Successive approximation analysis and experimental validation of viscoelastic geometric nonlinear response for thick-walled cylindrical pressure vessels with application to solid rocket motor grains

The structural response of thick-walled cylindrical pressure vessels made of viscoelastic materials can be strongly affected by finite deformation. This study develops a successive approximation method for the geometrically nonlinear analysis of a case-bonded tubular solid rocket motor grain. A linear hereditary viscoelastic constitutive relation is combined with finite-deformation kinematics; thus, the nonlinearity considered is geometric rather than constitutive. The displacement, strain, and stress fields are expanded into asymptotic power series, from which a first-order linear solution and a second-order geometric nonlinear correction are derived. The resulting analytical solution is compared with the linear viscoelastic, initial-modulus, and equilibrium-modulus solutions to examine the effects of geometric nonlinearity, outer-to-inner radius ratio, and Poisson’s ratio. The model predicts pronounced geometric nonlinear effects near the inner wall, with strains approaching 80% in the investigated large-radius-ratio case. Cold pressurization tests were conducted for M = 4 and M = 6 over the pressure range of 2–10 MPa. The predicted inner-wall radial displacements agreed with the measurements, with relative errors below 15% under the tested conditions. The analysis further indicates that Poisson’s ratio can alter the stress state and may produce a triaxial compressive state throughout the vessel wall under the adopted assumptions. The proposed method provides an efficient analytical estimate of the geometrically nonlinear response of linear viscoelastic thick-walled cylinders. Material nonlinearity, damage, interface degradation, and broader loading conditions require further experimental and numerical investigation.