A New Koiter Asymptotic Analysis for Buckling-Sensitive Structures

The Koiter-Newton (K-N) approach is a new reduced basis path-following technique, which combines Koiter's analysis as a predictor and Newton method as a correc-tor. To trace the entire equilibrium path, a Koiters asymp-totic expansion is carried out to construct a reduced order model (ROM) at a known equilibrium point in each in-cremental step. The estimation of the response of the full model can be obtained by solving the ROM. A conventional Newton method can then be used to restore the equilibrium of the full model in a corrector step. The new found equilibrium point becomes the staring point of next incremental step. The proposed technique requires derivatives of the element load vectors with respect to the degrees of freedom up to the third order, which is two orders more than traditionally needed for a Newton method. Nonlinear elements based on the element independent co-rotational frame are applied to facilitate differentiation. The good performance of the method using co-rotational kinematics is illustrated with several numerical examples of shell models