New nonlinear solution of nearly incompressible hyperelastic FGM cylindrical shells with arbitrary variable thickness and non-uniform pressure based on perturbation theory

Abstract In this paper, nonlinear analysis of thick cylindrical shells with arbitrary variable thickness made of hyperelastic FGM with radially variation of material properties in nearly incompressible state under non-uniform pressure loading is presented. Thickness and pressure of the shell vary in axial direction by linear and/or nonlinear functions. The governing equilibrium equations are derived based on shear deformation theory (SDT). The Mooney-Rivlin type material is considered which is a suitable hyperelastic model for rubbers. Boundary Layer Method of the perturbation theory which is known as Matched Asymptotic Expansion (MAE) is used for solving the governing equations. A new ingenious solution and formulation have been defined during current study to simplify and abbreviate the representation of inner and outer equations components in MAE. In order to validate the results of the current analytical solution, a numerical modeling based on Finite Element Method (FEM) have been investigated. Afterwards, for different rubber case studies, the effect of material constants, inhomogeneity index, geometry and pressure profiles on displacements, stresses and hydrostatic pressure distributions resulting from MAE and FEM solution have been illustrated. This approach enables insight into the nature of the deformation and stress distribution across the wall of rubber vessels and offers the potential for investigating the mechanical functionality of blood vessels such as arteries in physiological pressure range. The results prove the effectiveness of SDT and MAE combination to derive and solve the governing equations of nonlinear problems such as nearly incompressible hyperelastic FG shells.