论文标题
完美可塑性的最佳控制第一部分：压力跟踪
Optimal Control of Perfect Plasticity Part I: Stress Tracking
论文作者
论文摘要
该论文涉及一个最佳控制问题，该问题由准静态弹性塑性性的速率无关系统控制。目的是通过控制边界规定部分的位移来优化应力场。因此，控制在Dirichlet边界条件下进入系统。因此，安全负载条件会自动实现，以便系统接收一个解决方案，其应力场是唯一的。这引起了一个定义明确的控制状态运算符，该操作员是连续但不是gateaux差异的。因此，首先通过Yosida正则化，然后通过第二次平滑以获得平滑的问题，然后通过Yosida正规化，然后通过Yosida正则化。显示了原始非平滑最佳控制问题的全局最小化器的近似值，并确定了正规化问题的最佳条件。一个数字示例说明了平滑方法的可行性。
The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is to optimize the stress field by controlling the displacement at prescribed parts of the boundary. The control thus enters the system in the Dirichlet boundary conditions. Therefore, the safe load condition is automatically fulfilled so that the system admits a solution, whose stress field is unique. This gives rise to a well defined control-to-state operator, which is continuous but not Gateaux-differentiable. The control-to-state map is therefore regularized, first by means of the Yosida regularization and then by a second smoothing in order to obtain a smooth problem. The approximation of global minimizers of the original non-smooth optimal control problem is shown and optimality conditions for the regularized problem are established. A numerical example illustrates the feasibility of the smoothing approach.
