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Mechanical Behavior of Functionally Graded Nano-Cylinders Under Radial Pressure Based on Strain Gradient Theory

Published online by Cambridge University Press:  26 December 2018

M. Shishesaz  and
M. Hosseini
M. Shishesaz
Affiliation:
Department of Mechanical Engineering Shahid Chamran University of Ahvaz Ahvaz, Iran
M. Hosseini*
Affiliation:
Department of Mechanical Engineering Shahid Chamran University of Ahvaz Ahvaz, Iran
*
* Corresponding author ([email protected])
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Abstract

In this paper, the mechanical behavior of a functionally graded nano-cylinder under a radial pressure is investigated. Strain gradient theory is used to include the small scale effects in this analysis. The variations in material properties along the thickness direction are included based on three different models. Due to slight variations in engineering materials, the Poisson’s ratio is assumed to be constant. The governing equation and its corresponding boundary conditions are obtained using Hamilton’s principle. Due to the complexity of the governed system of differential equations, numerical methods are employed to achieve a solution. The analysis is general and can be reduced to classical elasticity if the material length scale parameters are taken to be zero. The effect of material index n, variations in material properties and the applied internal and external pressures on the total and high-order stresses, are well examined. For the cases in which the applied external pressure at the inside (or outside) radius is zero, due to small effects in nano-cylinder, some components of the high-order radial stresses do not vanish at the boundaries. Based on the results, the material inhomogeneity index n, as well as the selected model through which the mechanical properties may vary along the thickness, have significant effects on the radial and circumferential stresses.

Keywords

Nano-cylinderStrain gradient theoryStress analysisFunctionally graded materials (FGMs)Size effect
Type
Research Article
Information
Journal of Mechanics , Volume 35 , Issue 4 , August 2019 , pp. 441 - 454
Copyright
© The Society of Theoretical and Applied Mechanics 2018 

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References

REFERENCES

Aouani, H., Rahmani, M., Navarro-Cía, M. and Maier, S. A., “Third-Harmonic-Upconversion Enhancement from a Single Semiconductor Nanoparticle Coupled to a Plasmonic antenna,” Nature Nanotechnology, 9, pp. 290–294 (2014).CrossRefGoogle ScholarPubMed
Cai, G. et al., “Modeling and Design of a Plasmonic Sensor for High Sensing Performance and Clear Registration,” IEEE Photonics Journal, 8, pp. 1–11 (2016).Google Scholar
Nishikawa, T. et al., “Nanocylinder-Array Structure Greatly Increases the Soft X-Ray Intensity Generated from Femtosecond-Laser-Produced Plasma,” Applied Physics B, 73, pp. 185–188 (2001).CrossRefGoogle Scholar
Karoro, A. et al., “Laser Nanostructured Co Nanocylinders-Al2O3 Cermets for Enhanced & Flexible Solar Selective Absorbers Applications,” Applied Surface Science, 347, pp. 679–684 (2015).CrossRefGoogle Scholar
Maksymov, I. S. et al., “Metal-Coated Nanocylinder Cavity for Broadband Nonclassical Light Emission,” Physical Review Letters, 105, pp. 180502 (2010).CrossRefGoogle ScholarPubMed
Salata, O., “Applications of Nanoparticles in Biology and Medicine,” Journal of Nanobiotechnology, 2, pp. 3 (2004).CrossRefGoogle ScholarPubMed
Ebrahimi, F. and Barati, M. R., “Buckling Analysis of Smart Size-Dependent Higher Order Magneto-Electro-Thermo-Elastic Functionally Graded Nanosize Beams,” Journal of Mechanics, 33, pp. 23–33 (2016).CrossRefGoogle Scholar
Mashat, D. S., Zenkour, A. M. and Sobhy, M., “Investigation of Vibration and Thermal Buckling of Nanobeams Embedded in An Elastic Medium under Various Boundary Conditions,” Journal of Mechanics, 32, pp. 277–287 (2015).CrossRefGoogle Scholar
Wang, Y. G., Song, H. F. and Lin, W. H., “Nonlinear Pull-In Characterization of a Nonlocal Nanobeam with an Intermolecular Force,” Journal of Mechanics, 32, pp. 737–747 (2016).CrossRefGoogle Scholar
Jandaghian, A. A. and Rahmani, O., “An Analytical Solution for Free Vibration of Piezoelectric Nanobeams Based on a Nonlocal Elasticity Theory,” Journal of Mechanics, 32, pp. 143–151 (2015).CrossRefGoogle Scholar
Eringen, A. C., “Nonlocal Polar Elastic Continua,” International Journal of Engineering Science, 10, pp. 1–16 (1972).CrossRefGoogle Scholar
Ji, X., Li, A. Q. and Zhou, S. J., “The Strain Gradient Elasticity Theory in Orthogonal Curvilinear Coordinates and its Applications,” Journal of Mechanics, pp. 1–13 (2016).Google Scholar
Shahriari, B. and Shirvani, S., “Small-Scale Effects on the Buckling of Skew Nanoplates Based on Non-Local Elasticity and Second-Order Strain Gradient Theory,” Journal of Mechanics, pp. 1–10 (2017).CrossRefGoogle Scholar
Aifantis, E. C., “Strain Gradient Interpretation of Size Effects,” International Journal of Fracture, 95, pp. 299–314 (1999).CrossRefGoogle Scholar
Altan, B. and Aifantis, E., “On Some Aspects in the Special Theory of Gradient Elasticity,” Journal of the Mechanical Behavior of Materials (UK), 8, pp. 231–282 (1997).Google Scholar
Zhou, S. S., Zhou, S. J., Li, A. Q. and Wang, B. L., “Analysis of Residual Stresses on the Vibration of a Circular Sensor Diaphragm with Surface Effects,” Journal of Mechanics, 33, pp. 323–329 (2016).CrossRefGoogle Scholar
Keivani, M., Koochi, A. and Abadyan, M., “A New Bilayer Continuum Model Based on Gurtin-Murdoch and Consistent Couple-Stress Theories for Stability Analysis of Beam-Type Nanotweezers,” Journal of Mechanics, 33, pp. 137–146 (2016).CrossRefGoogle Scholar
Ji, X. and Li, A. Q., “The Size-Dependent Electro-mechanical Coupling Response in Circular Micro-Plate Due to Flexoelectricity,” Journal of Mechanics, pp. 1–11 (2016).Google Scholar
Ansari, R., Gholami, R. and Shahabodini, A., “Size-Dependent Geometrically Nonlinear Forced Vibration Analysis of Functionally Graded First-Order Shear Deformable Microplates,” Journal of Mechanics, 32, pp. 539–554 (2016).CrossRefGoogle Scholar
Mazarei, Z., Nejad, M. and Hadi, A., “Thermo-Elasto-Plastic Analysis of Thick-Walled Spherical Pressure Vessels Made of Functionally Graded Materials,” International Journal of Applied Mechanics (2016).CrossRefGoogle Scholar
Ebrahimi, F., Ehyaei, J. and Babaei, R., “Thermal Buckling of FGM Nanoplates Subjected to Linear and Nonlinear Varying Loads on Pasternak Foundation,” Advances in Materials Research-An International Journal, 5, pp. 245–261 (2016).CrossRefGoogle Scholar
Nejad, M., Rastgoo, A. and Hadi, A., “Exact Elas-to-Plastic Analysis of Rotating Disks Made of Functionally Graded Materials,” International Journal of Engineering Science, 85, pp. 47–57 (2014).CrossRefGoogle Scholar
Ebrahimi, F., “Dynamic Stability of FGM Cylindrical Shells,” Journal of Advanced Research in Mechanical Engineering, 1 (2010).Google Scholar
Gharibi, M., Nejad, M. Z. and Hadi, A., “Elastic Analysis of Functionally Graded Rotating Thick Cylindrical Pressure Vessels with Exponentially-Varying Properties Using Power Series Method of Frobenius,” Journal of Computational Applied Mechanics, 48, pp. 89–98 (2017).Google Scholar
Ebrahimi, F. and Mokhtari, M., “Semi-Analytical Vibration Characteristics of Rotating Timoshenko Beams Made of Functionally Graded Materials,” Latin American Journal of Solids and Structures, 12, pp. 1319–1339 (2015).CrossRefGoogle Scholar
Zamani Nejad, M., Jabbari, M. and Hadi, A., “A Review of Functionally Graded Thick Cylindrical and Conical Shells,” Journal of Computational Applied Mechanics, 48, pp. 357–370 (2017).Google Scholar
Li, L. and Hu, Y., “Buckling Analysis of Size-Dependent Nonlinear Beams Based on a Nonlocal Strain Gradient Theory,” International Journal of Engineering Science, 97, pp. 84–94 (2015).CrossRefGoogle Scholar
Rezaiee-Pajand, M. and Yaghoobi, M., “An Efficient Formulation for Linear and Geometric Non-Linear Membrane Elements,” Latin American Journal of Solids and Structures, 11, pp. 1012–1035 (2014).CrossRefGoogle Scholar
Li, L., Hu, Y. and Ling, L., “Flexural Wave Propagation in Small-Scaled Functionally Graded Beams via a Nonlocal Strain Gradient Theory,” Composite Structures, 133, pp. 1079–1092 (2015).CrossRefGoogle Scholar
Koochi, A., Sedighi, H. M. and Abadyan, M., “Modeling the Size Dependent Pull-in Instability of Beam-Type NEMS Using Strain Gradient Theory,” Latin American Journal of Solids and Structures, 11, pp. 1806–1829 (2014).CrossRefGoogle Scholar
Hosseini, M., Shishesaz, M., Tahan, K. N. and Hadi, A., “Stress Analysis of Rotating Nano-Disks of Variable Thickness Made of Functionally Graded Materials,” International Journal of Engineering Science, 109, pp. 29–53 (2016).CrossRefGoogle Scholar
Shokrieh, M. M. and Zibaei, I., “Determination of the Appropriate Gradient Elasticity Theory for Bending Analysis of Nano-Beams by Considering Boundary Conditions Effect,” Latin American Journal of Solids and Structures, 12, pp. 2208–2230 (2015).CrossRefGoogle Scholar
Lazopoulos, A., “Dynamic Response of Thin Strain Gradient Elastic Beams,” International Journal of Mechanical Sciences, 58, pp. 27–33 (2012).CrossRefGoogle Scholar
Ansari, R. et al., “Size-Dependent Bending, Buckling and Free Vibration Analyses of Microscale Functionally Graded Mindlin Plates Based on the Strain Gradient Elasticity Theory,” Latin American Journal of Solids and Structures, 13, pp. 632–664 (2016).CrossRefGoogle Scholar
Thai, H.-T. and Kim, S.-E., “A Size-Dependent Functionally Graded Reddy Plate Model Based on a Modified Couple Stress Theory,” Composites Part B: Engineering, 45, pp. 1636–1645 (2013).CrossRefGoogle Scholar
Vatankhah, R. and Kahrobaiyan, M., “Investigation of Size-Dependency in Free-Vibration of Micro-Resonators Based on the Strain Gradient Theory,” Latin American Journal of Solids and Structures, 13, pp. 498–515 (2016).CrossRefGoogle Scholar
Wang, B., Hoffman, M. and Yu, A., “Buckling Analysis of Embedded Nanotubes Using Gradient Continuum Theory,” Mechanics of Materials, 45, pp. 52–60 (2012).CrossRefGoogle Scholar
Farahmand, H., Naseralavi, S. S., Iranmanesh, A. and Mohammadi, M., “Navier Solution for Buckling Analysis of Size-Dependent Functionally Graded Micro-Plates,” Latin American Journal of Solids and Structures, 13, pp. 3161–3173 (2016).CrossRefGoogle Scholar
Li, L. and Hu, Y., “Post-Buckling Analysis of Functionally Graded Nanobeams Incorporating Nonlocal Stress and Microstructure-Dependent Strain Gradient Effects,” International Journal of Mechanical Sciences (2016).CrossRefGoogle Scholar
Mohammadi, M., Moradi, A., Ghayour, M. and Farajpour, A., “Exact Solution for Thermo-Mechanical Vibration of Orthotropic Mono-Layer Graphene Sheet Embedded in an Elastic Medium,” Latin American Journal of Solids and Structures, 11, pp. 437–458 (2014).CrossRefGoogle Scholar
Li, L., Li, X. and Hu, Y., “Free Vibration Analysis of Nonlocal Strain Gradient Beams Made of Functionally Graded Material,” International Journal of Engineering Science, 102, pp. 77–92 (2016).CrossRefGoogle Scholar
Li, L. and Hu, Y., “Nonlinear Bending and Free Vibration Analyses of Nonlocal Strain Gradient Beams Made of Functionally Graded Material,” International Journal of Engineering Science, 107, pp. 77–97 (2016).CrossRefGoogle Scholar
Li, X., Li, L., Hu, Y., Ding, Z. and Deng, W., “Bending, Buckling and Vibration of Axially Functionally Graded Beams Based on Nonlocal Strain Gradient Theory,” Composite Structures, 165, pp. 250–265 (2017).CrossRefGoogle Scholar
Kananipour, H., “Static Analysis of Nanoplates Based on the Nonlocal Kirchhoff and Mindlin Plate Theories Using DQM,” Latin American Journal of Solids and Structures, 11, pp. 1709–1720 (2014).CrossRefGoogle Scholar
Akgöz, B. and Civalek, Ö., “Strain Gradient Elasticity and Modified Couple Stress Models for Buckling Analysis of Axially Loaded Micro-Scaled Beams,” International Journal of Engineering Science, 49, pp. 1268–1280 (2011).CrossRefGoogle Scholar
Daneshmehr, A., Rajabpoor, 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, pp. 23–35 (2015).CrossRefGoogle Scholar
Nejad, M. Z. and Hadi, A., “Non-Local Analysis of Free Vibration of Bi-Directional Functionally Graded Euler–Bernoulli Nano-Beams,” International Journal of Engineering Science, 105, pp. 1–11 (2016).CrossRefGoogle Scholar
Romanoff, J., Reddy, J. N. and Jelovica, J., “Using Non-Local Timoshenko Beam Theories for Prediction of Micro- and Macro-Structural Responses,” Composite Structures, 156, pp. 410–420 (2016).CrossRefGoogle Scholar
Nejad, M. Z. and Hadi, A., “Eringen’s Non-Local Elasticity Theory for Bending Analysis of Bi-Directional Functionally Graded Euler–Bernoulli Nano-Beams,” International Journal of Engineering Science, 106, pp. 1–9 (2016).CrossRefGoogle Scholar
Akgöz, B. and Civalek, Ö., “A Size-Dependent Shear Deformation Beam Model Based on the Strain Gradient Elasticity Theory,” International Journal of Engineering Science, 70, pp. 1–14 (2013).CrossRefGoogle Scholar
Nejad, M. Z., Hadi, A. and Rastgoo, A., “Buckling Analysis of Arbitrary Two-Directional Functionally Graded Euler–Bernoulli Nano-Beams Based on Nonlocal Elasticity Theory,” International Journal of Engineering Science, 103, pp. 1–10 (2016).CrossRefGoogle Scholar
Romano, G. and Barretta, R., “Stress-Driven Versus Strain-Driven Nonlocal Integral Model for Elastic Nano-Beams,” Composites Part B: Engineering, 114, pp. 184–188 (2017).CrossRefGoogle Scholar
Shishesaz, M., Hosseini, M., Naderan Tahan, K. and Hadi, A., “Analysis of Functionally Graded Nano-disks under Thermoelastic Loading Based on the Strain Gradient Theory,” Acta Mechanica (2017).CrossRefGoogle Scholar
Romano, G., Barretta, R. and Diaco, M., “On Nonlocal Integral Models for Elastic Nano-Beams,” International Journal of Mechanical Sciences, 131, pp. 490–499 (2017).CrossRefGoogle Scholar
Adeli, M. M., Hadi, A., Hosseini, M. and Gorgani, H. H., “Torsional Vibration of Nano-Cone Based on Nonlocal Strain Gradient Elasticity Theory,” The European Physical Journal Plus, 132, pp. 393 (2017).CrossRefGoogle Scholar
Beni, Y. T., “A Nonlinear Electro-Mechanical Analysis of Nanobeams Based on the Size-Dependent Piezoelectricity Theory,” Journal of Mechanics, 33, pp. 289–301 (2016).CrossRefGoogle Scholar
Hosseini, M., Gorgani, H. H., Shishesaz, M. and Hadi, A., “Size-Dependent Stress Analysis of Single-Wall Carbon Nanotube Based on Strain Gradient Theory,” International Journal of Applied Mechanics, 9, pp. 1750087 (2017).CrossRefGoogle Scholar
Nejad, M. Z., Hadi, A. and Farajpour, A., “Consistent Couple-Stress Theory for Free Vibration Analysis of Euler-Bernoulli Nano-Beams Made of Arbitrary Bi-Directional Functionally Graded Materials,” Structural Engineering and Mechanics, 63, pp. 161–169 (2017).Google Scholar
Shishesaz, M., Zakipour, A. and Jafarzadeh, A., “Magneto-Elastic Analysis of an Annular FGM Plate Based on Classical Plate Theory Using GDQ Method,” Latin American Journal of Solids and Structures, 13, pp. 2736–2762 (2016).CrossRefGoogle Scholar
Chen, Y. Z. and Lin, X. Y., “Elastic Analysis for Thick Cylinders and Spherical Pressure Vessels Made of Functionally Graded Materials,” Computational Materials Science, 44, pp. 581–587 (2008).CrossRefGoogle Scholar