Quasi-static analysis of viscoelastic cylindrical shell panels using an exponential time function

Purpose This study presents a quasi-static analysis of viscoelastic cylindrical shell panels based on the first-order shear deformation theory and the finite strip method. Design/methodology/approach The viscoelastic behavior of the material is modeled using the Boltzmann integral law, and the governing equilibrium equations are derived through the principle of virtual work. The displacement field is expressed as the product of spatial and temporal functions, where the spatial part is represented by a finite-strip discretization and the temporal variation is captured through an exponential time function with three unknown coefficients. These coefficients are determined analytically, allowing explicit evaluation of the deflection at any time without the need for numerical time integration. Findings The proposed analytical framework enables accurate prediction of the time-dependent deflection of viscoelastic shells under static loading with minimal computational effort. Originality/value This study introduces an analytical–semi-discrete formulation that avoids numerical time-stepping and offers an efficient alternative for the quasi-static analysis of viscoelastic shell structures. The method’s explicit temporal representation and reduced computational demand highlight its value for engineering applications involving viscoelastic materials.