基于自由度分析的三维模型几何约束求解

针对三维几何约束模型的求解问题,在充分研究了二维几何约束模型自由度分析技术的基础上,采用几何推理的方法,给出了一种三维模型几何约束求解的自由度分析算法,该算法可归纳为活动分析和场所分析两个过程.算法为三维几何约束模型提供了一种求解方案,解决了过约束和欠约束状态时的约束求解问题,并展示了一个实例.     

面向对象的约束系统分析与实现框架

通过分析工程设计中的几何约束问题，运用面向对象方法对通用约束求解器（CBA）进行了剖析。从约束建模和求解的算法共性出发，确立了虚体、约束关系和约束分量的概念，由此解决了不同应用领域和不同几何层次的几何实体和几何约束的统一建模问题。详细解释了CBA主要对象族的设计思想，简述了CBA的实现框架。     

基于约束图的三维服装约束问题求解

采用样条曲线作为基本几何元素,建立了三维服装几何约束关系。以此为基础构造了三维服装的约束图,有效地表达了几何元素及其相互关系。提出了基于约束图的改进的三维服装几何约束求解方法,完成了构造服装和对服装的交互参数化修改问题。通过应用实例将参数化方法向高层次图素进行了推广,并成功应用于服装CAD系统中,运行效果良好。     

基于有向图的约束求解新算法

针对一般几何约束系统欠约束状态下约束分解的多样性,通过对剩余自由度的分析,提出了几何元素优先级的概念,给出了约束有向图生成算法,实现了对约束系统的优化分解.本算法在AutoCAD 2000提供的二次开发接口ObjectARX上成功实现,运行结果表明具有良好的约束求解效率.对于欠约束系统的分解结果可以最大限度满足用户的需求.     

离散变量结构优化设计的拟满应力遗传算法

以力学准则法为基础,提出了一种求解离散变量结构优化设计的拟满应力方法;这种方法能直接求解具有应力约束和几何约束的离散变量结构优化设计问题.通过在遗传算法中定义拟满应力算子,建立了一种离散变量结构优化设计的混合遗传算法拟满应力遗传算法.算例表明;这种混合遗传算法对于离散变量结构优化设计问题具有较高的计算效率.     

雅克比矩阵近似更新的三维装配约束求解研究

提出了三维装配约束求解中雅克比矩阵近似更新的方法。该方法通过对迭代过程中满秩以及行秩秩亏雅克比矩阵进行近似更新,提高了约束求解的效率。首先在非线性迭代求解过程中添加雅克比矩阵及其逆矩阵近似更新的公式;然后给出使用近似更新公式需要满足的限制条件;最后通过对奇异点扰动算法的描述介绍迭代求解过程中雅克比矩阵发生行秩秩亏的处理办法。文中提出的策略与算法已在三维装配约束求解引擎 CBABench中实现,给出的实例表明本文提出的方法效果显著。     

几何约束求解可构造模式研究

针对完整几何约束系统刚性复合顶点的装配求解问题,细化和分离出可几何构造模式,并提出几何增量构造的方法求解这类模式。通过对可构造模式子构型的构造,求出刚性体的自由转动和自由移动运动空间,在自由运动空间中构造未满足的几何约束。该方法在几何约束求解中具有实际的应用价值,克服了数值整体迭代的不稳定性和符号法的低效率,并实现于几何约束求解器CBA中。     

几何约束求解的去并拟合方法

依据有向图理论提出了去并拟合方法,由此导出了对于几何约束求解问题的去并拟合的并行处理及串行处理策略,进而得到了一套求解几何约束问题的完备算法。通过将该理论引入到参数化CAD的设计中,使得在算法复杂度增加不大的情况下,几何自动作图的范围大大拓宽。还将其应用于智能动态几何软件的设计中,取得了较好的结果。     

资源约束项目排序问题的一种修正蚁群算法

根据蚁群算法的性质与资源约束项目排序问题(CPSP:Resource-Constrained Project Schedul- ing Problem)的特征,本文给出了蚁群算法中信息素的表示及更新方案、启发信息的计算方法等,由此提出了一种求解RCPSP的修正蚁群算法。最后,通过对项目排序问题库中的标准问题集进行计算,结果表明本文提出的修正蚁群算法是可行优良的。     

改进的蚂蚁算法在几何约束求解中的应用

将几何约束问题转化为数值优化问题。把蚂蚁算法引入几何约束求解中。在所有的操作中,由于没有涉及到在 Newton-Raphson 中遇到的矩阵求逆操作,因此蚂蚁算法具有很强的鲁棒性。笔者在基本蚂蚁算中混入局部优化算法,对每代的最优解进行改进,进一步加快蚂蚁算法的收敛速度。为了避免蚂蚁一开始就失去解的多样性,笔者改进了选择策略。为了克服蚂蚁算法计算时间较长的缺陷,这里引入遗传算法中的变异算子,经过局部优化后,整个群体的性能会有明显改善,使得算法保持更好的多样性。由于该算法对方程的个数和变量的个数没有什么特殊的要求,因此可以处理欠约束问题。     

AutoCAD 中基于超图约束驱动参数化设计的实现

 使用超图表示约束模型,采用基于超图约束驱动的几何推理约束满足法进行参数化设计,几何实体的计算基于特征点。作者结合在ＡｕｔｏＣＡＤ上开发参数化设计模块的实践,得出该方法能处理多实体约束关系（如面积约束）,提高求解效率,降低时间复杂度。     

基于点簇归约的几何约束求解器研究

提出了一种新的几何约束推理求解算法，该算法基于点簇对约束网络图进行归约，求得归约序列然后重构几何模型，具有求解速度快、可靠性高，应用范围广等优点，已利用面向对象的C 开发实现了以该算法为核心的几何约束求解器，并且作为白玉兰CAD系统的重要组成部分得到了推广应用。     

A mass constraint formulation for structural topology optimization with multiphase materials

This work is focused on the topology optimization of lightweight structures consisting of multiphase materials. Instead of adopting the common idea of using volume constraint, a new problem formulation with mass constraint is proposed. Meanwhile, recursive multiphase materials interpolation (RMMI) and uniform multiphase materials interpolation (UMMI) schemes are discussed and compared based on numerical tests and theoretical analysis. It is indicated that the nonlinearity of the mass constraint introduced by RMMI brings numerical difficulties to attain the global optimum of the optimization problem. On the contrary, the UMMI‐2 scheme makes it possible to formulate the mass constraint in a linear form with separable design variables. One such formulation favors very much the problem resolution by means of mathematical programming approaches, especially the convex programming methods. Moreover, numerical analysis indicates that fully uniform initial weighting is beneficial to seek the global optimum when UMMI‐2 scheme is used. Besides, the relationship between the volume constraint and mass constraint is theoretically revealed. The filtering technique is adapted to avoid the checkerboard pattern related to the problem with multiphase materials. Numerical examples show that the UMMI‐2 scheme with fully uniform initial weighting is reliable and efficient to deal with the structural topology optimization with multiphase materials and mass constraint. Meanwhile, the mass constraint formulation is evidently more significant than the volume constraint formulation. Copyright © 2011 John Wiley & Sons, Ltd.     

Continuum structural topological optimizations with stress constraints based on an active constraint technique

Stress‐related problems have not been given the same attention as the minimum compliance topological optimization problem in the literature. Continuum structural topological optimization with stress constraints is of wide engineering application prospect, in which there still are many problems to solve, such as the stress concentration, an equivalent approximate optimization model and etc. A new and effective topological optimization method of continuum structures with the stress constraints and the objective function being the structural volume has been presented in this paper. To solve the stress concentration issue, an approximate stress gradient evaluation for any element is introduced, and a total aggregation normalized stress gradient constraint is constructed for the optimized structure under the r?th load case. To obtain stable convergent series solutions and enhance the control on the stress level, two p‐norm global stress constraint functions with different indexes are adopted, and some weighting p‐norm global stress constraint functions are introduced for any load case. And an equivalent topological optimization model with reduced stress constraints is constructed,being incorporated with the rational approximation for material properties, an active constraint technique, a trust region scheme, and an effective local stress approach like the qp approach to resolve the stress singularity phenomenon. Hence, a set of stress quadratic explicit approximations are constructed, based on stress sensitivities and the method of moving asymptotes. A set of algorithm for the one level optimization problem with artificial variables and many possible non‐active design variables is proposed by adopting an inequality constrained nonlinear programming method with simple trust regions, based on the primal‐dual theory, in which the non‐smooth expressions of the design variable solutions are reformulated as smoothing functions of the Lagrange multipliers by using a novel smoothing function. Finally, a two‐level optimization design scheme with active constraint technique, i.e. varied constraint limits, is proposed to deal with the aggregation constraints that always are of loose constraint (non active constraint) features in the conventional structural optimization method. A novel structural topological optimization method with stress constraints and its algorithm are formed, and examples are provided to demonstrate that the proposed method is feasible and very effective. © 2016 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.     

基于约束矩阵的几何约束传播研究

为了保证几何约束系统的一致性和几何约束求解的正确性,对几何约束传播进行了研究,指出几何约束传播是几何约束系统的本质特征。提出了几何约束矩阵和约束传播矩阵来表达和揭示约束传播的内在机制,并提出了一种闭环约束识别的新方法。通过约束传播分析,为几何约束求解引擎的实现提供了理论依据和快速算法。     

Strategy of Concurrent Optimization for an Assembly Sequence

An effective constraint release based approach to realize concurrent optimization for an assembly sequence is proposed. To quantify the measurement of assembly efficiency, a mathematical model of concurrency evaluation index was put forward at first, and then a technology to quantify assembly constraints was developed by application of some fuzzy logic algorithms. In the process of concurrent optimization of the assembly sequence, two kinds of constraints were involved. One was self-constraints of components, which was used to evaluate the assemble capability of components under the condition of full-freedom. Another was an assembly constraint between components represented by geometric constraints between points, lines and planes under physical restriction conditions. The concept of connection strength degree （CSD） was introduced as one efficient indicator and the value of it was evaluated by the intersection of the two constraints mentioned above. The equivalent constraints describing the connection weights between components were realized by a well designed constraints reduction, and then the connection weights based complete assembly liaison graph was applied to release virtual connections between components. Under a given threshold value, a decomposition and reconstituting strategy for the graph with the focus on high assembly concurrency was used to realize an optimized assembly concurrency evaluation index. Finally, the availability of the approach was illustrated in an example to optimize the assembly of a shift pump.     

基于约束和邻域的炼钢连铸重调度算法

针对机器故障扰动,研究了炼钢连铸重调度问题及其求解算法。通过将机器故障映射为资源约束,建立了基于动态约束满足的炼钢连铸重调度模型,模型以最大化连浇量与调度方案相似度为目标。针对问题的模型及其特点,采用约束满足和邻域搜索相结合的混合算法对其进行了求解。仿真实验表明本文提出的模型和算法是有效的。     

工程液压油缸的拆解能量分析

拆解能量是产品可拆卸性评价的关键指标,对产品的可拆卸性设计和再制造回收决策具有重要意义.基于图论思想,构建油缸的拆解约束图并生成油缸的拆卸序列;定义零部件拆解能量的组成模型和传送带移出零部件的能量消耗模型;讨论油缸零部件间典型连接方式与约束解除所消耗能量的数学关系.以某型号工程液压油缸为例,对其零部件的不同拆卸序列进行总的拆解能量分析计算与评估,为油缸的拆卸序列规划、专用拆卸设备设计和液压油缸的可拆卸性设计提供参考.