On structural safety assessment by load factor maximization in piecewise linear plasticity

The safety assessment of structures by the maximization of a load factor up to a critical threshold is considered in this paper and a procedure is developed which generalizes limit analysis by the static approach. The following issues are dealt with: (a) piecewise linear approximation of material models is adopted as a unifying framework; (b) a procedure is developed apt to reduce the computing effort by means of yield mode selection or “sifting”; (c) a method which combines limit and deformation analysis is presented, based on mathematical optimization under linear and complementarity constraints and apt to compute, also in the presence of nonassociativity and softening, the safety factor with respect to either plastic collapse or local fracture or unserviceability because of excessive deformations, alternatively. Classical limit analysis rooted in associative perfect plasticity has well-known limitations, which are substantially mitigated in its generalization represented by method (c) proposed herein.