Evaluating Shakedown for Structures Based on the Element Bearing-Ratio


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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.



Edited by:

Robert Zhu






W. Zhang et al., "Evaluating Shakedown for Structures Based on the Element Bearing-Ratio", Applied Mechanics and Materials, Vol. 137, pp. 16-23, 2012

Online since:

October 2011




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