Creep analysis of axisymmetric VFG cylindrical shells under axial and lateral pressure based on FSDT

• Deriving equilibrium equations for cylindrical shells with viscoelastic functionally graded properties (VFG). • Viscoelastic properties are modeled using Zener three-parameter models for shear behavior, while assuming elastic behavior for bulk properties. • The loadings consist of axial and lateral pressures, either long or short duration, and continuous or piecewise distribution. The presented solution does not depend on the duration of loading. • No need for new modeling for sensitivity analysis and optimization. This manuscript presents an analytical method for determining the deformations of cylindrical shells with viscoelastic functionally graded (VFG) properties under axial and transverse pressures. The displacement field follows first-order shear deformation theory (FSDT), with a standard linear solid (SLS) model representing viscoelastic behavior. Property variations through the shell thickness are modeled using a continuous power function. Kinematics adhere to von Kármán relations, and Hooke's law serves as the constitutive equation. Equilibrium equations are derived via the virtual work principle, resulting in a system of coupled nonlinear partial differential equations. The Galerkin method is applied to remove the spatial part of the equations. The remaining ordinary differential equations are solved analytically using the multiple-scale method. The results indicate the creep phenomenon of the shell under constant loads. Sensitivity analysis shows that the power law index as well as the viscoelastic properties can affect the deformation rate. Additionally, for piecewise loading, recovery behavior is observed in the response. The analytical procedure presented can be an effective formulation for optimization through trial and error. The results are compared with the finite element (FE) method for special cases.