论文标题
拓扑优化用于准危机的弹性性
Topology optimization for quasistatic elastoplasticity
论文作者
论文摘要
拓扑优化与给定目标功能相对于可变形物体的最佳形状鉴定。本文的重点在于在运动硬化下，随着时间发展的弹性培养基的拓扑优化问题。我们采用相位场方法，并通过随后的近似值来争论，首先是通过离散时间，然后通过正规化流量规则来进行论证。最佳形状的存在是在时间污染和时间脉络上证明的，独立于正则化。首先在正规时间污染设置中获得一阶最佳条件，然后证明传递到非规范化的时间连续限制。相位场的近似显示通过进化的变分收敛参数传递到其尖锐的界限限制。
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic medium under kinematic hardening. We adopt a phase-field approach and argue by subsequent approximations, first by discretizing time and then by regularizing the flow rule. Existence of optimal shapes is proved both at the time-discrete and time-continous level, independently of the regularization. First order optimality conditions are firstly obtained in the regularized time-discrete setting and then proved to pass to the nonregularized time-continuous limit. The phase-field approximation is shown to pass to its sharp-interface limit via an evolutive variational convergence argument.
