Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening Part I: Existence and Discretization in Time

Topology optimization for quasistatic elastoplasticity

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 re…

含惯性的塑性最优控制

Optimal Control of Plasticity with Inertia

本文针对含惯性项的小应变弹塑性系统，通过Yosida逼近与光滑化处理演化变分不等式，研究以体积力控制位移场和塑性应变的最优控制问题，并推导最优性条件。

Applications of conic programming in non-smooth mechanics

In the field of nonlinear mechanics, many challenging problems (e.g. plasticity, contact, masonry structures, nonlinear membranes) turn out to be expressible as conic programs. In general, such problems are non-smooth in nature (plasticity condition, unilateral condition, etc.), which makes their numerical resolution through standard Newton methods quite difficult. Their formulation as conic programs alleviates this difficulty since large-scale conic optimization problems can now be solved in a very robust and efficient manner, thanks to the development of dedicated interior-point algorithms. …

正则性丢失：弹塑性问题中的基本局限性与约束规范

Regularity lost: the fundamental limitations and constraint qualifications in the problems of elastoplasticity

本文从对偶表述视角研究弹塑性模型中函数值应变解的存在性，通过法锥可加性与约束规范失效解释应变正则性丢失，并指出硬化模型因满足约束规范而保证解的存在性。

度量空间中临界点的平衡准静态演化

Balanced quasistatic evolutions of critical points in metric spaces

本文提出了一种基于分离能量演化与系统过渡时标的平衡准静态演化方法，适用于度量空间中的临界点问题，无需非退化临界点假设。

Identification of some nonsmooth evolution systems with illustration on adhesive contacts at small strains

A class of evolution quasistatic systems which leads, after a suitable time discretization, to recursive nonlinear programs, is considered and optimal control or identification problems governed by such systems are investigated. The resulting problem is an evolutionary Mathematical Programs with Equilibrium Constraints (MPEC). A subgradient information of the (in general nonsmooth) composite objective function is evaluated and the problem is solved by the Implicit programming approach. The abstract theory is illustrated on an identification problem governed by delamination of a unilateral adhe…