基于参数化水平集法的材料非线性子结构拓扑优化

针对利用传统水平集法进行非线性结构拓扑优化计算过程复杂及计算效率低等问题,将参数化水平集方法引入材料非线性结构拓扑优化中。通过全局径向基函数插值初始水平集函数,建立了以插值系数为设计变量、结构的应变能最小为目标函数、材料用量为约束条件的材料非线性结构拓扑优化模型,利用有限元分析对材料非线性结构建立平衡方程,并用迭代法求解。同时,采用子结构法划分设计区域为若干个子区域,将全自由度平衡方程的求解分解为缩减的平衡方程和多个子结构内部位移的求解,减小了计算成本。算例表明,这种处理非线性关系的方法可以在保证数值稳定的同时提高计算效率,得到边界清晰、结构合理的拓扑优化构形。     

Topology Optimization of 3D Elastic Structures Using Boundary Elements

A numerical approach for the topological optimization of 3D linear elastic problems using boundary elements and the topological derivative is presented in this work. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

应力和位移约束下连续体结构拓扑优化

同时考滤应力和位移约束的连续体结构拓扑优化问题,很难用现有的均匀方法或变密度方法等求解。主要困难在于难以建立应力和位移约束与拓扑设计变量间显式关系式;即使建立了这种关系,也由于优化问题规模过大,利用常规的数学规划方法难以求解。隋允康、杨德庆曾提出了基于独立连续拓扑变量及映射变换（ＩＣＭ）的桁架结构拓扑优化模型。本文在此基础上,建立了以重量为目标,考虑应力和位移约束的连续体结构拓扑优化模型,并推导出     

Weight‐Reduction of Sandwich Structures by an Efficient Topology Optimization Technique

A heuristic algorithm for the weight minimization of sandwich structures by a specific kind of topology optimization is presented. The method employs a preexisting algorithm for the layerwise topology optimization of symmetric laminates under in‐plane loads and expands this method for the case of bending. During the optimization procedure the algorithm adds or subtracts material from the layers of the face sheets and the core of the sandwich plate in regions of high or low stresses respectively. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Topology Optimization Procedure Based on Structure Stress History

The structure design points stress analysis for succeeding optimization steps is the base of the topology optimization algorithm. Because the material density of the material is proportional to the strain energy we can predict how to change the density for each design point for the next optimization steps. Proposed procedure make the optimization process faster and final topology is finally more optimal than topology obtained using standard optimization procedures. This stress analyzing procedure, can be treated as a hardware of the sensors being the part of the smart structure for the real time structure reconstruction. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于离散变量的拓扑优化方法

单元敏度的不准确估计是离散拓扑优化算法数值不稳定的原因之一,特别是添加材料时,传统的敏度计算公式给出的估计误差较大,甚至有时估计符号都是错误的．为了克服这一问题,通过对弹性平衡增量方程的摄动分析构造了新的增量敏度估计公式．这一新的公式无论是添加材料还是删除材料都能较准确地估计出目标函数增量,它可以看作是通过非局部单元刚度阵对传统敏度分析公式的修正．以此为基础构建了一种基于离散变量的拓扑优化算法,它可以从任意单元上添加或删除材料以使目标函数减小,同时为避免优化过程中重新划分网格,采用了单元软杀策略以小刚度材料模拟空单元．这一方法的主要优点是简单,不需要太多的数学计算,特别有利于工程实际的应用．     

基于图论的防空兵力优化配置研究

应用图论将防空系统抽象成二维网络的拓扑结构图,通过指定点对间最小拦截概率的计算,得到防空拓扑图的子图,并应用复杂网络理论,建立了防空节点攻击价值的计算方法.在此基础上设计了防空兵力优化配置算法,给出了能够满足任务要求的兵力配置方案.     

具有图结构和联盟结构的Banzhaf值及应用

Banzhaf值是经典可转移效用合作对策中一个著名的分配规则,可以用来评估参与者在对策中的不同作用。本文将Banzhaf值推广到具有联盟结构和图结构的TU-对策中,首先提出并定义了具有联盟结构和图结构的Banzhaf值(简称PL-Banzhaf值),证明了PL-Banzhaf值满足公平性、平衡贡献性和分割分支总贡献性,并给出了该值的两种公理性刻画。其次,讨论了PL-Banzhaf值在跨国天然气管道案例中的应用,并和其他分配规则进行了比较分析。     

基于可靠性的工程结构动力响应优化设计

在考虑结构物理参数和作用荷栽同时具有随机性的情况下,建立了具有动应力、动位移可靠性约束和设计变量上下限约束的工程结构优化设计数学模型;分别对结构动力响应的数字特征和基于可靠性的结构动力响应的灵敏度进行了推导.利用内罚函数法求解.算例表明文中构建的优化模型和提出的求解方法是合理与可行的.     

组合拓扑方法在组合学和图论中的应用

本文介绍组合拓扑方法在图论和组合学中的应用，探索一些新的离散问题和连续问题的关系，介绍目前有关这方面的新结果及发展动向。本文主要介绍同调理论在图论中的应用，与图有关的复形及性质，不动点定理在离散问题中的应用等。文中提出了一些新结果及可供研究的新问题。     

图的k-单圈划分中的优化问题

图的划分问题曾引起图论界的广泛关注，在文献[4]中讨论了k-单圈划分，本文进一步研究基于k-单圈划分的优化问题，即在一个赋权图中求一个最小权可k-单圈划分的支撑子图，以及对一个不存在k-单圈划分支撑子图的图，如何添最少的边使得它有k-单圈划分的支撑子图。     

Topology Optimization of Members of Elastic Multibody Systems

Lightweight techniques are applied increasingly often for modern machine designs in order to reduce the moving masses and therewith the energy consumption. However, as a result the stiffness of the system decreases causing undesired elastic deformations and therewith end-effector deviations. In this work a topology optimization procedure for elastic multibody systems based on the solid isotropic material with penalization approach is presented to lower end-effector tracking errors. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Primal-Dual Newton-Type Interior-Point Method for Topology Optimization

We consider the problem of minimization of energy dissipation in a conductive electromagnetic medium with a fixed geometry and a priori given lower and upper bounds for the conductivity. The nonlinear optimization problem is analyzed by using the primal-dual Newton interior-point method. The elliptic differential equation for the electric potential is considered as an equality constraint. Transforming iterations for the null space decomposition of the condensed primal-dual system are applied to find the search direction. The numerical experiments treat two-dimensional isotropic systems.     

基于LiToSim平台的海上风机过渡段优化软件开发

针对海上风机过渡段结构,考虑风机多尺度优化模型和所受环境荷载采取极端情况下,引入双向渐进结构拓扑优化方法,以全局应力最小化为目标、体积为约束,对风机过渡段进行优化设计;并在自主研发的LiToSim平台基础上,嵌入风机优化数值计算程序,最终形成一款关于海上风机过渡段拓扑优化的定制化软件TUR/TOPT.借助定制化软件TUR/TOPT平台,对比过渡段传统柔度优化与应力优化结果,突显出应力优化在减材设计过程中结构应力明显降低且能有效避免应力集中等方面的优势;TUR/TOPT软件的生成在风机建设选型过程中具有重要指导价值.     

Class of Maximal Graph Surfaces on Multidimensional Two-Step Sub-Lorentzian Structures

Necessary maximality conditions for graph surfaces in a class of two-step sub-Lorentzian structures are obtained. The concept of a sub-Lorentzian mean curvature is introduced, and equations for maximal surfaces are deduced.     

Lock-Gain Based Graph Partitioning

We propose a new heuristic for the graph partitioning problem. Based on the traditional iterative improvement framework, the heuristic uses a new type of gain in selecting vertices to move between partitions. The new type of gain provides a good explanation for the performance difference of tie-breaking strategies in KL-based iterative improvement graph partitioning algorithms. The new heuristic performed excellently. Theoretical arguments supporting its efficacy are also provided. As the proposed heuristic is considered a good candidate for local optimization engines in metaheuristics, we combined it with a genetic algorithm as a sample case and obtained a surprising result that even the average results over 1,000 runs equalled the best known for most graphs.