自适应材料插值在柔顺常力机构非线性拓扑优化中的应用

为解决柔顺常力机构的非线性拓扑优化中存在的数值不稳定问题,对非线性拓扑优化的材料插值方法进行了研究。首先,根据常力机构的工作特点以及输出特性,分别构建了其非线性拓扑优化的设计域以及优化模型;然后,对数值不稳定问题产生的原因展开了讨论,从控制应变以避免数值不稳定问题的角度出发,提出了一种新的材料插值模型,模型中引入了参数α,对低密度单元抗变形能力进行了统一调节,并根据最大等效应变给出了一种参数α的自适应调整策略;最后,基于提出的材料插值模型,推导了常力机构优化模型的目标函数敏度表达式,对不同常力区间的常力机构进行了优化,分别对优化结果以及优化效率进行了讨论;并搭建了实验平台,对优化得到的常力机构的实际输出性能进行了验证。实验结果显示:该方法优化得到的常力机构在特定的常力区间内,最大输出力误差为2.3%。研究结果表明:自适应材料插值方法有效地避免了数值不稳定问题,稳定性得到了提升,且优化效率相比于附加超弹材料方法得到了提升。

超冷原子动量光晶格中的非线性拓扑泵浦

在拓扑系统中,探索相互作用引起的新奇的拓扑泵浦现象日益受到人们的关注,其中包括由相互作用诱导的非线性拓扑泵浦.本文提出可以利用超冷原子动量光晶格系统,有效地模拟一维非线性的非对角Aubry-André-Harper(AAH)模型,研究非线性拓扑泵浦的实验方案.首先,通过数值方法计算了一维非对角AAH模型的非线性能带结构随相互作用强度的变化,得到了非线性系统的孤子态解.然后,分析了不同相互作用强度下孤子态的拓扑输运,发现其质心的移动距离具有量子化的输运特征,由所占据能带的陈数决定,并讨论了非线性拓扑泵浦对相互作用符号的依赖性.同时还计算了在不同相互作用强度下,系统最低能带和最高能带对应陈数的分布.最后,基于^(7)Li原子的动量光晶格实验系统,提出了一个非线性拓扑泵浦方案.本文构造了一种近似于孤子态分布的初始态并演示了其动力学演化过程,并分析了绝热演化条件对泵浦过程的影响.结果表明,在动量晶格系统中演示非线性拓扑泵浦具有可行性.本文的工作为在超冷原子系统中研究非线性拓扑泵浦提供了一个可行的途径,有助于进一步探测非线性引起的拓扑相变和边界效应.

汽车碰撞关键件非线性拓扑优化设计

由于汽车碰撞安全法规的升级以及轻量化的需求,对汽车碰撞关键件的优化提出了更高的要求。基于混合元胞自动机法,给出了汽车开发详细设计阶段在复杂工况下实现非线性拓扑优化的流程。首先,将整车模型根据工况特点简化为等效模型;然后,基于等效模型开展非线性拓扑优化设计;最后,将等效模型优化结果应用于整车模型中进行验证,完成轻量化设计,其中,对于侧面柱碰撞工况动力电池的防护,以门槛梁为优化对象,在原有优化结果的基础上通过设计使重量减小了12%。针对《中国保险汽车安全指数测试评价规程》(2023版征求意见稿)中侧面碰撞工况后的车门侵入过大问题,采用非线性拓扑优化对C柱钣金进行设计,使重量减小了13%。

试析非线性泛函分析中的辩证思想

本文利用数学的结果分析了非线性泛函分析中某些内容所蕴含的辩证思想,揭示了它们所体现的哲学基本规律,探讨了非线性泛函某些课题的发展趋势.

光子拓扑绝缘体:超快激光直写加工与应用(特邀)

超快激光直写技术可以高精度加工任意三维波导结构,从而实现新型拓扑模型以及集成化的拓扑光子器件。通过经典的拓扑结构(如一维二元复式晶格、非对角Aubry-André-Harper晶格、蜂窝晶格),阐述拓扑光学的基本原理和现象(如Thouless泵浦,手性边缘态、局域态与拓扑不变量之间的关系),介绍最新的拓扑光子学进展与应用(如高阶拓扑绝缘体、Floquet拓扑绝缘体、非厄米拓扑、非线性拓扑,以及量子拓扑保护),重点综述在超快激光直写平台下实现的拓扑现象与应用。

广义拓扑度

拓扑度理论的公理体系,已在1973年由Aman和Weiss给出,空间C(X,X)取一致收敛拓扑。本文用较一般的拓扑代替一致收敛拓扑,推广了拓扑度理论,这种广义拓扑度具有通常拓扑度的基本性质。

Anti-synchronization Between Coupled Networks with Two Active Forms

This paper studies anti-synchronization and its control between two coupled networks with nonlinear signal＇s connection and the inter-network actions. If anti-synchronization does not exist between two such networks, adaptive controllers are designed to anti-synchronize them. Different node dynamics and nonidentical topological structures are considered and useful criteria for anti-synchronization between two networks are given. Numerical examples are presented to show the efficiency of our derived results.

A GLKKM Type Theorem for Noncompact Complete L-Convex Metric Spaces with Applications to Variational Inequalities and Fixed Points

In this paper,a new GLKKM type theorem is established for noncompact complete L-convex metric spaces.As applications,the properties of the solution set of variational in-equalities,intersection point sets,Ky Fan sections and maximal element sets are shown,and a Fan-Browder fixed point theorem is obtained.

Data-Driven Leader-Follower Output Synchronization for Networked Non-Linear Multi-Agent Systems with Switching Topology and Time-Varying Delays

This paper studies the output synchronization problem for a class of networked non-linear multi-agent systems with switching topology and time-varying delays. To synchronize the outputs,a leader is introduced whose connectivity to the followers varies with time, and a novel data-driven consensus protocol based on model free adaptive control is proposed, where the reference input of each follower is designed to be the time-varying average of the neighboring agents＇ outputs. Both the case when the leader is with a prescribed reference input and the case otherwise are considered.The proposed protocol allows for time-varying delays, switching topology, and does not use the agent structure or the dynamics information implicitly or explicitly. Sufficient conditions are derived to guarantee the closed-loop stability, and conditions for consensus convergence are obtained, where only a joint spanning tree is required. Numerical simulations and practical experiments are conducted to demonstrate the effectiveness of the proposed protocol.