The Elastic Modulus Adjustment Procedure (EMAP) for Shakedown

A simple and systematic procedure is proposed for shakedown analysis using combination of linear and non-linear finite element analysis (FEA). The method can identify the boundary between the shakedown and ratcheting domains directly does not require a time history analysis (non-cyclic). The proposed method is based on elastic modulus adjustment procedure (EMAP) and non-cyclic elastic-plastic FEA. The aim of EMAP is to generate statically admissible stress distributions and kinematically admissible strain distributions. By modifying the local elastic moduli it is possible to obtain an inelastic-like stress redistribution. The method is first demonstrated with a two-bar structure model based on analytical routine. The analysis is then applied to some typical shakedown problems including the “classical Bree problem” and the “bi-material cylinder”.