Material gradation effects on twisting statics of bi-directional functionally graded micro-tubes
Source abstract
Abstract
This study aims to characterize the twisting behavior of bi-directional functionally graded (FG) micro-tubes under torsional loads within the modified couple stress theory framework. The two material properties involved in the torsional static model of FG small-scale tubes, i.e., shear modulus and material length scale parameter, are assumed to possess smooth spatial variations in both radial and axial directions. Through the utilization of Hamilton’s principle, the governing equations and boundary conditions are derived, and then, the system of partial differential equations is numerically solved by using the differential quadrature method. A verification study is conducted by comparing limiting cases with the analytical results available in the literature to check the validity of the developed procedures. A detailed study is carried out on the influences of the phase distribution profile and geometric parameters upon twist angles and shear stresses developed in FG micro-tubes undergoing external distributed torques.
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Research context
OpenAlex topics: Nonlocal and gradient elasticity in micro/nano structures · Composite Structure Analysis and Optimization · Numerical methods in engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Aeronautical Engineering, University of Turkish Aeronautical Association 1 , Ankara 06790, Türkiye
Department of Mechanical Engineering, Başkent University 2 , Ankara 06790, Türkiye
Department of Mechanical Engineering, Guru Nanak Dev Engineering College 3 , Ludhiana 141006, India
Department of Industrial Engineering, King Khalid University 4 , Abha 61421, Saudi Arabia
Funding
Deanship of Scientific Research, King Khalid University
References (53)
Show source-provided references
1. Recent and prospective development of functionally graded materials in Japan10.4028/www.scientific.net/MSF.308-311.509 ↗
2. The activities of FGM on new application10.4028/www.scientific.net/MSF.423-425.1 ↗
3. Titanium powder sintering for preparation of a porous functionally graded material destined for orthopaedic implants10.1023/A:1008958914818 ↗
4. Porosity-graded hydroxyapatite ceramics to replace natural bone10.1016/S0142-9612(00)00290-8 ↗
5. Application of functionally graded material for solid insulator in gaseous insulation system10.1109/TDEI.2006.1624281 ↗
6. The use of functionally graded poly-SiGe layers for MEMS applications10.4028/www.scientific.net/MSF.492-493.255 ↗
7. Functionally graded TiN/TiNi shape memory alloy films10.1016/S0167-577X(02)01419-2 ↗
8. Net shape manufacturing of ceramic micro parts with tailored graded layers10.1088/0960-1317/24/1/015018 ↗
9. Experiments and theory in strain gradient elasticity10.1016/S0022-5096(03)00053-X ↗
10. A microbend test method for measuring the plasticity length scale10.1016/S1359-6454(98)00153-0 ↗
11. Role of material microstructure in plate stiffness with relevance to microcantilever sensors10.1088/0960-1317/15/5/024 ↗
12. Strain gradient plasticity: Theory and experiment10.1016/0956-7151(94)90502-9 ↗
13. Nonlocal polar elastic continua10.1016/0020-7225(72)90070-5 ↗
14. The general theory of curved deformable interfaces in solids at equilibrium10.1080/01418619808239977 ↗
15. Strain gradient interpretation of size effects10.1023/A:1018625006804 ↗
16. Effects of couple-stresses in linear elasticity10.1007/BF00253946 ↗
17. Elastic materials with couple-stresses10.1007/BF00253945 ↗
18. Couple stress based strain gradient theory for elasticity10.1016/S0020-7683(02)00152-X ↗
19. Design, fabrication and operation of MEMS gimbal gyroscope10.1016/j.sna.2005.02.012 ↗
20. Comb-actuated resonant torsional microscanner with mechanical amplification10.1109/JMEMS.2010.2048095 ↗
21. A study of the static characteristics of a torsional micromirror10.1016/S0924-4247(01)00453-8 ↗
22. Strain gradient torsional vibration analysis of micro/nano rods10.7508/ijnd.2012.01.001 ↗
23. Size dependent torsional vibration of nanotubes10.1016/j.physe.2010.06.015 ↗
24. Torsional vibrations of restrained nanotubes using modified couple stress theory10.1007/s00542-018-3735-3 ↗
25. Size-dependent vibration analysis of three-dimensional cylindrical microbeams based on modified couple stress theory: A unified treatment10.1016/j.ijengsci.2013.03.004 ↗
26. Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models10.1016/j.apm.2013.04.050 ↗
27. A nonlocal finite element method for torsional statics and dynamics of circular nanostructures10.1016/j.ijmecsci.2015.03.002 ↗
28. Torsional statics and dynamics of nanotubes embedded in an elastic medium10.1016/j.compstruct.2014.03.053 ↗
29. Torsional characteristics of graphene nanoribbons encapsulated in single-walled carbon nanotubes10.1016/j.physe.2016.05.006 ↗
30. Twisting statics of functionally graded nanotubes using Eringen’s nonlocal integral model10.1016/j.compstruct.2017.06.067 ↗
31. Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory10.1080/15397734.2019.1642766 ↗
32. Torsion of a functionally graded material10.1016/j.ijengsci.2016.09.003 ↗
33. Linear and nonlinear torsional free vibration of functionally graded micro/nano-tubes based on modified couple stress theory10.1007/s10483-016-2085-6 ↗
34. Size-dependent torsion of functionally graded bars10.1016/j.compositesb.2015.08.011 ↗
35. Vibration of bi-dimensional functionally graded Timoshenko beams excited by a moving load10.1007/s00707-016-1705-3 ↗
36. Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions10.1016/j.compstruct.2015.08.021 ↗
37. Natural frequency analysis of 2D-FGM thick hollow cylinder based on three-dimensional elasticity equations10.1016/j.euromechsol.2010.10.002 ↗
38. Static response and free vibration of two-dimensional functionally graded metal/ceramic open cylindrical shells under various boundary conditions10.1007/s00707-011-0563-2 ↗
39. NURBS-based modeling and analysis for free vibration and buckling problems of in-plane bi-directional functionally graded plates10.1080/15376494.2018.1430273 ↗
40. Torsion of functionally graded nonlocal viscoelastic circular nanobeams10.1016/j.compositesb.2014.12.018 ↗
41. Torsional vibration of bi-directional functionally graded nanotubes based on nonlocal elasticity theory10.1016/j.compstruct.2017.03.097 ↗
42. Torsional statics of two-dimensionally functionally graded microtubes10.1080/15376494.2017.1400617 ↗
43. On the origin of size effects in small-strain elasticity of solid polymers10.1016/j.ijsolstr.2006.06.039 ↗
44. Second gradient of strain and surface-tension in linear elasticity10.1016/0020-7683(65)90006-5 ↗
45. Influence of couple-stresses on stress concentrations10.1007/BF02327219 ↗
46. Bernoulli–Euler beam model based on a modified couple stress theory10.1088/0960-1317/16/11/015 ↗
47. Mechanics of fluid-conveying microtubes: Coupled buckling and post-buckling10.3390/vibration2010007 ↗
48. A strain gradient functionally graded Euler–Bernoulli beam formulation10.1016/j.ijengsci.2011.11.010 ↗
49. Static and free vibration analyses of small-scale functionally graded beams possessing a variable length scale parameter using different beam theories10.1016/j.euromechsol.2014.01.002 ↗
50. Bending and free vibrations of functionally graded annular and circular micro-plates under thermal loading10.1016/j.compstruct.2015.11.024 ↗
51. Free vibration analysis of functionally graded rectangular nano-plates considering spatial variation of the nonlocal parameter10.24423/aom.2414 ↗
52. Modelling of graded rectangular micro-plates with variable length scale parameters10.12989/sem.2018.65.5.573 ↗
53. Thermal effect on bending, buckling and free vibration of functionally graded rectangular micro-plates possessing a variable length scale parameter10.1007/s00542-018-3773-x ↗