SavedAdd your journal

Journals / International Journal of Engineering and Applied Sciences / 2026 / Volume: 10 Issue: 3

Defination of length-scale parameter in Eringen’s Nonlocal Elasticity via Nolocal Lattice and Finite Element Formulation

Büşra Uzun0000-0002-7636-7170
Hayri Metin Numanoğlu0000-0003-0556-7850
Ömer Civalek0000-0003-1907-9479
Pages
—
Publication Date
2018-11-04
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Weak form and final finite element formulation for axial vibration case have been derived.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Nonlocal elasticity theory is one of the popular approaches for nano mechanic problems.
📊
Key Findings & Data:In this study, nonlocal parameter is defined via different approach.
💡
Conclusion & Impact:Weak form and final finite element formulation for axial vibration case have been derived.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Nonlocal elasticity · finite element · axial vibration

Abstract

Nonlocal elasticity theory is one of the popular approaches for nano mechanic problems. In this study, nonlocal parameter is defined via different approach. Nonlocal finite element formulations for axial vibration of nanorods have been given and some parameters are compared with the lattice dynamics. Weak form and final finite element formulation for axial vibration case have been derived.

🔖

Cite This Article

Uzun, B., Numanoğlu, H. M., Civalek, Ö. (2018). Defination of length-scale parameter in Eringen’s Nonlocal Elasticity via Nolocal Lattice and Finite Element Formulation. International Journal of Engineering and Applied Sciences, Volume: 10 Issue: 3. https://doi.org/10.24107/ijeas.471539

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (39)

  1. Ari, N., Eringen A.C., Nonlocal Stress-Field at Griffith Crack, Crystal Lattice Defects and Amorphous Materials, 10(1), 33-38, 1983.
  2. Eringen, A. C., Linear theory of micropolar elasticity, Journal of Mathematics and Mechanics, 909-923, 1966.
  3. Eringen, A. C., A unified theory of thermomechanical materials, International Journal of Engineering Science, 4(2), 179-202, 1966.
  4. Eringen, A. C., Micropolar fluids with stretch, International Journal of Engineering Science, 7(1), 115-127, 1969.
  5. Eringen, A. C., Linear Theory of Nonlocal Elasticity and Dispersion of Plane-Waves, International Journal of Engineering Science, 10(5), 425-435, 1972.
  6. Thoft-Christensen, P., Continuum Mechanics Aspects of Geodynamics and Rock Fracture Mechanics: Proceedings of the NATO Advanced Study Institute held in Reykjavik, Iceland, 11—20 August, 1974. (Vol. 12), Springer Science & Business Media, 2012.
  7. Eringen, A. C., Nonlocal Polar Elastic Continua, International Journal of Engineering Science, 10(1), 1-16, 1972. doi: 10.1016/0020-7225(72)90070-5
  8. Eringen, A. C., On nonlocal fluid mechanics, International Journal of Engineering Science, 10(6), 561-575, 1972.
  9. Eringen, A. C., Nonlocal polar field theories, Continuum physics, 4(Part III), 205-264, 1976.
  10. Eringen, A. C., Screw Dislocation in Nonlocal Elasticity, Journal of Physics D-Applied Physics, 10(5), 671-678, 1976. doi: 10.1088/0022-3727/10/5/009.
  11. Eringen, A. C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of applied physics, 54(9), 4703-4710, 1983.
  12. Eringen, A. C., Nonlocal continuum field theories, Springer Science & Business Media, 2002.
  13. Eringen, A. C., Edelen, D. G. B., On nonlocal elasticity, International Journal of Engineering Science, 10(3), 233-248, 1972.
  14. Eringen, A. C., Kim, B. S., Stress concentration at the tip of crack, Mechanics Research Communications, 1(4), 233-237, 1974.
  15. Eringen, A. C., Kim, B. S., Relation between Nonlocal Elasticity and Lattice-Dynamics, Crystal Lattice Defects, 7(2), 51-57, 1977.
  16. Lazar, M., Maugin, G. A., Aifantis, E. C., On a theory of nonlocal elasticity of bi-Helmholtz type and some applications, International Journal of Solids and Structures, 43(6), 1404-1421, 2006.
  17. Mercan, K., Civalek, O., DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix, Composite Structures, 143, 300-309, 2016.
  18. Baltacıoglu, A. K., Akgoz, B., Civalek, O., Nonlinear static response of laminated composite plates by discrete singular convolution method, Composite Structures, 93, 153–161, 2010.
  19. Civalek, O, Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns, Engineering Structures, 26, 171–186, 2004.
  20. Demir, C., Mercan, K., Civalek, O., Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel, Composites Part B, 94, 1-10, 2016.
  21. Civalek, O., Finite Element analysis of plates and shells, Elazığ, Fırat University, 1998.
  22. Phadikar, J. K., Pradhan, S. C., Variational formulation and finite element analysis for nonlocal elastic nanobeams and nanoplates, Computational materials science, 49(3), 492-499, 2010.
  23. Mercan, K., Ersoy, H., Civalek, Ö., Free vibration of annular plates by discrete singular convolution and differential quadrature methods, Journal of Applied and Computational Mechanics, 2(3), 128-133, 2016.
  24. Akgöz, B., Civalek, O., Buckling analysis of cantilever carbon nanotubes using the strain gradient elasticity and modified couple stress theories, Journal of Computational and Theoretical Nanoscience, 8(9), 1821-1827, 2011.
  25. Chen, Y., Lee, J. D., Eskandarian, A., Atomistic viewpoint of the applicability of microcontinuum theories, International Journal of Solids and Structures, 41(8), 2085-2097, 2004.
  26. Baltacıoglu, A.K., Civalek, O., Akgoz, B., Demir, F., Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution, International Journal of Pressure Vessels and Piping, 88, 290-300, 2011.
  27. Omurtag, M. H., Çubuk sonlu elemanlar, Birsen Yayınevi, 2010.
  28. Civalek, O., Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method, Composites Part B, 111, 45-59, 2017.
  29. Peddieson, J., Buchanan, G. R., McNitt, R. P., Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science, 41(3), 305-312, 2003.
  30. Civalek, O., Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches. Composites: Part B, 50, 171–179, 2013.
  31. Mercan, K., Civalek, O., Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ, Composites Part B, 114, 34-45, 2017.
  32. Chen, W. J., Li, X. P., Size-dependent free vibration analysis of composite laminated Timoshenko beam based on new modified couple stress theory, Archive of Applied Mechanics, 83, 431–444, 2013.
  33. Civalek, O., Demir, C., Buckling and bending analyses of cantilever carbon nanotubes using the euler-bernoulli beam theory based on non-local continuum model, Asian Journal of Civil Engineering, 12(5), 651-661, 2011.
  34. Narendar, S., Gopalakrishnan, S., Nonlocal scale effects on ultrasonic wave characteristics of nanorods, Physica E: Low-dimensional Systems and Nanostructures, 42(5), 1601-1604, 2010.
  35. Civalek, O., Geometrically non-linear static and dynamic analysis of plates and shells resting on elastic foundation by the method of polynomial differential quadrature (PDQ), Elazığ, Fırat University, 2004.
  36. Houari, M. S. A., Bessaim, A., Bernard, F., Tounsi, A., Mahmoud, S. R., Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter, Steel and Composite Structures, 28, 13-24, 2018.
  37. Narendar, S., Nonlocal thermodynamic response of a rod, Journal of Thermal Stresses, 40(12), 1595-1605, 2017.
  38. Karlicic, D., Murmu, T., Adhikari, S., Mccarthy, M., Non-local structural mechanics, John Wiley & Sons, 2015.
  39. Zhang, Y. Q., Liu, X., Liu, G. R., Thermal effect on transverse vibrations of double-walled carbon nanotubes, Nanotechnology, 18(44), 445701, 2007.