Modification of B-Spline Surfaces with Optimization

Algorithms of modifying a surface to approximate some scattered points, or pass through some characteristic points/curves are presented. Similar to variational approach, the algorithms are based on optimization. For the deviation between the modified surface and the original one is adopted as the objective functions, the change of the surface shape is as small as possible with the modified surface satisfying the specified requirements.

Reconstruction of B-spline surface by interpolating boundary curves and approximating inner points

In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given bound- ary curves and simultaneously approximates some given inner points. The main idea of our method is： first, we construct an initial surface which interpolates the four given boundary curves; then, while keeping the boundary control points of the initial surface un- changed, we reposition the inner control points of the surface with energy optimization method. Examples show that our algorithm is practicable and effective.

G^0 and G^1 connection between two adjacent B-spline surfaces

In this paper, the smooth connection between two B-spline surfaces is discussed. First, a brief proof of some simple sufficient conditions of Go and G1 continuity is given. On this basis, a novel method for Go or G1 connection between two adjacent B-spline surfaces is presented. A reparameterization step is firstly taken for one of the surfaces such that they have the same parameterization in v direction, then, adjust their boundary control vertices to make them Go or Gl connected. The GI connection parameter is determined by an optimization problem. Compared with the existed methods, our method is simple and easy to be used in practice.

基于CAD模型引导测量的自由曲面定位及轮廓度误差评定

提出将粒子群优化算法与拟随机序列法相结合对基于CAD模型引导测量的自由曲面进行高精度检测和轮廓度误差评定的方法。为解决用三坐标测量仪检测自由曲面时存在的设计坐标系与测量坐标系不重合问题,提出用拟粒子群优化算法来实现被测曲面与设计曲面精确定位;针对自由曲面特点,采用轮廓峰谷误差和轮廓均方根误差综合评定自由曲面的形状误差。最后,阐述了用拟粒子群优化算法实现曲面匹配时目标函数值的计算方法,确立了用拟粒子群优化算法优化求解参数向量的具体步骤。对仿真实例和大量实测零件自由曲面轮廓度误差的计算表明:采用本文方法能够实现自由曲面精确定位,其轮廓度误差评定精度比由三坐标测量仪内置软件计算的结果高8%～15%,适用于对高精度自由曲面零件形状误差的评定。

Isogeometric Analysis-Based Topological Optimization for Heterogeneous Parametric Porous Structures

Porous structures widely exist in nature and artifacts,which can be exploited to reduce structural weight and material usage or improve damage tolerance and energy absorption.In this study,the authors develop an approach to design optimized porous structures with Triply Periodic Minimal Surfaces(TPMSs)in the framework of isogeometric analysis(IGA)-based topological optimization.In the developed method,by controlling the density distribution,the designed porous structures can achieve the optimal mechanical performance without increasing the usage of materials.First,the implicit functions of the TPMSs are adopted to design several types of porous elements parametrically.Second,to reduce the cost of computation,the authors propose an equivalent method to forecast the elastic modulus of these porous elements with different densities.Subsequently,the relationships of different porous elements between the elastic modulus and the relative density are constructed.Third,the IGA-based porous topological optimization is developed to obtain an optimal density distribution,which solves a volume constrained compliance minimization problem based on IGA.Finally,an optimum heterogeneous porous structure is generated based on the optimized density distribution.Experimental results demonstrate the effectiveness and efficiency of the proposed method.

Quasi-Developable B-Spline Surface Design with Control Rulings

We propose a method for generating a ruled B-spline surface fitting to a sequence of pre-defined ruling lines and the generated surface is required to be as-developable-as-possible.Specifically,the terminal ruling lines are treated as hard constraints.Different from existing methods that compute a quasi-developable surface from two boundary curves and cannot achieve explicit ruling control,our method controls ruling lines in an intuitive way and serves as an effective tool for computing quasi-developable surfaces from freely-designed rulings.We treat this problem from the point of view of numerical optimization and solve for surfaces meeting the distance error tolerance allowed in applications.The performance and the efficacy of the proposed method are demonstrated by the experiments on a variety of models including an application of the method for path planning in 5-axis computer numerical control(CNC)flank milling.

B-SPLINE SURFACE SMOOTH JOINING

Optimization techniques are being applied to solve the problems of surface interpolation, approximation, smooth joining and fairing, aiming at corresponding objective functions. This paper focuses on the construction of fair surface interpolating the given mesh of curved boundaries with G 2 adjustment at comers and G 1, G 2 smoothness between adjacent patches. Many papers on surface blending have been presented, but almost all of them are restricted to the discussion of Bezier patches, there are no good results for B-spline surface. This paper gives a solution to the B-spline surface, allowing the surface to degenerate at comer in and have different parameterization along the common boundary of two patches.

Smoothing Parametric Design of Addendum Surfaces for Sheet Metal Forming

The manual design of addendum surfaces on common CAD platforms is very tedious which requires many trialscorrections,which will certainly a ect the construction e ciency and quality of addendum surfaces,and then a ect the formability and quality of the workpiece in the process of sheet forming.In this paper,an automatic procedure based on parametric design method is proposed for the rapid construction of the addendum surfaces.The kernel of the parametric method is constructing boundary curves based on the shape of surfaces of workpiece and designing guide curves based on Hermite curve interpolation.By some simple parameters,the shape of the addendum surfaces could be controlled and adjusted easily.In addition,a minimum energy optimization method is employed to further optimize the constructed addendum surface.A finite element analysis for the sheet forming process is performed to evaluate the forming quality of constructed addendum surfaces.The instance illustrates that the addendum surface constructed by the proposed method could ensure both the overall smoothing of surfaces and the final forming quality,and it has a good e ect on springback after forming.This research proposes a smoothing parametric design method for addendum surfaces construction which could construct and optimize addendum surfaces rapidly.

Novel decoupled framework for reliability-based design optimization of structures using a robust shifting technique

In a reliability-based design optimization (RBDO), computation of the failure probability (Pf) at all design points through the process may suitably be avoided at the early stages. Thus, to reduce extensive computations of RBDO, one could decouple the optimization and reliability analysis. The present work proposes a new methodology for such a decoupled approach that separates optimization and reliability analysis into two procedures which significantly improve the computational efficiency of the RBDO. This technique is based on the probabilistic sensitivity approach (PSA) on the shifted probability density function. Stochastic variables are separated into two groups of desired and non-desired variables. The three-phase procedure may be summarized as: Phase 1, apply deterministic design optimization based on mean values of random variables;Phase 2, move designs toward a reliable space using PSA and finding a primary reliable optimum point;Phase 3, applying an intelligent self-adaptive procedure based on cubic B-spline interpolation functions until the targeted failure probability is reached. An improved response surface method is used for computation of failure probability. The proposed RBDO approach could significantly reduce the number of analyses required to less than 10% of conventional methods. The computational efficacy of this approach is demonstrated by solving four benchmark truss design problems published in the structural optimization literature.

基于CAD/CAE的汽车车门内饰板注塑模设计

运用Moldflow软件对最佳浇注点进行了分析,采用Pro/E软件建立了塑件实体模型,创建模具体积块,对模具分模和温度调节系统进行了模拟,确保了模具运行可靠。最后基于模具体积块利用EMX软件进行了模架调用与装配,设计了汽车车门内饰板注塑模具。结果表明:采用三维CAD/CAE技术能直接进行从产品到模具体积块的设计,缩短了产品的开发周期降,低了模具的设计和制造成本。

区间Bézier曲面的降阶

论文讨论了用低阶的区间Bzier曲面来界定高阶的区间Bzier曲面的问题 ,提出了两种不同的解决方法———线性规划及最佳一致逼近 ,最后提供的实例结果表明线性规划方法能得到一个界 。

口腔预备体颈缘线裁剪算法

由于高质量全瓷冠、桥体制作的需要,基于CAD/CAM的口腔修复体制作技术成为研究的热点。口腔预备体特征线的三角网格裁剪技术是口腔CAD/CAM修复工艺中的关键环节之一,对口腔修复体制作质量有重要影响。提出一种渐进三角网格裁剪算法:首先,采用"种子"区域扩展进行网格粗裁剪;然后,采用三角片剖分技术完成三角片的精裁剪;最后对剖分后的边界三角片进行优化,获得边界均匀的裁剪曲面。应用实例证实本算法是有效的、可行的,可满足临床应用要求。

露天矿设计规划计算机辅助设计系统

基于以有向图系统模拟理论为核心的综合优化法，采用系统模拟与数学规划相结合的方法，建立了适用于不同矿床埋藏条件的露天矿设计规划计算机辅助设计（ＳＭＣＡＤ）系统．其功能覆盖了露天矿设计中采矿设计决策的基本内容，可进行一系列采矿模拟计算、优化决策和开采方案的对比寻优．该系统实现了微机化，具有多级菜单、模块结构、图文显示、动态跟踪、交互设计等特点．应用表明，ＳＭＣＡＤ系统具有较强的通用性和实用性，运算结果准确可靠．

PDE曲面的Bézier逼近

为了实现PDE(panial differential equation)曲面造型技术与传统CAD(computer aided design)造型系统的数据交换,基于约束优化的思想,给出了PDE曲面的Bézier逼近算法,并利用张量积Bézier曲面的细分性质对该算法进行了优化.所给出的计算实例及误差比较结果说明了该算法的有效性.

自动化技术在飞机活动翼面结构方案论证中的应用

为了探讨飞机活动翼面结构布局方法 ,并提供一种基于现代集成设计技术的、具有良好操作性的、用于结构方案论证时的新方法 ,本文采用模块化策略和几种手段相结合的思想作为技术途径 ,具体表现为将CAD、CAE和结构拓扑优化组合使用 ,以UG作为CAD几何造型平台 ,以ANSYS作为CAE建模平台 ,利用作者提出的敏度阀值概念和约束补偿措施构造出一种拓扑优化新算法。以实际飞机型号作为算例 ,优化结果与真实的结构布局形式相比较 ,能够指出传统设计的不足之处 ,这既验证了本文建立的物理模型的合理性 ,又考核了该优化算法的有效性 ,同时 ,也说明了本文提出的“结构布局方法”具有一定的实用性。最后 ,从该方法的良好操作性可以预示出它对未来飞机活动翼面结构设计 。

基于步长优化的扫略自由曲面加工效率的研究

提出了一种提高扫略曲面三坐标加工速度的优化方法;在曲面加工中,经常使用比较昂贵的商业CAD/CAM软件来生成加工程序,对刀具位置和路径规划进行大量的计算;由于这些商业软件都基于一种比较可靠的算法,所以在功能上都具有相似的功能和效率;也就是说,现在使用的大多数的CAD/CAM系统,都是基于零件的几何特征来加工的;文中提出了主要集中在提出一种基于被加工零件精度自由曲面刀具路径生成方法,推导出前进步距函数,在给定加工误差和没有损失加工精度的情况下,计算出最大的CC(刀具接触点)点间的距离,来减少生成的CC点,减少加工时间,提高了加工效率。