Nonlocal strain gradient shell theory for bending analysis of FG spherical nanoshells in thermal environment

In this study, we focus on the bending of the functionally graded spherical nanoshells using first-order shell theory in the thermal environment. Nonlocal strain gradient theory is applied to consider the small-scale impacts with considering both softening and stiffness enhancement effects of the spherical panel. The governing equations are deduced by applying Hamilton's principle, and Navier's series is used to solve the bending deflection of spherical nanoshells. The work provides a possibility that the bending behaviors of spherical shallow and deep spherical nanoshells can allow being investigated in a general framework. The simulations indicate that the temperature variation has a significant influence when the nonlocal parameter value is greater than 1 nm. Furthermore, the impacts of several parameters like a nonlocal parameter, strain gradient length scale parameter, and temperature variation are investigated on the deflection response of the spherical panel.