Solution methods and initialization techniques in SFE analysis of structural stability

Computational efficiency is a significant issue in simulation-based stochastic stability analysis of structures with random material properties. The efficiency of the analysis is affected by the selection of eigenproblem solution method and, for a specific eigensolution, how the iterations are initialized. This study applies the inverse and shifted inverse iteration methods to solve the eigensystem for the lowest eigenpair (the smallest buckling load and corresponding buckled shape). The efficiency and accuracy of these two methods are investigated in combination with several initialization strategies to start the solution processes. Among these strategies is a novel tree-type ordering strategy. The impact of the use of the solution methods and initialization strategies on the efficiency of the stochastic stability analysis is investigated and is illustrated in analyses of three systems: a sway frame, a column with a spring support at the mid-span, and a two-bay frame structure.