Topology optimization for incremental elastoplasticity: a phase-field approach

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…

有限应变弹塑性多材料拓扑优化：理论、方法与应用

Multimaterial topology optimization for finite strain elastoplasticity: theory, methods, and applications

本文提出有限应变弹塑性多材料拓扑优化框架，同时优化结构几何与材料相，结合反向伴随法和自动微分处理历史依赖与复杂导数，在2D/3D结构中实现刚度、强度与韧性的定制。

Topology Optimization with Frictional Self-Contact

Contact-aware topology optimization faces challenges in robustness, accuracy, and applicability to internal structural surfaces under self-contact. This work builds on the recently proposed barrier-based Incremental Potential Contact (IPC) model and presents a new self-contact-aware topology optimization framework. A combination of SIMP, adjoint sensitivity analysis, and the IPC frictional-contact model is investigated. Numerical examples for optimizing varying objective functions under contact are presented. The resulting algorithm proposed solves topology optimization for large deformation a…

Piecewise Linear Topology, Evolutionary Algorithms, and Optimization Problems

Schemata theory, Markov chains, and statistical mechanics have been used to explain how evolutionary algorithms (EAs) work. Incremental success has been achieved with all of these methods, but each has been stymied by limitations related to its less-than-global view. We show that moving the investigation into topological space improves our understanding of why EAs work.

A fast randomized incremental gradient method for decentralized non-convex optimization

We study decentralized non-convex finite-sum minimization problems described over a network of nodes, where each node possesses a local batch of data samples. In this context, we analyze a single-timescale randomized incremental gradient method, called GT-SAGA. GT-SAGA is computationally efficient as it evaluates one component gradient per node per iteration and achieves provably fast and robust performance by leveraging node-level variance reduction and network-level gradient tracking. For general smooth non-convex problems, we show the almost sure and mean-squared convergence of GT-SAGA to a…

凸优化的增量随机次梯度法

Incremental Stochastic Subgradient Algorithms for Convex Optimization

本文研究了随机误差对两种约束增量次梯度算法的影响。我们认为，增量次梯度算法作为分散的网络优化算法，应用于最小化的功能和，当每个组件功能是已知的，只有一个特定的代理的分布式网络。我们首先研究了标准的循环增量次梯度算法，其中的代理形成一个环结构，并通过在一个循环中的迭代。我们考虑的方法与随机误差的次梯度评估，并提供了充分条件的随机误差的时刻，保证几乎必然收敛时，使用一个递减的步长。我们还获得了几乎必然的边界上的算法的性能时，使用一个恒定的步长。然后，我们考虑\ram{the}马尔可夫随机增量次梯度方法，这是一个非循环版本的增量算法，其中的计算代理的序列被建模为时间非齐次马尔可夫链。这种模型适用于移动网络，因为这些网络中的网络拓扑随时间而变化。我们建立了收敛结果和误差界的马尔可夫随机化方法存在的随机误差，分别为递减和恒定的步长。