Evaluating Shakedown for Structures Based on the Element Bearing-Ratio
Based on Melan’s theorem, an improved numerical solution procedure for evaluating shakedown loads by non-linear superposition method is presented, and the relationship between the classical non-linear programming formulation of shakedown problem and the numerical method is disclosed. The stress term in classical optimization problem is replaced by the element bearing-ratio (EBR) in the procedure, and series of residual EBR fields can be generated by the D-value of the elastic-plastic EBR fields and the elastic EBR fields at every incremental loading step. The shakedown load is determined by performing the incremental non-linear static analysis when the yield criterion is arrived either by the elastic-plastic EBR fields or residual EBR fields. By introducing the EBR, the proposed procedure can be easily used to those complex structures with multi-material and complicated configuration. The procedure is described in detail and some numerical results, that show the efficiency and effectiveness of the proposed method, are reported and discussed.
W. Zhang et al., "Evaluating Shakedown for Structures Based on the Element Bearing-Ratio", Applied Mechanics and Materials, Vol. 137, pp. 16-23, 2012