Iterative techniques for non-linear eigenvalue buckling problems

Structural stability problems under displacement‐dependent loads often take the form of non‐linear eigenvalue problems in which the eigenvalue is raised to an exponent. Iterative techniques are considered in this work for the solution of non‐linear eigenproblems of the form (K ‐ λK1 ‐ K2(λp))x = 0. The problem is linearized at each iteration using two alternative procedures: through updating the stiffness matrix K or else by updating the initial stress matrix. Numerical examples are used to illustrate the difficulties associated with the first technique, whereas it is shown that the second one yields better convergence rates than other existing techniques.