Numerical non-linear analysis of secondary buckling in stability problems Original Research Article

In this paper we discuss the numerical calculation of secondary buckling of structures. This kind of stability problem contains two parameters (one is conservative load parameter, the other is auxiliary one) and satisfies Z2-symmetry. By using the symmetry and introducing a new parameter we construct an augmented system. The system avoids the singularities of usual ones. Adjusting the newly introduced parameter, one can calculate a double buckling load and two corresponding buckling modes, secondary buckling load and secondary buckling mode directly without tracing primary post-buckling path. Here, the use of the augmented system yields a quadratically convergent iteration scheme. We also discuss the implementation of Newtonʹs method solving the system — a partitioning procedure. With this algorithm the amount of computation is largely saved.