Variational asymptotic modeling of the multilayer functionally graded cylindrical shells

An efficient high-fidelity shell model is developed for heterogeneous multilayer cylindrical shells made of functionally graded material by using the variational asymptotic method (VAM). Taking advantage of the smallness parameters inherent in the shell structure, the VAM is applied to rigorously decouple the 3-D, anisotropic elasticity problem into a 1-D through-the-thickness analysis and a 2-D shell analysis. The through-the-thickness analysis servers as a link between the original 3-D analysis and the shell analysis by providing a constitutive model for the shell analysis and recovering the 3-D field variables in terms of global responses calculated by the shell analysis. The present model is valid for large displacements and global rotations and can capture all the geometric nonlinearity of a shell when the strains are small. A cylindrical bending example of a homogeneous substrate with a thin SiC–Al functionally graded coating under sinusoidal pressure on the top surface is used to validate this model.