., Priya, S., Uchino, K., Kim, H.E. 2002, Magnetoelectriceffect in composites of magnetostrictive andpiezoelectric materials, Jour. Electroceramics, 8, 107-119.
Sladek, J., Stanak, P., Han, Z.D., Sladek, V. Atluri, S.N., 2013,Applications of the MLPG method in engineering & sciences:A review, CMES-Computer Model. Engn. Sci.,92, 423-475.
Sladek, J., Sladek, V., Pan, E. 2016a, Effective properties ofcoated fiber-composites with piezoelectric andpiezomagnetic phases. Jour. Intell. Mater. Syst. Struct.,DOI: 10.1177/1045389X16644786.
Sladek, J., Sladek, V., Pan, E. 2016b, Effective properties ofcoated fiber-composites with piezoelectric andpiezomagnetic phases. Int. J. Solids Struct. DOI:10.1016/j.ijsolstr.2016.08.011 .
Tang, Z., Xu, Y., Li, G., Aluru, N.R. 2005, Physical models forcoupled electromechanical analysis of silicon nanoelectromechanicalsystems, J. Appl. Phys., 97, 114304.