In-Plane Static Analysis of Curved Nanobeams Using Exact-Solution-Based Finite Element Formulation
Source abstract
Abstract
Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nanobeams. Opposite to traditional curved finite elements developed by using approximate interpolation functions, the proposed curved finite element is developed by using exact analytical solutions. Although this approach was first introduced for analyzing the mechanical behaviors of macro-scale curved beams by adopting the local theory of elasticity, the exact analytical expressions used in this study were obtained from the solutions of governing equations that were expressed via the differential form of the nonlocal theory of elasticity. Therefore, the effects of shear strain and axial extension included in the analytical formulation are also inherited by the curved finite element developed here. The rigidity matrix and the consistent force vector are developed for a circular finite element. To demonstrate the applicability of the method, static analyses of various curved nanobeams subjected to different boundary conditions and loading scenarios are performed, and the obtained results are compared with the exact analytical ones. The presented study provides an accurate and low computational cost method for researchers to investigate the in-plane static behavior of curved nanobeams.
Source: openalex_inverted_index · Quality: baseline
Research context
OpenAlex topics: Advanced Surface Polishing Techniques · Metal and Thin Film Mechanics · Metal Forming Simulation Techniques
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (60)
Show source-provided references
1. Flexoelectric nanostructure design using explicit topology optimization10.1016/j.cma.2022.114943 ↗
2. Carbon nanotube field-effect transistor (CNT-FET)-based biosensor for rapid detection of SARS-CoV-2 (COVID-19) surface spike protein S110.1016/j.bioelechem.2021.107982 ↗
3. Controllable synthesis of graphene-based titanium dioxide nanocomposites by atomic layer deposition10.1088/0957-4484/22/16/165602 ↗
4. Carbon nanotube actuators10.1126/science.284.5418.1340 ↗
5. Carbon nanotubes as cancer therapeutic carriers and mediators10.2147/IJN.S112660 ↗
6. A structural mechanics approach for the analysis of carbon nanotubes10.1016/S0020-7683(03)00056-8 ↗
7. Nonlocal Timoshenko modeling effectiveness for carbon nanotube-based mass sensors10.1016/j.euromechsol.2021.104462 ↗
8. Forced vibration analysis of functionally graded anisotropic nanoplates resting on Winkler/Pasternak-foundation
9. Nonlocal boundaries and paradoxes in thermoelastic vibrations of functionally graded non-uniform cantilever nanobeams and annular nanoplates10.1016/j.istruc.2023.06.095 ↗
10. On the mechanics of nanobeams on nano-foundations10.1016/j.ijengsci.2022.103747 ↗
11. A review on the size-dependent bulking, vibration and, wave propagation of nanostructures10.1088/1361-648X/acc62b ↗
12. On nonlocal elasticity10.1016/0020-7225(72)90039-0 ↗
13. Review and critique of the stress gradient elasticity theories of Eringen and Aifantis10.1007/978-1-4419-5695-8_21 ↗
14. A refined nonlocal thermoelasticity theory for the vibration of nanobeams induced by ramp-type heating
15. Three-to-one internal resonances of stepped nanobeam of nonlinearity10.1515/zna-2023-0215 ↗
16. Elastic medium and torsional spring effects on the nonlocal dynamic of functionally graded porous nanotubes10.1007/s00419-024-02576-8 ↗
17. Static bending and vibration of composite nanobeams taking into the effect of geometrical imperfection10.1007/s42417-024-01384-2 ↗
18. PINN-based forward and inverse bending analysis of nanobeams on a three-parameter nonlinear elastic foundation including hardening and softening effect using nonlocal elasticity theory
19. Bending, buckling and free vibration analysis of Euler-Bernoulli nanobeams using Eringen’s nonlocal integral model via finite element method10.1016/j.compstruct.2017.07.019 ↗
20. Gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results10.1016/j.ijsolstr.2011.03.006 ↗
21. On the gradient approach—Relation to Eringen’s nonlocal theory10.1016/j.ijengsci.2011.03.016 ↗
22. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves10.1063/1.332803 ↗
23. Nonlocal elasticity and boundary condition paradoxes: a review10.1007/s11051-020-05107-y ↗
24. Static analysis of nanobeams using Rayleigh-Ritz Method10.2140/jomms.2017.12.603 ↗
25. Analytical solutions for thermal vibration of nanobeams with elastic boundary conditions10.1016/j.camss.2017.08.001 ↗
26. Vibration of nanobeams of different boundary conditions with multiple cracks based on nonlocal elasticity theory10.1016/j.apm.2013.08.011 ↗
27. Axial vibration of the nanorods with the nonlocal continuum rod model10.1016/j.physe.2009.01.007 ↗
28. Static bending and buckling of perforated nonlocal size-dependent nanobeams10.1007/s00542-018-3905-3 ↗
29. Application of nonlocal continuum models to nanotechnology10.1016/S0020-7225(02)00210-0 ↗
30. A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams10.1016/j.ijengsci.2012.01.009 ↗
31. Comprehensive semi-analytical vibration analysis of rotating tapered AFG nanobeams based on nonlocal elasticity theory considering various boundary conditions via differential transformation method10.1016/j.compositesb.2018.12.085 ↗
32. Dynamic interaction between bi-directional functionally graded materials and magneto-electro-elastic fields: a nano-structure analysis10.1016/j.compstruct.2021.113746 ↗
33. Dynamic stiffness of nonlocal damped nano-beams on elastic foundation10.1016/j.euromechsol.2020.104144 ↗
34. Free vibrations analysis of stepped nanobeams using nonlocal elasticity theory
35. Analysis of the magneto-thermoelastic vibrations of rotating Euler-Bernoulli nanobeams using the nonlocal elasticity model10.1186/s13661-023-01706-5 ↗
36. Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams10.12989/sem.2013.48.3.351 ↗
37. Nanomechanical resonators and their applications in biological/chemical detection
38. Size-dependent secondary resonance of a piezoelectrically laminated bistable MEMS arch resonator10.1016/j.compositesb.2019.05.061 ↗
39. Vibration analysis of initially curved single walled carbon nanotube with vacancy defect for ultrahigh frequency nanoresonators10.1007/s00542-015-2470-2 ↗
40. Rigorous modal analysis of plasmonic nanoresonators10.1103/PhysRevB.97.205422 ↗
41. Bistability of curved microbeams actuated by fringing electrostatic fields10.1007/s11071-011-0038-y ↗
42. The effect of size scale parameters on the structural behavior of carbon nanotube based nano-actuator
43. Single-crystal nanorings formed by epitaxial self-coiling of polar nanobelts10.1126/science.1092356 ↗
44. Investigating surface effects on thermomechanical behavior of embedded circular curved nanosize beams10.1155/2016/9848343 ↗
45. Free vibration of nanorings/arches based on nonlocal elasticity
46. Nonlocal bending analysis of curved nanobeams reinforced by graphene nanoplatelets10.1016/j.compositesb.2018.11.092 ↗
47. Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model10.1007/s00339-016-9696-4 ↗
48. Modeling the size effect on the mechanical behavior of functionally graded curved micro/nanobeam
49. Thermal stress and deformation analysis of a size-dependent curved nanobeam based on sinusoidal shear deformation theory10.1016/j.aej.2017.07.003 ↗
50. Free vibration of deep and shallow curved FG nanobeam based on nonlocal elasticity
51. In-plane static analysis of nonlocal curved beams with varying curvature and cross-section10.1142/S1758825116500101 ↗
52. Vibration study of curved nanobeams based on nonlocal higher-order shear deformation theory using finite element approach10.1016/j.compstruct.2017.10.066 ↗
53. A nonlocal higher-order curved beam finite model including thickness stretching effect for bending analysis of curved nanobeams10.1080/15376494.2017.1410903 ↗
54. Free vibration analysis of functionally graded porous curved nanobeams on elastic foundation in hygro-thermo-magnetic environment10.1007/s11709-023-0916-7 ↗
55. Nonlocal nonlinear higher-order finite element model for static bending of curved nanobeams including graphene platelets reinforcement10.1080/15376494.2024.2315603 ↗
56. A new two-noded curved beam finite element formulation based on exact solution10.1007/s00366-016-0470-1 ↗
57. A new finite element formulation for free vibrations of planar curved beams10.1080/15397734.2018.1456343 ↗
58. Analytical solutions of in-plane static problems for non-uniform curved beams including axial and shear deformations10.12989/sem.2006.22.2.131 ↗
59. Reddy · Introduction to the finite element method · 2019
60. Oldaç · Nanoteknolojide yerel olmayan çubuk teorisinin statik ve dinamik problemleri · 2016