Nonlocal buckling of embedded magnetoelectroelastic sandwich nanoplate using refined zigzag theory

doi:10.1007/s10483-018-2319-8

Abstract

Abstract:

This paper is concerned with a buckling analysis of an embedded nanoplate integrated with magnetoelectroelastic (MEE) layers based on a nonlocal magnetoelectroelasticity theory. A surrounding elastic medium is simulated by the Pasternak foundation that considers both shear and normal loads. The sandwich nanoplate (SNP) consists of a core that is made of metal and two MEE layers on the upper and lower surfaces of the core made of BaTiO₃/CoFe₂O₄. The refined zigzag theory (RZT) is used to model the SNP subject to both external electric and magnetic potentials. Using an energy method and Hamilton's principle, the governing motion equations are obtained, and then solved analytically. A detailed parametric study is conducted, concentrating on the combined effects of the small scale parameter, external electric and magnetic loads, thicknesses of MEE layers, mode numbers, and surrounding elastic medium. It is concluded that increasing the small scale parameter decreases the critical buckling loads.

Key words: controllable mechanical system, relativity, variable mass, nonholonomic constraint, variation principle equation or motion, sandwich nanoplate (SNP), nonlocal magnetoelectroelasticity theory, buckling, magnetostrictive layer, refined zigzag theory (RZT)

2010 MSC Number:

A. GHORBANPOUR-ARANI, F. KOLAHDOUZAN, M. ABDOLLAHIAN. Nonlocal buckling of embedded magnetoelectroelastic sandwich nanoplate using refined zigzag theory. Applied Mathematics and Mechanics (English Edition), 2018, 39(4): 529-546.

TrendMD

References

[1] Grover, N., Singh, B. N., and Maiti, D. K. Free vibration and buckling characteristics of laminated composite and sandwich plates implementing a secant function based shear deformation theory. Proceedings of the Institution of Mechanical Engineering, Part C:Journal of Mechanical Engineering Science, 229, 391-406(2015)
[2] Kheirkhah, M. M., Khalili, S. M. R., and Malekzadeh-Fard, K. Biaxial buckling analysis of softcore composite sandwich plates using improved high-order theory. European Journal of Mechanics-A/Solid, 31, 54-66(2012)
[3] Du, G. J. and Ma, J. Q. Nonlinear vibration and buckling of circular sandwich plate under complex load. Applied Mathematics and Mechanics (English Edition), 28, 1081-1091(2007) https://doi.org/10.1007/s10483-007-0810-z
[4] Nguyen, T. K., Vo, T. P., and Thai, H. T. Vibration and buckling analysis of functionally graded sandwich plates with improved transverse shear stiffness based on the first-order shear deformation theory. Proceedings of the Institution of Mechanical Engineering, Part C:Journal of Mechanical Engineering Science, 228, 2110-2131(2013)
[5] Zenkour, A. M. A comprehensive analysis of functionally graded sandwich plates/:buckling and free vibrations. International Journal of Solids and Structures, 42, 5243-5258(2005)
[6] Thai, H. T., Nguyen, T. K., Vo, T. P., and Lee, J. Analysis of functionally graded sandwich plates using a new first-order shear deformation theory. European Journal of Mechanics-A/Solid, 45, 211-225(2014)
[7] Natarajan, S., Haboussi, M., and Manickam, G. Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets. Composite Structures, 113, 197-207(2014)
[8] Kant, T. and Swaminathan, K. Analytical solution for free vibration of laminated composite and sandwich plates based on higher order refined theory. Composite Structures, 53, 73-85(2001)
[9] Sahoo, R. and Singh, B. N. A new inverse hyperbolic zigzag theory for the static analysis of laminated composite and sandwich plates. Composite Structures, 105, 385-397(2013)
[10] Cho, M. and Oh, J. Higher order zig-zag theory for fully coupled thermo-electric-mechanical smart composite plates. International Journal of Solids and Structures, 41, 1331-1356(2004)
[11] Ren, J. G. A new theory of laminated plates. Composites Science and Technology, 26, 225-239(1986)
[12] Ren, J. G. Bending theory of laminated plate. Composites Science and Technology, 27, 225-248(1986)
[13] Iurlaro, L., Gherlone, M., Sciuva, M. D., and Tessler, A. Refined zigzag theory for laminated composite and sandwich plates derived from Reissner's mixed variational theorem. Composite Structures, 133, 809-817(2015)
[14] Sciuva, M. D., Gherlone, M., Iurlaro, L., and Tessler, A. A class of higher-order C⁰ composite and sandwich beam elements based on the refined zigzag theory. Composite Structures, 132, 784-803(2015)
[15] Iurlaro, L., Gherlone, M., and Sciuva, M. The (3,2)-mixed refined zigzag theory for generally laminated beams:theoretical development and C⁰ finite element formulation. International Journal of Solids and Structures, 73-74, 1-19(2015)
[16] Chakrabarti, A., Topdar, P., and Sheikh, A. H. Vibration and buckling of laminated plates having interfacial imperfections. European Journal of Mechanics-A/Solid, 25, 981-995(2006)
[17] Iurlaro, L., Gherlone, M., di Sciuva, M., and Tessler, A. Assessment of the refined zigzag theory for bending, vibration, and buckling of sandwich plates:a comparative study of different theories. Composite Structures, 106, 777-792(2013)
[18] Iurlaro, L., Gherlone, M., and di Sciuva, M. Bending and free vibration analysis of functionally graded sandwich plates using the refined zigzag theory. Journal of Sandwich Structures and Materials, 11, 669-699(2014)
[19] Tessler, A., di Sciuva, M., and Gherlone, M. A. A consistent refinement of first-order shear deformation theory for laminated composite and sandwich plates using improved zigzag kinematics. Journal of Mechanics of Materials and Structures, 5, 341-367(2010)
[20] Gherlone, M., Tessler, A., and Sciuva, M. D. C⁰ beam elements based on the refined zigzag theory for multilayered composite and sandwich laminates. Composite Structures, 93, 2882-2894(2011)
[21] Versino, D., Gherlone, M., Mattone, M., Sciuva, M. D., and Tessler, A. C⁰ triangular elements based on the refined zigzag theory for multilayer composite and sandwich plates. Composite Structures, 44, 218-230(2013)
[22] Daneshmehr, A., Rajabpour, A., and Hadi, A. Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories. International Journal of Engineering Science, 95, 23-35(2015)
[23] Hosseini-Hashemi, S., Bedroud, M., and Nazemnezhad, R. An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity. Composite Structures, 103, 108-118(2013)
[24] Hosseini-Hashemi, S., Zare, M., and Nazemnezhad, R. An exact analytical approach for free vibration of Mindlin rectangular nano-plates via nonlocal elasticity. Composite Structures, 100, 290-299(2013)
[25] Alibeigloo, A. and Pasha-Zanoosi, A. A. Static analysis rectabgular nano-plates using threedimensional theory of elasticity. Applied Mathematical Modelling, 37, 7016-7026(2013)
[26] Shen, J. P. and Li, C. A semi-continuum-based bending analysis for extreme-thin micro/nanobeams and new proposal for nonlocal differential constitution. Composite Structures, 172, 210-220(2017)
[27] Li, C. Torsional vibration of carbon nanotubes:comparison of two nonlocal models and a semicontinuum model. International Journal of Mechanical Sciences, 82, 25-31(2014)
[28] Li, C., Yao, L., Chen, W., and Li, S. Comments on nonlocal effects in nano-cantilever beams. International Journal of Engineering Science, 87, 47-57(2015)
[29] Li, C., Zheng, Z. J., Yu, J. L., and Lim, C. W. Static analysis of ultra-thin beams based on a semi-continuum model. Acta Mechanica Sinica, 27, 713-719(2011)
[30] Malekzadeh, P., Setoodeh, A. R., and Alibeygi-Beni, A. Small scale effect on the thermal buckling of orthotropic arbitrary straight-sided quadrilateral nanoplates embedded in an elastic medium. Composite Structures, 93, 2083-2089(2011)
[31] Rahim-Nami, M., Janghorban, M., and Damadam, M. Thermal buckling analysis of functionally graded rectangular nanoplates based on nonlocal third order shear deformation theory. Aerospace Science and Technology, 41, 7-15(2015)
[32] Golmakani, M. E. and Rezatalab, J. Nonuniform biaxial buckling of orthotropic nanoplates embedded in an elastic medium based on nonlocal Mindlin plate theory. Composite Structures, 119, 238-250(2015)
[33] Analooei, H. R., Azhari, M., and Heidarpour, A. Elastic buckling and vibration analyses of orthotropic nanoplates using nonlocal continuum mechanics and spline finite strip method. Applied Mathematical Modelling, 37, 6703-6717(2013)
[34] Loghman, A., Abdollahian, M., Jafarzadeh-Jazi, A., and Ghorbanpour-Arani, A. Semi-analytical solution for electromagnetothermoelastic creep response of functionally graded piezoelectric rotating disk. International Journal of Thermal Sciences, 65, 254-266(2013)
[35] Pan, Z. W., Dai, Z. R., and Wang, Z. L. Nanobelts of semiconducting oxides. Science, 291, 1947-1949(2001)