Ratchet Boundary Determination Using a Noncyclic Method

A simple and systematic procedure is proposed for shakedown analysis using a combination of linear and nonlinear finite element analysis (FEA). The method can identify the boundary between the shakedown and ratcheting domains directly and does not require a cyclic analysis (noncyclic). The proposed method performs an elastic-plastic FEA to determine the reduction in load carrying capacity due to the cyclic secondary loads. An elastic modulus adjustment procedure is then used to generate statically admissible stress distributions and kinematically admissible strain distributions under the applied primary loads. By modifying the local elastic moduli it is possible to obtain inelastic-like stress redistribution. The method is 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,” the “bimaterial cylinder,” and the “plate with a hole subjected to radial temperature gradient.”