A hybrid-stress formulation based reduced-order method using a solid-shell element for geometrically nonlinear buckling analysis

The high computational efficiency of the Koiter reduced-order methods for structural buckling analysis has been extensively validated; however the high-order strain energy variations in constructing reduced-order models is still time-consuming, especially when involving the fully nonlinear kinematics. This paper presents a reduced-order method with the hybrid-stress formulation for geometrically nonlinear buckling analysis. A solid-shell element with Green-Lagrange kinematics is developed for three-dimensional analysis of thin-walled structures, in which the numerical locking is eliminated by the assumed natural strain method and the hybrid-stress formulation. The fourth-order strain energy variation is avoided using the two-field variational principle, leading to a significantly lower computational cost in construction of the reduced-order model. The numerical accuracy of the reduced-order model is not degraded, because the third-order approximation to equilibrium equations is recovered by condensing the stress. Numerical examples demonstrate that although the fourth-order strain energy variation is not involved, the advantage in path-following analysis using large step sizes is not only unaffected, but also enhanced in some cases with respect to the displacement based reduced-order method. The small computational extra-cost for the hybrid-stress formulation is largely compensated by the reduced-order analysis.