Static analysis of a circular nanotube made of functionally graded bi-semi-tubes using nonlocal strain gradient theory and a refined shear model

• Published in: European journal of mechanics, A, Solids Vol. 82; p. 103979
• Main Authors: Xiao, Wan-shen, Dai, Pei
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Masson SAS 01.07.2020; Elsevier BV
• Subjects: Bending; Bi-semi-tubes; Boundary conditions; Deformation; Exact solutions; Functionally graded materials; Functionally gradient materials; Hamilton's principle; Material properties; Mathematical models; Mechanical properties; Nanotubes; Nonlinear bending; Nonlocal strain gradient Theory; Parameters; Performance indices; Perturbation methods; Physical properties; Shear; Shear model; Titanium base alloys; Tubes; Zirconium dioxide; Nonlinear bending; Bi-semi-tubes; Shear model; Nonlocal strain gradient Theory; Functionally graded materials
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2020.103979

We in this article put forward a novel size-dependent beam model for static bending deformation of a functionally graded bi-semi-tube subjected to different boundary conditions based on the nonlocal strain gradient theory. The tube is formed by bonding together a ZrO2/Ti–6Al–4V functionally graded lower semi-tube and a Si3N4/SUS304 functionally graded upper one. The effective material properties Pf of FG bi-semi-tubes are assumed to vary along the radius of tube. We propose a refined shear model without requiring a shear correction factor for bars with circular cross section. Next the model is used to derive the governing equations of the tube based on the Hamilton's principle. The obtained equations form present a detailed analysis include a nonlocal parameter as well as a material length scale parameter, so much that they can account for the size-dependent in static bending of FG bi-semi-tubes. Later, these equations are resolved analytically by using an improved perturbation method. The analytical solutions are used to discuss the influence of various physical parameters on static mechanical performance of nanotubes, such as double volume fraction indexes, inner radius, the variation of temperature, strain gradient parameter, nonlocal parameter, scale parameter ratio. At last, compared with the conventional approaches, the novel approach is suggested in such work to lead to more accurate bending deformation in the same dimensionless size of tubes. •Nonlinear bending of nano-tubes made of functionally graded bi-semi-tubes has n been studied in detail.•We put forward a novel displacement function without acquiring a shear correction factor.•Nonlocal strain gradient theory is used to characterize size-dependent of nanostructures.•The perturbation method is used for solving the problem to obtain an analytical solution.•In contrast to conventional approach, the present approach results in more accurate bending control in the same conditions.