Analysis and Numerical Techniques for Optimal Control Problems Involving Variational Inequalities Arising in Elastoplasticity

涉及弹塑性变分不等式的最优控制问题的分析和数值技术

• 批准号: 133426576
• 负责人: Professor Dr. Roland Herzog
• 金额: --
• 依托单位: Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/133426576?language=en
• 关键词: Analysis; Numerical; Techniques; Optimal; Control

Solid bodies depart from their rest shape under the influence of applied loads. In case the applied loads or stresses are sufficiently small, many solids exhibit a linearly elastic and reversible behavior. If, however, the stress induced by the applied loads exceeds a certain threshold (the yield stress), the material behavior switches from the elastic to the so-called plastic regime. In this state, the overall loading process is no longer reversible and permanent deformations remain even after the loads are withdrawn. Mathematically, this leads to a description involving variational inequalities.Plastic deformation is desired for instance as an industrial shaping technique of metal workpieces. The task of finding appropriate time-dependent loads which effect a desired final deformation leads to optimal control problems for elastoplasticity systems. The main goals of this project are to investigate these optimization problems, to quantify the error due to discretization, and to develop fast algorithms for their solution.

固体在外加载荷的影响下会偏离其静止形状。在所施加的载荷或应力足够小的情况下，许多固体表现出线性弹性和可逆行为。然而，如果由所施加的载荷引起的应力超过某个阈值（屈服应力），则材料行为从弹性状态切换到所谓的塑性状态。在这种状态下，整个加载过程不再可逆，即使在负载撤回后，永久变形仍然存在。从数学上讲，这导致了涉及变分不等式的描述。例如，作为金属工件的工业成形技术，需要塑性变形。找到适当的时间依赖性的负载，影响所需的最终变形的任务导致弹塑性系统的最优控制问题。这个项目的主要目标是研究这些优化问题，量化由于离散化的错误，并开发快速算法解决这些问题。