In the incremental analysis of the critical behavior of an elastic-plastic structure, a conventional iterative procedure for finding the set of element stiffness coefficients consistent with the material flow law may often lead to a pitfall of cyclic process, in which a multiple inconsistent sets of stiffness coefficients are to be alternately or recurrently selected. This is one of the most serious difficulties left unsolved in combined nonlinear analysis. In this paper, the intrinsic mechanism and characteristics of these cyclic processes are clarified for a simple rigid body-spring column model. On the basis of the results, an effective strategy for finding the consistent set is proposed with the use of the eigenvector associated with the smallest negative eigenvalue of system stiffness matrix.
