Exact solutions of bending deflections for nano-beams and nano-plates based on nonlocal elasticity theory
Source abstract
Abstract
Abstract In this paper, we applied the nonlocal continuum mechanics to deriving a complete and asymptotic representation of the infinite higher-order governing differential equations for nano-beam and nano-plate models. Results show that the vanishing issue of small scale effects under some boundary conditions such as a clamped nano-beam subjected to distributed uniformly load is solved by using the present nonlocal continuum model. Several typical examples for nano-beam and nano-plate are studied and the scale effect on bending deflection is discussed at length. The analytical prediction for nonlocal bending deflection gives a good prediction of molecular dynamics simulation results which confirms the accuracy of the present model. It is found that when the external characteristic length tends to internal characteristic length, a property of a rigid body for the nano-beam and nano-plate is presented.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Nonlocal and gradient elasticity in micro/nano structures · Numerical methods in engineering · Thermoelastic and Magnetoelastic Phenomena
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (46)
Show source-provided references
1. Helical microtubules of graphitic carbon10.1038/354056a0 ↗
2. Bending, buckling and vibration problems of nonlocal Euler beams using Ritz method10.1016/j.compstruct.2012.08.024 ↗
3. Ultra-sensitive analysis of a cantilevered single-walled carbon nanocone-based mass detector10.1088/0957-4484/24/12/125703 ↗
4. A higher-order gradient theory for modeling of the vibration behavior of single-wall carbon nanocones10.1016/j.apm.2013.11.010 ↗
5. Molecular dynamics modeling and simulations of carbon nanotube-based gears
6. Calibration of nonlocal scale effect parameter for bending single-layered graphene sheet under molecular10.1142/S1793292012500336 ↗
7. Molecular simulations of pristine and defective carbon nanotubes under monotonic and combined loading10.1016/j.commatsci.2012.07.007 ↗
8. On differential-equations of nonlocal elasticity and solutions of screw dislocation and surface-waves10.1063/1.332803 ↗
9. Application of nonlocal continuum models to nanotechnology10.1016/S0020-7225(02)00210-0 ↗
10. Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory10.1088/0022-3727/39/17/029 ↗
11. Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams10.1063/1.2435878 ↗
12. A nonlocal beam theory for bending, buckling, and vibration of nanobeams10.1016/j.ijengsci.2011.11.011 ↗
13. Nonlocal continuum theories of beams for the analysis of carbon nanotubes10.1063/1.2833431 ↗
14. Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates10.1016/j.ijengsci.2010.09.020 ↗
15. The small length scale effect for a non-local cantilever beam: a paradox solved10.1088/0957-4484/19/34/345703 ↗
16. The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory10.1088/0022-3727/41/22/225404 ↗
17. Variational formulation and finite element analysis for nonlocal elastic nanobeams and nanoplates10.1016/j.commatsci.2010.05.040 ↗
18. Vibration of nonlocal Timoshenko beams10.1088/0957-4484/18/10/105401 ↗
19. Wave propagation in carbon nanotubes: nonlocal elasticity-induced stiffness and velocity enhancement effects10.2140/jomms.2010.5.459 ↗
20. Torsional vibration of carbon nanotubes: comparison of two nonlocal models and a semi-continuum model10.1016/j.ijmecsci.2014.02.023 ↗
21. Dynamics and stability of transverse vibrations of nonlocal nanobeams with a variable axial load10.1088/0964-1726/20/1/015023 ↗
22. Application of nonlocal elastic shell theory in wave propagation analysis of carbon nanotubes10.1088/0964-1726/16/1/022 ↗
23. Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes10.1016/j.jmps.2008.08.010 ↗
24. Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory10.1016/j.physleta.2009.09.021 ↗
25. Explicit analytical expressions for the critical buckling stresses in a monolayer graphene sheet based on nonlocal elasticity10.1016/j.ssc.2011.11.004 ↗
26. Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory10.1016/j.physe.2010.11.024 ↗
27. Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory10.1088/0957-4484/18/38/385704 ↗
28. Nonlocal elasticity theory for vibration of nanoplates10.1016/j.jsv.2009.03.007 ↗
29. Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates10.1016/j.jsv.2009.04.044 ↗
30. Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method10.1007/s00419-010-0469-9 ↗
31. Nonlocal continuum models for carbon nanotubes subjected to static loading10.2140/jomms.2006.1.663 ↗
32. Vibration of carbon nanotubes studied using nonlocal continuum mechanics10.1088/0964-1726/15/2/050 ↗
33. Buckling analysis of carbon nanotubes modeled using nonlocal continuum theories10.1063/1.2901201 ↗
34. Thermal buckling of multi-walled carbon nanotubes by nonlocal elasticity10.1115/1.2200656 ↗
35. Thermal buckling of nanorod based on non-local elasticity theory10.1016/j.ijnonlinmec.2011.09.023 ↗
36. Wave propagation in carbon nanotubes via nonlocal continuum mechanics10.1063/1.2141648 ↗
37. Scale effect on wave propagation of double-walled carbon nanotubes10.1016/j.ijsolstr.2005.11.005 ↗
38. Small-scale effect on the vibration of nonuniform nanocantilever based on nonlocal elasticity theory10.1016/j.physe.2009.04.015 ↗
39. Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets10.1016/j.commatsci.2010.06.032 ↗
40. Nonlocal integral elasticity: 2D finite element based solutions10.1016/j.ijsolstr.2009.07.009 ↗
41. Ventsel · 2001
42. Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nano-tubes10.1007/s00707-006-0417-5 ↗
43. Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures10.1016/j.physleta.2006.10.093 ↗
44. Beam bending solutions based on nonlocal Timoshenko beam theory10.1061/(ASCE)0733-9399(2008)134:6(475) ↗
45. Bending, buckling and vibration analyses of nonhomogeneous nanotubes using GDQ and nonlocal elasticity theory10.12989/sem.2009.33.2.193 ↗
46. The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes10.1088/0957-4484/18/7/075702 ↗