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

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 P-f 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.