Table of Contents Author Guidelines Submit a Manuscript
Modelling and Simulation in Engineering
Volume 2016, Article ID 5934814, 5 pages
http://dx.doi.org/10.1155/2016/5934814
Research Article

A Note on Torsion of Nonlocal Composite Nanobeams

Department of Civil Engineering, University of Salerno, Via Ponte don Melillo, 84084 Fisciano, Italy

Received 4 December 2015; Accepted 5 October 2016

Academic Editor: Theodoros C. Rousakis

Copyright © 2016 Luciano Feo and Rosa Penna. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. Barretta, “On Cesàro-Volterra method in orthotropic Saint-Venant beam,” Journal of Elasticity, vol. 112, no. 2, pp. 233–253, 2013. View at Google Scholar · View at MathSciNet
  2. R. Barretta and M. Diaco, “On the shear centre in Saint-Venant beam theory,” Mechanics Research Communications, vol. 52, pp. 52–56, 2013. View at Publisher · View at Google Scholar · View at Scopus
  3. G. Romano, A. Barretta, and R. Barretta, “On torsion and shear of Saint-Venant beams,” European Journal of Mechanics. A. Solids, vol. 35, pp. 47–60, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. R. Barretta, “On stress function in Saint-Venant beams,” Meccanica, vol. 48, no. 7, pp. 1811–1816, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. F. Marmo and L. Rosati, “Analytical integration of elasto-plastic uniaxial constitutive laws over arbitrary sections,” International Journal for Numerical Methods in Engineering, vol. 91, no. 9, pp. 990–1022, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. F. Marmo and L. Rosati, “The fiber-free approach in the evaluation of the tangent stiffness matrix for elastoplastic uniaxial constitutive laws,” International Journal for Numerical Methods in Engineering, vol. 94, no. 9, pp. 868–894, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. L. Rosati and F. Marmo, “Closed-form expressions of the thermo-mechanical fields induced by a uniform heat source acting over an isotropic half-space,” International Journal of Heat and Mass Transfer, vol. 75, pp. 272–283, 2014. View at Publisher · View at Google Scholar · View at Scopus
  8. F. Marmo and L. Rosati, “A general approach to the solution of Boussinesq's problem for polynomial pressures acting over polygonal domains,” Journal of Elasticity, vol. 122, no. 1, pp. 75–112, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. R. Barretta, “Analogies between Kirchhoff plates and Saint-Venant beams under torsion,” Acta Mechanica, vol. 224, no. 12, pp. 2955–2964, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. R. Barretta, “Analogies between Kirchhoff plates and Saint-Venant beams under flexure,” Acta Mechanica, vol. 225, no. 7, pp. 2075–2083, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. A. M. Tarantino, “Homogeneous equilibrium configurations of a hyperelastic compressible cube under equitriaxial dead-load tractions,” Journal of Elasticity, vol. 92, no. 3, pp. 227–254, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. V. A. Salomoni, G. Mazzucco, C. Pellegrino, and C. E. Majorana, “Three-dimensional modelling of bond behaviour between concrete and FRP reinforcement,” Engineering Computations, vol. 28, no. 1, pp. 5–29, 2011. View at Publisher · View at Google Scholar · View at Scopus
  13. V. A. Salomoni, C. E. Majorana, B. Pomaro, G. Xotta, and F. Gramegna, “Macroscale and mesoscale analysis of concrete as a multiphase material for biological shields against nuclear radiation,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 38, no. 5, pp. 518–535, 2014. View at Publisher · View at Google Scholar · View at Scopus
  14. G. Romano, R. Barretta, and M. Diaco, “The geometry of nonlinear elasticity,” Acta Mechanica, vol. 225, no. 11, pp. 3199–3235, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. G. Romano, R. Barretta, and M. Diaco, “Geometric continuum mechanics,” Meccanica, vol. 49, no. 1, pp. 111–133, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. A. Caporale, R. Luciano, and L. Rosati, “Limit analysis of masonry arches with externally bonded FRP reinforcements,” Computer Methods in Applied Mechanics and Engineering, vol. 196, no. 1–3, pp. 247–260, 2006. View at Publisher · View at Google Scholar · View at Scopus
  17. A. Caporale and R. Luciano, “Limit analysis of masonry arches with finite compressive strength and externally bonded reinforcement,” Composites Part B: Engineering, vol. 43, no. 8, pp. 3131–3145, 2012. View at Publisher · View at Google Scholar · View at Scopus
  18. A. Caporale, L. Feo, R. Luciano, and R. Penna, “Numerical collapse load of multi-span masonry arch structures with FRP reinforcement,” Composites Part B: Engineering, vol. 54, no. 1, pp. 71–84, 2013. View at Publisher · View at Google Scholar · View at Scopus
  19. A. Caporale, L. Feo, D. Hui, and R. Luciano, “Debonding of FRP in multi-span masonry arch structures via limit analysis,” Composite Structures, vol. 108, no. 1, pp. 856–865, 2014. View at Publisher · View at Google Scholar · View at Scopus
  20. F. Greco and R. Luciano, “A theoretical and numerical stability analysis for composite micro-structures by using homogenization theory,” Composites Part B: Engineering, vol. 42, no. 3, pp. 382–401, 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. A. M. Tarantino, “Nonlinear fracture mechanics for an elastic Bell material,” The Quarterly Journal of Mechanics and Applied Mathematics, vol. 50, no. 3, pp. 435–456, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  22. A. M. Tarantino, “The singular equilibrium field at the notch-tip of a compressible material in finite elastostatics,” Journal of Applied Mathematics and Physics, vol. 48, no. 3, pp. 370–388, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  23. A. M. Tarantino, “On extreme thinning at the notch tip of a neo-Hookean sheet,” The Quarterly Journal of Mechanics and Applied Mathematics, vol. 51, no. 2, pp. 179–190, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  24. A. M. Tarantino, “On the finite motions generated by a mode I propagating crack,” Journal of Elasticity, vol. 57, no. 2, pp. 85–103, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. A. M. Tarantino, “Crack propagation in finite elastodynamics,” Mathematics and Mechanics of Solids, vol. 10, no. 6, pp. 577–601, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. V. A. Salomoni, C. E. Majorana, G. M. Giannuzzi, and A. Miliozzi, “Thermal-fluid flow within innovative heat storage concrete systems for solar power plants,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 18, no. 7-8, pp. 969–999, 2008. View at Publisher · View at Google Scholar · View at Scopus
  27. F. Marotti de Sciarra and M. Salerno, “On thermodynamic functions in thermoelasticity without energy dissipation,” European Journal of Mechanics. A. Solids, vol. 46, pp. 84–95, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. G. Xotta, G. Mazzucco, V. A. Salomoni, C. E. Majorana, and K. J. Willam, “Composite behavior of concrete materials under high temperatures,” International Journal of Solids and Structures, vol. 64, pp. 86–99, 2015. View at Publisher · View at Google Scholar · View at Scopus
  29. R. Luciano and J. R. Willis, “Bounds on non-local effective relations for random composites loaded by configuration-dependent body force,” Journal of the Mechanics and Physics of Solids, vol. 48, no. 9, pp. 1827–1849, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. R. Luciano and J. R. Willis, “Non-local effective relations for fibre-reinforced composites loaded by configuration-dependent body forces,” Journal of the Mechanics and Physics of Solids, vol. 49, no. 11, pp. 2705–2717, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  31. R. Luciano and J. R. Willis, “Boundary-layer corrections for stress and strain fields in randomly heterogeneous materials,” Journal of the Mechanics and Physics of Solids, vol. 51, no. 6, pp. 1075–1088, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. R. Luciano and J. R. Willis, “Hashin-Shtrikman based FE analysis of the elastic behaviour of finite random composite bodies,” International Journal of Fracture, vol. 137, no. 1–4, pp. 261–273, 2006. View at Publisher · View at Google Scholar · View at Scopus
  33. R. De Borst and H.-B. Muehlhaus, “Gradient-dependent plasticity: formulation and algorithmic aspects,” International Journal for Numerical Methods in Engineering, vol. 35, no. 3, pp. 521–539, 1992. View at Publisher · View at Google Scholar · View at Scopus
  34. E. C. Aifantis, “Strain gradient interpretation of size effects,” International Journal of Fracture, vol. 95, no. 1–4, pp. 299–314, 1999. View at Publisher · View at Google Scholar · View at Scopus
  35. E. C. Aifantis, “Gradient deformation models at nano, micro, and macro scales,” Journal of Engineering Materials and Technology, Transactions of the ASME, vol. 121, no. 2, pp. 189–202, 1999. View at Publisher · View at Google Scholar · View at Scopus
  36. R. H. J. Peerlings, R. De Borst, W. A. M. Brekelmans, and J. H. P. De Vree, “Gradient enhanced damage for quasi-brittle materials,” International Journal for Numerical Methods in Engineering, vol. 39, no. 19, pp. 3391–3403, 1996. View at Publisher · View at Google Scholar · View at Scopus
  37. R. H. J. Peerlings, M. G. D. Geers, R. de Borst, and W. A. M. Brekelmans, “A critical comparison of nonlocal and gradient-enhanced softening continua,” International Journal of Solids and Structures, vol. 38, no. 44-45, pp. 7723–7746, 2001. View at Publisher · View at Google Scholar · View at Scopus
  38. H. Askes and E. C. Aifantis, “Gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results,” International Journal of Solids and Structures, vol. 48, no. 13, pp. 1962–1990, 2011. View at Publisher · View at Google Scholar · View at Scopus
  39. D. Ieşan, “Classical and generalized models of elastic rods,” in Modern Mechanics and Mathematics, D. Gao and R. W. Ogden, Eds., CRC Series, CRC Press, 2008. View at Google Scholar
  40. D. Ieşan, “Saint-Venant's problem in micropolar elasticity,” in Mechanics of Micropolar Media, O. Brulin and R. K. T. Hsieh, Eds., pp. 281–390, World Scientific, Singapore, 1982. View at Google Scholar
  41. D. Ieşan, “Generalized twist for the torsion of micropolar cylinders,” Meccanica, vol. 21, no. 2, pp. 94–96, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  42. D. Ieşan, “Generalized torsion of elastic cylinders with microstructure,” Note di Matematica, vol. 27, no. 2, pp. 121–130, 2007. View at Google Scholar · View at MathSciNet · View at Scopus
  43. R. D. Gauthier and W. E. Jahsman, “Quest for micropolar elastic constants,” Journal of Applied Mechanics, Transactions ASME, vol. 42, no. 2, pp. 369–374, 1975. View at Publisher · View at Google Scholar · View at Scopus
  44. G. V. K. Reddy and N. K. Venkatasubramanian, “Saint-Venant's problem for a micropolar elastic circular cylinder,” International Journal of Engineering Science, vol. 14, no. 11, pp. 1047–1057, 1976. View at Publisher · View at Google Scholar · View at Scopus
  45. G. Dinelli, G. Belz, C. E. Majorana, and B. A. Schrefler, “Experimental investigation on the use of fly ash for lightweight precast structural elements,” Materials and Structures/Materiaux et Constructions, vol. 29, no. 194, pp. 632–638, 1996. View at Google Scholar · View at Scopus
  46. J. Peddieson, G. R. Buchanan, and R. P. McNitt, “Application of nonlocal continuum models to nanotechnology,” International Journal of Engineering Science, vol. 41, no. 3–5, pp. 305–312, 2003. View at Publisher · View at Google Scholar · View at Scopus
  47. J. N. Reddy, “Nonlocal theories for bending, buckling and vibration of beams,” International Journal of Engineering Science, vol. 45, no. 2–8, pp. 288–307, 2007. View at Publisher · View at Google Scholar · View at Scopus
  48. Q. Wang and K. M. Liew, “Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures,” Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 363, no. 3, pp. 236–242, 2007. View at Publisher · View at Google Scholar · View at Scopus
  49. M. Aydogdu, “A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration,” Physica E: Low-Dimensional Systems and Nanostructures, vol. 41, no. 9, pp. 1651–1655, 2009. View at Publisher · View at Google Scholar · View at Scopus
  50. O. Civalek and Ç. Demir, “Bending analysis of microtubules using nonlocal Euler-Bernoulli beam theory,” Applied Mathematical Modelling, vol. 35, no. 5, pp. 2053–2067, 2011. View at Publisher · View at Google Scholar
  51. H.-T. Thai and T. P. Vo, “A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams,” International Journal of Engineering Science, vol. 54, pp. 58–66, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  52. R. Barretta and F. Marotti De Sciarra, “A nonlocal model for carbon nanotubes under axial loads,” Advances in Materials Science and Engineering, vol. 2013, Article ID 360935, 6 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  53. F. Marotti de Sciarra and R. Barretta, “A gradient model for Timoshenko nanobeams,” Physica E: Low-Dimensional Systems and Nanostructures, vol. 62, pp. 1–9, 2014. View at Publisher · View at Google Scholar · View at Scopus
  54. R. Barretta, L. Feo, R. Luciano, and F. Marotti de Sciarra, “Application of an enhanced version of the Eringen differential model to nanotechnology,” Composites B, vol. 96, pp. 274–280, 2016. View at Publisher · View at Google Scholar
  55. R. Barretta, L. Feo, R. Luciano, F. Marotti de Sciarra, and R. Penna, “Functionally graded Timoshenko nanobeams: a novel nonlocal gradient formulation,” Composites B, vol. 100, pp. 208–219, 2016. View at Publisher · View at Google Scholar
  56. B. Arash and Q. Wang, “A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes,” Computational Materials Science, vol. 51, no. 1, pp. 303–313, 2012. View at Publisher · View at Google Scholar · View at Scopus
  57. R. Rafiee and R. M. Moghadam, “On the modeling of carbon nanotubes: a critical review,” Composites Part B: Engineering, vol. 56, pp. 435–449, 2014. View at Publisher · View at Google Scholar · View at Scopus
  58. R. Barretta, R. Luciano, and F. M. de Sciarra, “A fully gradient model for Euler-Bernoulli nanobeams,” Mathematical Problems in Engineering, vol. 2015, Article ID 495095, 8 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  59. M. A. Eltaher, S. A. Emam, and F. F. Mahmoud, “Static and stability analysis of nonlocal functionally graded nanobeams,” Composite Structures, vol. 96, pp. 82–88, 2013. View at Publisher · View at Google Scholar · View at Scopus
  60. F. Marotti de Sciarra, M. Čanadija, and R. Barretta, “A gradient model for torsion of nanobeams,” Comptes Rendus—Mecanique, vol. 343, no. 4, pp. 289–300, 2015. View at Publisher · View at Google Scholar · View at Scopus
  61. K. A. Lazopoulos and A. K. Lazopoulos, “On the torsion problem of strain gradient elastic bars,” Mechanics Research Communications, vol. 45, pp. 42–47, 2012. View at Publisher · View at Google Scholar · View at Scopus
  62. A. C. Eringen, “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves,” Journal of Applied Physics, vol. 54, no. 9, pp. 4703–4710, 1983. View at Publisher · View at Google Scholar · View at Scopus