Incremental Method for Unloading Phenomenon Fixation At Shakedown

Incremental method for shakedown analysis of the elastic perfectly plastic structures is based on the extremum energy principles and non-linear mathematical programming approach. Residual force increment calculation problem is developed applying minimum complementary deformation energy principle. The Rozen project gradient and equilibrium finite element methods were applied for solution. The Rozen optimality criterion (Kuhn-Tucker conditions) ensures compatibility of residual strains and allows plastic strain and residual displacement increment calculation without dual problem solution. The possibility to fix the structure cross-section unloading phenomenon during shakedown process was developed. The proposed technique is illustrated by annular bending plate residual force and deflection calculation examples, when the von Mises criterion is taken into account.