Analysis and verification of geometric nonlinear response in solid rocket motor grains using successive approximation method

To investigate the influence of geometric nonlinearity on the mechanical response of solid rocket motor (SRM) grains, this study proposes an analytical framework based on the successive approximation method, aiming to elucidate the nonlinear response characteristics of tubular propellant structures under internal pressure loading. By incorporating finite deformation theory, the displacement, strain, and stress fields are decomposed into asymptotic power series. The first-order linear solution (primary successive approximation) and the second-order nonlinear correction term (secondary successive approximation) are sequentially derived, ultimately establishing an analytical expression for the mechanical response that accounts for geometric nonlinearity. To validate the theoretical model, cold-pressurization tests were conducted on tubular SRM grains, and systematic comparisons were made using numerical simulations and experimental data. The results demonstrate that, within an internal pressure range of 2–10 MPa, the maximum relative error between the successive approximation solutions and experimental values is below 15%, with an average error controlled within 8%, significantly outperforming traditional linear theories. The proposed analytical method accurately characterizes geometric nonlinear effects induced by finite deformation, providing critical theoretical support for structural integrity assessment and optimized design of SRM grains.