Elastic plastic analysis by the asymptotic pivoting method

Elastoplastic analysis of frames composed of softening materials by restricted basis linear programming

“…8. Here, again, the plastic joints distribution at peak load coincides with that reported in [16]. The CPU time used for the analyses of this example via the proposed algorithm was 0.92 second for combined bending and axial with softening, 0.19 second for pure flexural with softening, and 0.38 second for perfect plasticity [21].…”

“…In case (b), the solution process reaches to the peak load k = 119.8446 without any specific event at the horizontal deflection of 0.3957 m. Continuing with the analysis, the sway limit of 0.75 m is reached for a load level of 114.0656 and the procedure stops at this stage. The same peak load (119.845) is reported in [16] for this case, which is exact as a result of ''no events''.…”

“…In order to increase the efficiency of the solution procedure, in some later researches the QP formulation was replaced by a Linear Complementarity Problem (LCP), [13], and by a Restricted Basis Linear Programming (RBLP) [14]. This approach was also improved and generalized to shakedown and nonlinear dynamic analyses [15,16]. Cocchetti and Maier implemented the aforementioned approach in the analysis of softening frames [17].…”

Elastoplastic analysis of plane stress/strain structures via restricted basis linear programming

“…The use of linear comple-mentarity problem (LCP) solvers was also found to be efficient and a restricted basis linear programming (RBLP) was proposed as an alternative to QP [9]. Therefore LCP concept was extended to various engineering problems such as dynamic analysis [10], shakedown analysis [11], and softening frames [12,13]. Also some researchers dealt with piecewise-linearization of yield surfaces, so as to be uti-lized in optimization approaches as linear constraints [14][15][16].…”

Complementarity framework for non‐linear dynamic analysis of skeletal structures with softening plastic hinges

“…As pointed out by Krabbenhoft et al 4, related efforts have so far been more on casting various incremental state update problems as mathematical programs, than on developing algorithms for practical size problems. Examples of work on algorithms include 4, where an interior point algorithm is developed for optimization problems, 35, where an asympototic pivoting method is developed for linear complementarity problems, and 36, where an iterative algorithm is presented for linear complementarity problems.…”