An integrated approach for all necessary variations within direct analysis, variational design sensitivity analysis and shakedown analysis based on Melan’s static shakedown theorem for linear unlimited kinematic hardening material behavior is formulated. Remarks on the computer implementation and numerical examples show the efficiency of the proposed formulation. Important effects of shakedown ...

An optimal control problem is considered for the variational inequality representing the stress-based (dual) formulation of static elastoplasticity. The linear kinematic hardening model and the von Mises yield condition are used. The forward system is reformulated such that it involves the plastic multiplier and a complementarity condition. In order to derive necessary optimality conditions, a ...

An optimal control problem of static plasticity with linear kinematic hardening and von Mises yield condition is studied. The problem is treated in its primal formulation, where the state system is a variational inequality of the second kind. First-order necessary optimality conditions are obtained by means of an approximation by a family of control problems with state system regularized by Hub...

We consider a model for one-dimensional transversal oscillations of an elastic-ideally plastic beam. It is based on the von Mises model of plasticity and leads after a dimensional reduction to a fourth-order partial differential equation with a hysteresis operator of Prandtl-Ishlinskii type whose weight function is given explicitly. In this paper, we study the case of clamped beams involving a ...

The algorithmic consistency conditions are derived which yield the plastic loading index for the combined isotropic– kinematic hardening plasticity with the Armstrong–Frederick evolution equation for the back stress. Rate-independent elastic–plastic, and rate-dependent viscoelastic–plastic and elastic–viscoplastic material models are all encompassed by the analysis. The directions of the plasti...

An optimal control problem is considered for the variational inequality representing the stress-based (dual) formulation of static elastoplasticity. The linear kinematic hardening model and the von Mises yield condition are used. Existence and uniqueness of the plastic multiplier is rigorously proved, which allows for the re-formulation of the forward system using a complementarity condition. I...