Static analysis of tri-coated functionally graded nanoshells by Galerkin approach

Advancing theoretical research in structural modeling poses significant challenges compared to experimental investigations of complex systems. To explore size-dependent bending behavior, this study introduces a novel "Tri-coated FGM" shell model that incorporates spatial variations in material properties. The research examines two types of coated FG shells, Hardcore and Softcore, and proposes five distribution patterns. Four structures are analyzed: plates, cylindrical, spherical, and hyperbolic-paraboloid shells. By reducing the number of variables from five to four and incorporating shear deformation effects, a simplified displacement field is proposed. Analytical solutions, derived using the Galerkin method and the virtual work principle, address various boundary conditions. A comprehensive parametric analysis is performed to assess the impact of different FG nanoshell types, distribution patterns, gradient material distribution, length scale parameter (nonlocal), and material scale parameter (gradient).