The paper is concerned with an optimal control problem governed by the
equations of elasto plasticity with linear kinematic hardening and the inertia
term at small strain. The objective is to optimize the displacement field and
plastic strain by controlling volume forces. The idea given in [10] is used to
transform the state equation into an evolution variational inequality (EVI)
involving a certain maximal monotone operator. Results from [27] are then used
to analyze the EVI. A regularization is obtained via the Yosida approximation
of the maximal monotone operator, this approximation is smoothed further to
derive optimality conditions for the smoothed optimal control problem.
This paper proposes a modified scaled spectral-conjugate-based algorithm for finding solutions to monotone operator equations. The algorithm is a modification of the work of Li and Zheng in the sense that the uniformly monotone assumption on the operator is relaxed to just monotone. Furthermore, unlike the work of Li and Zheng, the search directions of the proposed algorithm are shown to be descent and bounded independent of the monotonicity assumption. Moreover, the global convergence is established under some appropriate assumptions. Finally, numerical examples on some test problems are provided to show the efficiency of the proposed algorithm compared to that of Li and Zheng.
Optimal Control of Plasticity with Inertia
