Nonlinear low-velocity impact analysis of functionally graded shallow spherical shells in thermal environments

Abstract

This article presents the nonlinear dynamic response of functionally graded (FG) shallow spherical shells in thermal environments subjected to low-velocity impact by an elastic ball. The material properties of a FG shallow spherical shell vary continuously through the thickness according to a power law distribution of the volume fraction of the constituents. The temperature field is considered to vary along the thickness direction due to the steady state heat transfer. Based on the higher order shear deformation theory, the governing equations of motion for the shell, which account for geometric nonlinearity is obtained using Hamilton's principle. The contact force between the shell and the impactor is relative to local deformation and calculated using a numerical method. Then, the governing equations of motion are solved numerically by the Chebyshev collocation method and Newmark scheme. This is a complete model that can not only fully model the dynamic behavior of the shell but also fully model the impactor's dynamic behavior. In the numerical example, the effects of material properties, temperature, initial impact velocity and mass of the impactor on the dynamic behavior of the shells, and contact force are discussed in detail.

Nonlinear thermo-mechanical buckling and postbuckling of sandwich FG-GPLRC spherical caps and circular plates with porous core by using higher-order shear deformation theory

“…The displacements of any point on the spherical caps and circular plates at a distance z from the middle surface according to the HSDT are respectively as 34,39 where λ=4/h2, ψ(r) is the rotation of a normal to the middle surface, and the initial imperfection of the spherical caps and circular plates w0(r) is taken into account.…”

“…The displacements of any point on the spherical caps and circular plates at a distance z from the middle surface according to the HSDT are respectively as 34,39…”

“…For sandwich FGM spherical caps and circular plates, the bending, buckling, vibration and nonlinear dynamic problems were analyzed by Reddy et al, 34 Phuong et al, 35 Minh et al, 36 Alipour and Shariyat, 37 Anh and Duc, 38 and Fu et al 39…”

“…For sandwich FGM spherical caps and circular plates, the bending, buckling, vibration and nonlinear dynamic problems were analyzed by Reddy et al, 34 Phuong et al, 35 Minh et al, 36 Alipour and Shariyat, 37 Anh and Duc, 38 and Fu et al 39 Based on the idea of FGM, in recent years, the types of nanocomposite including functionally graded graphene platelet reinforced composite (FG-GPLRC) and functionally graded carbon nanotube reinforced composite (FG-CNTRC) have also started to be studied. [40][41][42] These types of material also have the advantages of FGM such as lightness and good load capacity.…”