Published in Computers & Structures Vol. 32 (1), pp. 125-135, 1989
In the prebuckling range of the complete nonlinear response of a structure submitted to destabilizing loads, a linearized stability analysis is generally an interesting tool. Used in conjunction with an arc-length algorithm, incremental bifurcation analyses are able to give optimal definition for the increment predictor size. When the associated eigenvalue problem is solved by minimizing the finite element discretized form of the Rayleigh quotient via a preconditioned conjugate gradient technique, it can be very easily inserted in an automatic nonlinear equations solver. Such a procedure is presented in this paper after a review of existing arc-length schemes and step-size control methods. Moreover, for tracing the postbuckling range of the nonlinear response automatically, a new recurrence formula is proposed to control the step-size. The well behaviour of this algorithm is illustrated in two classical structural applications.