Optimal shakedown loading for circular plates

Optimization of shakedown loading under constrained residual displacement is considered for elastic and perfectly plastic circular plates. The load variation bounds, which satisfy the optimality criterion in concert with plate-strength and stiffness requirements, are identified. The actual strain fields of the plate depend on the loading history. Thus, the load optimization problem at shakedown is stated as a pair of problems that are executed in parallel: the main load optimization and the verification of the prescribed magnitudes of the bounds on the residual deflections. The problem must be solved by iteration. The Rozen projected gradient method is applied. A mechanical interpretation of the Rozen optimality criterion is given, which permits the simplification of the mathematical model for load optimization and the formulation of the solution algorithm. Numerical examples include circular annular plates with and without a rigid inclusion. The results are valid under the assumption of small displacements.