对象族拓扑约束求解的研究

针对当前对象族模型在求解拓扑约束时存在的缺陷,提出一种求解拓扑约束的新方法,这种方法在求解拓扑约束时,把拓扑约束映射为布尔约束满足问题,通过用SAT求解器求解布尔约束来求解拓扑约束。实践证明,该方法不仅直接关联与拓扑约束指定的特征的语义,而且当模型中存在大量相交的特征时也是可行的,提高了拓扑约束求解的效率。     

基于广义元球的一般约束变形

在计算机动画和形状设计中，变形是一个非常重要的工具.基于广义元球所具有的特殊势函数分布，提出了一个新的包含点、线、面和体约束的一般变形模型.用户定义一系列约束、每个约束的影响半径和偏移量，变形模型根据每个约束和其影响半径产生该约束的广义元球.广义元球确定了一个以约束点集为中心的势函数，该势函数在约束点集处为1，在影响半径处渐变为0.模型直接对整个空间进行变形，而与物体的表示无关，并且变形可由偏移量和广义元球的参数来细微调整.实验表明，该一般约束变形模型不仅有效，而且使传统方法难以做到的线、面、体约束变形成     

BBL布局的均场退火方法

均场退火方法既可以看作是一种新的神经网络计算模型,又可视为是对模拟退火的重大改进,提出了一个基于均场退火方法的任意单元布局算法,用一个三维二值换位矩阵将问题映射了为神经网络,建立包含重叠约束和优化目标的能量函数,再用均场退火方程迭代求解,每个单元只能放置在布局平面一个位置上的约束,用神经元归一化的方法解决。     

一个标识子系统的设计与实现

特征造型的关键是合理地确定新旧模型拓扑元素之间的对应关系，文中提出一个基于特征的标识子系统，使得产品模型中每个拓扑元素都对应一个唯一的标识，标识匹配算法可以建立新旧模型拓扑元素之间的对应关系，标识子系统是作者开发的特征造型系统GDS的重要线成部分，为特征编辑、语义操作，二三维约束统一求解等奠定了基础。     

基于区域延伸的定性空间表示

在区域连接演算(region connection calculus,RCC)理论基础上给出了区域延伸的形式定义.通过区域延伸,定义了关联空间的概念,进而提出了空间表示的一个模型,在这个模型中给出了空间中物体的空间拓扑关系、距离关系、方向关系以及位置等信息的定性表示.智能体对空间关系的确定是通过区域延伸实现的,模型为智能体在约束空间环境中的行动推理提供了一个新的表示方法.     

基于图的参数化设计方法

参数化系统中约束的表达和约束的求解是两大关键性技术问题。作者提出的基于图的参数化方法是将约束分成拓扑约束和几何约束,并以图结构表达这两类约束,然后对约束网络图进行拓扑排序、分解,以确定求解序列和检测约束一致性,最后按照几何约束网中的约束关系进行“几何参数驱动”,以实现参数化。     

基于ArcGIS GeoDatabase的宗地拓扑模型建模与实现

界址点、界址线，宗地之间有着复杂的拓扑关系约束，需要建立一个宗地拓扑数据模型来进行管理，这个模型是地籍管理信息系统的核心。首先介绍了界址点、界址线，宗地之间的拓扑关系约束。其次论述了如何用GeoDatabase建立该模型，包括如何表示各种实体，使用哪些拓扑规则建立拓扑关系以及如何建立开发接口等。最后对GeoDatabase和双重独立地图编码方式进行了比较，总结了各自的特点。模型已得到了成功应用。     

基于雁群启示的粒子群优化算法的几何约束求解

几何约束是约束求解技术中最关键的问题之一.求解一个几何约束问题的最终目的是确定几何图形中每一个几何体的具体坐标位置.几何约束问题可以等价为求解非线性方程组问题.约束问题转化为一个优化问题.本文采用基于雁群启示的粒子群优化算法来求解该问题.该算法受雁群飞行特征启发,一方面将粒子排序,每个粒子跟随其前面那个较优粒子飞行,保持了多样性;另一方面使每个粒子利用更多其他粒子的有用信息,粒子之间的竞争被增强.两个方面的结合将平衡速度和精度之间的矛盾.实验表明,该方法可以提高几何约束求解的效率和收敛性.     

语义特征模型中参数范围的计算

基于参数和语义特征的CAD系统,改变参数的值是最重要的操作,也通常是一种反复性的过程,针对适合的参数值对于用户来说提前是不知道的,提出一种新的方法用于自动侦测参数的适当的范围。先通过分析拓扑约束图,找到距离和角度约束,并将这些约束加入到其相应的几何约束中,然后通过分解找到子问题的临界参数值,再求解每个并列的参数区间内部的一个具体的实例,精确的参数范围就能够被确定。     

集成多方面信息的定性空间推理及应用

以往的定性空间或时空推理工作多数面向单一时空方面,这不符合实际应用需要.提出了集成拓扑、尺寸和时间3方面信息的定性表示和推理技术,并应用到时空GIS中.给出了面向GIS的拓扑、尺寸和时间的表示方法,并研究了它们之间的依赖性.提出了集成这3方面信息的约束满足问题求解算法TriRSAT.在时空GIS中,把定性时空表示用于约束关系库,把TriRSAT算法用于时空数据一致性检查和时空查询.应用结果显示,该理论和方法能有效地集成处理多方面时空信息,在时空数据库、机器人导航等领域有着广泛的应用前景.     

A level-set-based topology and shape optimization method for continuum structure under geometric constraints

Recent advances in level-set-based shape and topology optimization rely on free-form implicit representations to support boundary deformations and topological changes. In practice, a continuum structure is usually designed to meet parametric shape optimization, which is formulated directly in terms of meaningful geometric design variables, but usually does not support free-form boundary and topological changes. In order to solve the disadvantage of traditional step-type structural optimization, a unified optimization method which can fulfill the structural topology, shape, and sizing optimization at the same time is presented. The unified structural optimization model is described by a parameterized level set function that applies compactly supported radial basis functions (CS-RBFs) with favorable smoothness and accuracy for interpolation. The expansion coefficients of the interpolation function are treated as the design variables, which reflect the structural performance impacts of the topology, shape, and geometric constraints. Accordingly, the original topological shape optimization problem under geometric constraint is fully transformed into a simple parameter optimization problem; in other words, the optimization contains the expansion coefficients of the interpolation function in terms of limited design variables. This parameterization transforms the difficult shape and topology optimization problems with geometric constraints into a relatively straightforward parameterized problem to which many gradient-based optimization techniques can be applied. More specifically, the extended finite element method (XFEM) is adopted to improve the accuracy of boundary resolution. At last, combined with the optimality criteria method, several numerical examples are presented to demonstrate the applicability and potential of the presented method.     

Topological derivative-based topology optimization of structures subject to design-dependent hydrostatic pressure loading

In this paper the topological derivative concept is applied in the context of compliance topology optimization of structures subject to design-dependent hydrostatic pressure loading under volume constraint. The topological derivative represents the first term of the asymptotic expansion of a given shape functional with respect to the small parameter which measures the size of singular domain perturbations, such as holes, inclusions, source-terms and cracks. In particular, the topological asymptotic expansion of the total potential energy associated with plane stress or plane strain linear elasticity, taking into account the nucleation of a circular inclusion with non-homogeneous transmission condition on its boundary, is rigorously developed. Physically, there is a hydrostatic pressure acting on the interface of the topological perturbation, allowing to naturally deal with loading-dependent structural topology optimization. The obtained result is used in a topology optimization algorithm based on the associated topological derivative together with a level-set domain representation method. Finally, some numerical examples are presented, showing the influence of the hydrostatic pressure on the topology of the structure.     

Target-matching test problem for multiobjective topology optimization using genetic algorithms

This paper describes the multiobjective topology optimization of continuum structures solved as a discrete optimization problem using a multiobjective genetic algorithm (GA) with proficient constraint handling. Crucial to the effectiveness of the methodology is the use of a morphological geometry representation that defines valid structural geometries that are inherently free from checkerboard patterns, disconnected segments, or poor connectivity. A graph- theoretic chromosome encoding, together with compatible reproduction operators, helps facilitate the transmission of topological/shape characteristics across generations in the evolutionary process. A multicriterion target-matching problem developed here is a novel test problem, where a predefined target geometry is the known optimum solution, and the good results obtained in solving this problem provide a convincing demonstration and a quantitative measure of how close to the true optimum the solutions achieved by GA methods can be. The methodology is then used to successfully design a path-generating compliant mechanism by solving a multicriterion structural topology optimization problem.     

Optimization of microwave devices combining topology gradient and genetic algorithm

Topology optimization can be seen as optimizing a distribution of small topological elements within a domain with respect to given specifications. A numerical topology gradient (TG) algorithm is applied in the context of electromagnetism for optimizing microwave devices, computing the sensitivity on adding or removing small metallic elements. This method leads to an optimum topology with very little initial information in acceptable time consumption. The method is applied to the design of a microstrip component in which the topology gradient is directly used as a direction of descent. However, in some ill‐behavior problems, topology gradient is not sufficient to converge to the global optimum. In the latter case, the basic TG is coupled with a genetic algorithm (GA) to make a more suitable algorithm for solving local optima problems. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.     

物质点拓扑变量法在柔性机构设计中的应用

为克服柔性机构拓扑优化设计中的各类数值不稳定性问题,提出一种以物质点拓扑变量为设计变量的拓扑优化方法.物质点拓扑变量可视为节点密度概念的进一步拓展,基于修正网格无关性过滤函数提出了新的拓扑变量场插值形函数.基于弹簧模型,建立了柔性机构的多约束拓扑优化模型,推导了常见结构响应量的敏度表达式,采用移动渐进线法进行优化求解.最后通过二维数值算例验证了文中方法的可行性和有效性.     

动态种群划分量子遗传算法求解几何约束

几何约束问题的约束方程组可转化为优化模型,因此约束求解问题可以转化为优化问题。针对传统量子遗传算法个体间信息交换不足,易使算法陷入局部最优的缺点,提出了动态种群划分量子遗传算法（dynamic population divided quantum genetic algorithm,DPDQGA）,并将其应用于几何约束求解中。该算法种群中的个体按照一定规则自发地进行信息交换。在每一代进化的开始阶段,分别对两个初始种群中的个体计算个体适应度。将两个种群合并,使用联赛选择的方法为种群中的个体打分,并按照得分对种群进行排序。最后将合并的种群重新划分为两个子种群。实验表明,基于动态种群划分的量子遗传算法求解几何约束问题具有更好的求解精度和求解速率。     

Isogeometric Analysis for Topology Optimization with a Phase Field Model

We consider a phase field model for the formulation and solution of topology optimization problems in the minimum compliance case. In this model, the optimal topology is obtained as the steady state of the phase transition described by the generalized Cahn?CHilliard equation which naturally embeds the volume constraint on the amount of material available for distribution in the design domain. We reformulate the model as a coupled system and we highlight the dependency of the optimal topologies on dimensionless parameters. We consider Isogeometric Analysis for the spatial approximation which facilitates encapsulating the exactness of the representation of the design domain in the topology optimization and is particularly suitable for the analysis of phase field problems. We demonstrate the validity of the approach and numerical approximation by solving two and three-dimensional topology optimization problems.     

A computational study of symmetry and well-posedness of structural topology optimization

We are concerned with the computational topological optimization of elastic structures, in particular minimization of compliance subject to a constraint on the mass. Through computational experiments, it is discovered that even very simple optimization problems can exhibit complex behavior such as critical points and bifurcation. In the vicinity of critical points, structural topology optimization problems are not well-posed since infinitesimally small perturbations lead to distinct topologies.

     

基于商空间的产品设计问题求解模型研究

针对产品设计约束网络模型的求解难问题,提出了基于商空间的产品设计问题求解模型。将产品设计问题的约束网络转换为拓扑空间,使用等价关系对约束满足问题中的变量进行划分,建立了基于商空间的产品设计问题分层求解模型。通过商映射实现不同层次之间的映射和回溯。这种采用分层次、逐步细化的问题求解方法,降低了问题求解的计算复杂性。     

Topological sensitivity derivative and finite topology modifications: application to optimization of plates in bending

The concept of topological sensitivity derivative is introduced and applied to study the problem of optimal design of structures. It is assumed, that virtual topology variation is described by topological parameters. The topological derivative provides the gradients of objective functional and constraints with respect to these parameters. This derivative enables formulation of the conditions of topology transformation. In this paper formulas for the topological sensitivity derivative for bending plates are derived. Next, the topological derivative is used in the optimization process in order to formulate conditions of finite topology modifications and in order to localize positions of the modifications. In the case of plates they are related to introduction of holes and introduction of stiffeners. The theoretical considerations are illustrated by some numerical examples.