参数曲面自由变形新方法

提出一种新的参数曲面自由变形方法：构造出特殊的伸缩因子函数，用它去作用（伸缩）待变形曲面，从而使曲面发生形变，通过交互改变控制参数，可达到预期变形效果，实验表明，该方法数学背景简单，易于控制，重复使用可获得丰富的变形效果，适用于几何造型，计算机动画，CAD／CAM等领域。     

基于点位移约束的NURBS曲面变形研究

NURBS曲面变形涉及控制网格、控制点、权因子或一些物理参数等复杂计算,变形不够直观.应用Cao En曲面模型和合成函数对NURBS曲面提出一种新的变形方法,将变形后的曲面表示成NURBS原始曲面和位移函数的合成曲面.曲面变形与控制网格无关,关键点位置可随意选取,直接通过点的位移约束得到可控制的变形结果.实验证明该方法计算简单,变形操作简便直观,适用于曲面的交互设计.     

用于参数曲线自由变形的新的伸缩因子

构造了一种新的伸缩因子函数,以改进参数曲线自由变形方法.它不仅具有已有伸缩因子的特性,还可在区间上达到峰值,克服了现有伸缩因子仅在一点达到峰值的不足.在将新的伸缩因子作用于待变形的曲线方程时,可通过交互改变控制参数来控制曲线的形状,以获得丰富的变形效果.叙述了在混凝土骨料随机分布的二维优化数学仿真模型中的应用.     

局部区域地形地貌生成方法

分形技术应用于目标自动识别,传统的伪装方法已不适应现代信息化条件下伪装防护的需求。提出了一种基于分形技术的局部区域地形地貌生成方法,该方法通过选取典型地貌特征的区域作为原型,利用分形方法生成了随机分形曲面。为使区域达到随机变化的效果,把利用一定的权值将缩放后的地貌模型曲面与分形曲面进行曲面融合,得到伪装区域。实验结果表明,该方法可有效生成符合伪装需求的局部地形地貌区域,实现了伪装区域与周围阵地地貌的良好融合,达到良好的伪装效果。     

基于伸缩函数的平面参数曲线自由变形技术

提出了一种新的平面参数曲线自由变形方法，建立了相应的数学模型；构造出特殊的伸缩函数，在此基础上得到变形算子矩阵，用它作用待变形曲线方程，或乘以某一微量场再加到曲线方程上去，从而使曲线发生形变，通过交互改变控制参数，可达到预期变形效果，实验表明，该方法数学背景简单，易于控制，重复使用可获得丰富的变形效果，适用于几何造型，计算机动画，CAD／CAM等领域。     

NURBS曲面自由型特征处理方法研究

NURBS曲面自由型特征因不具有确定的参数、准确的边界,使其表示、编辑及操作十分困难.基于一种新的小波多分辨率分析技术将NURBS曲面从单一尺度几何表示的空域变换为频域的表示形式,借助于滤波器组将模型的整体结构和局部细节变换为其全局和局部多分辨率自由型特征,实现了对NURBS曲面的自由型特征的编辑、操作和控制.该方法不仅能提高NURBS曲面几何建模的效率,而且可以克服传统NURBS曲面建模的繁琐和费时.     

包装容器造型中的一种设计方法

给出了一种新的包装容器造型方法－－自由变形方法（ＦＦＤ）。该方法在包装容器曲面外形设计初期,可以直观、简洁、方便地获得高阶连续的曲面实体,该方法在包装容器造型设计方面具有广阔的发展前景。     

有理三次Hemite插值样条及其逼近性质

提高插值曲线曲面的逼近性是计算辅助几何设计中的一个重要问题.本文构建了一种带单参数的分段有理三次Hermite插值样条.讨论了该样条的逼近性,给出了一种提高插值曲线曲面逼近性的方法,并且给出数值例子.结果表明,对于给定的插值条件,通过选择合适的参数,依本文方法所生成的插值曲线曲面在逼近效果上好于标准三次Hermite插...     

一种实用的自由曲面上曲线插值算法

直接在自由曲面上构造曲线是非常实用的造型技术,实现在曲面上曲线插值的主要思路是将其转化为一般的曲线插值问题求解。基于曲面及其参数之间的对应关系,提出了一种实用的算法,即根据给定的曲面上型值点,首先在参数域平面上构造插值曲线,再将该参数域内插值曲线映射到曲面上,获得曲面上曲线,从而实现曲面上曲线插值的目的。给出了具体的算法步骤,并对参数曲线不在参数域内部的特殊情况进行了处理。图例显示该法具有满意的效果。     

天线结构参数化有限元分析及其变形反射面的拟合

基于ANSYS软件,以载荷作为变量,对某型天线结构进行参数化有限元分析,将反射面上的节点作为采样点,拟合变形反射面的精确数学方程;将非线性曲面目标函数伪线性化处理,并基于最小二乘法数值迭代方法,确定反应曲面几何方程的各个参数;该方法易于程序化,能有效地指导天线的结构设计.     

A thermodynamic approach to the influence of plastic deformation on crack instability

It is argued that the role of plastic deformation in crack growth has been widely misinterpreted. In particular the notion that the work of plastic deformation contributes to the energy balance in such a way as to give rise to an increased effective surface energy is shown to be physically incorrect. A fundamental reappraisal of the role of plastic deformation on the instability of cracks is undertaken and a thermodynamic formulation of the problem of the energetics of crack extension is developed. This is capable of treating both moving cracks and the dislocations producing plastic deformation in a unified manner and provides a powerful tool for the study of combined crack extension and plastic deformation. A rigorous definition of plastic work is also given and it is shown that the crack extension force is the only physically meaningful parameter which can be used in the formulation of a crack instability criterion. The work of plastic deformation is not a part of the crack extension force and should not be included in the criterion for crack instability. It is found that one of the important effects of plastic deformation on crack instability is the shielding effect or the reduction it causes in the magnitude of the stress at the crack tip resulting in a smaller crack extension force. Other possible effects of plastic deformation on crack propagation are briefly discussed.     

Analysis of smooth crack growth in brittle materials

When a fault in the crust extends, earthquake faults appear as a set of displacement discontinuities on the ground surface and cause strong motion and large deformation. For the prediction of such earthquake faults, one needs to analyze the propagation of smoothly growing cracks. This paper develops an analysis method based on a new formulation of growing crack problems. In this method, the change in the stress intensity factors due to a small extension is explicitly related to the curvature and length of the extension, and these geometrical parameters can be determined from assumed fracture criteria, without taking any trial-and-error routes of the extension geometry. The validity of the proposed method is numerically examined; in particular, the predicted stress intensity factor changes coincide with numerically computed ones. The proposed method is applied to reproduce two experimental observations. It is shown that in both cases, the configuration of the simulated crack is in good agreement with the observed one.     

Packaging Parameters Analysis for the Fatigue Reliability of Stacked Chip Ball Grid Array by Using the Optimal Equivalent Solder Balls

A global/local method with the modified sub‐modeling approach of the two‐parametric optimal equivalent volume solder balls is introduced to predict the deformation and reliability of the package. The equivalent solder balls as exhibit in this method can obviously reduce the required elements/nodes quantities to enhance computing efficiency. A package model of wire‐bonded stacked chip ball grid array under cyclic thermal loading is used as a test vehicle to verify the influences of design factors by fatigue life indicator. Comparing the proposed method with the global fine mesh model, it is found that the difference in the accumulated strain energy density is merely 5.77%, but the optimal equivalent model has highly saved 90% finite element analysis required elements, which means the adopted method can effectively replace the global fine mesh model because both results are in accordance with each other. Using design of experiments to efficiently verify each factor influence with their cross‐coupling effects, this paper adopts two kinds of response surface methods that confirm the fatigue life of the proposed approach can be improved by as much as 123.7% for the dual response surface method and 126.3% for the mixed response surface method when comparing with the baseline model. In addition, the optimization of generic algorithm for both response surface methods is demonstrated in this study. From the reviews of factor coupling effects, it is concluded that the response surface method is eligible to achieve the optimum design for package reliability improving. Copyright © 2013 John Wiley & Sons, Ltd.     

Algebraic grid generation on trimmed parametric surface using non‐self‐overlapping planar Coons patch

Using a Coons patch mapping to generate a structured grid in the parametric region of a trimmed surface can avoid the singularity of elliptic PDE methods when only C¹ continuous boundary is given; the error of converting generic parametric C¹ boundary curves into a specified representation form is also avoided. However, overlap may happen on some portions of the algebraically generated grid when a linear or naïve cubic blending function is used in the mapping; this severely limits its usage in most of engineering and scientific applications where a grid system of non‐self‐overlapping is strictly required. To solve the problem, non‐trivial blending functions in a Coons patch mapping should be determined adaptively by the given boundary so that self‐overlapping can be averted. We address the adaptive determination problem by a functional optimization method. The governing equation of the optimization is derived by adding a virtual dimension in the parametric space of the given trimmed surface. Both one‐ and two‐parameter blending functions are studied. To resolve the difficulty of guessing good initial blending functions for the conjugate gradient method used, a progressive optimization algorithm is then proposed which has been shown to be very effective in a variety of practical examples. Also, an extension is added to the objective function to control the element shape. Finally, experiment results are shown to illustrate the usefulness and effectiveness of the presented method. Copyright © 2004 John Wiley & Sons, Ltd.     

基于黎曼度量参数曲面四边形网格生成方法及UG实现

论文给出了基于黎曼度量的参数曲面网格生成的改进铺砖算法。阐述了曲面自身的黎曼度量,并且运用黎曼度量计算二维参数域上单元节点的位置,从而使映射到三维物理空间的四边形网格形状良好。文中对原有铺砖法相交处理进行了改进,在运用铺砖法的同时调用UG-NX强大的二次开发库函数获取相应的信息,直接在UG-NX模型的表面生成四边形网格。算例表明,该法能在曲面上生成质量好的网格。     

Evaluation of subsurface damage in CAD/CAM machined dental ceramics

Commercial ceramics for dental computer aided design/computer aided manufacture (CAD/CAM) restorations suffer from surface chipping defects and microcracking. The influence of CAD/CAM machining of dental materials on the mechanical strength and extension of the damage zone was studied. Two different commercial dental ceramics, a feldspathic porcelain and a glass–ceramic, were CAD/CAM machined according to dental practice. The extension of the damage zone was analysed by a stepwise erosion of the surface, and the biaxial flexural strength was measured. To simulate the adhesive fixing of ceramic inlays, the specimens were sealed using a light-curing monomer. The different machining behaviour is dominated by the microstructure of the investigated materials. Owing to the high amount of glassy phase, the feldspathic porcelain shows extensive microcracking and chipping defects. The extent of the damage zone can be determined as 40–60 m. Sealing of the surface did not affect the flexural strength of the machined samples. The dominating response to machining of the glass–ceramic is crushing and crumbling with a major contribution of plastic deformation on a microscopic scale. The extent of the damage zone is less than 20 m. These cracks can be bridged by sealing of the surface, resulting in a substantial increase in strength. © 1998 Chapman & Hall     

Parametric shape and topology optimization: A new level set approach based on cardinal basis functions

The parametric level set approach is an extension of the conventional level set methods for topology optimization. By parameterizing the level set function, level set methods can be directly coupled with mathematical programming to achieve better numerical robustness and computational efficiency. Moreover, the parametric level set scheme can not only inherit the primary advantages of the conventional level set methods, such as clear boundary representation and the flexibility in handling topological changes, but also alleviate some undesired features from the conventional level set methods, such as the need for reinitialization. However, in the existing radial basis function–based parametric level set method, it is difficult to identify the range of the design variables. Besides, the parametric level set evolution often struggles with large fluctuations during the optimization process. Those issues cause difficulties both in numerical stability and in material property mapping. In this paper, a cardinal basis function is constructed based on the radial basis function partition of unity collocation method to parameterize the level set function. The benefit of using cardinal basis function is that the range of the design variables can now be clearly specified as the value of the level set function. A distance regularization energy functional is also introduced, aiming to maintain the desired signed distance property during the level set evolution. With this desired feature, the level set evolution is stabilized against large fluctuations. In addition, the material properties mapped from the level set function to the finite element model can be more accurate.     

多体非连续变形系统的计算力学模型及其应用

针对由不同特性物体所组成的多体系统,探讨了能够涵盖各种变形状态和运动形式的广义有限单元模式及其插值函数形式。对于多体接触问题,发展了能够合理描述界面特性的接触力元模型,即采用某种应力插值函数将界面上的相互作用力由接触对上的接触应力来表达,并将接触对上的接触应力当作需满足界面上屈服准则与流动法则等状态控制条件的参变量,将其作为约束条件加入系统控制方程。根据非连续变形系统的分区参变量最小势能变分原理,联立变分驻值条件与参变量的状态控制条件建立了多体系统非连续变形计算力学分析的基本控制方程,将问题最终归结为一个含有自由变量和等式约束条件的线性互补问题,对此发展了数值解法,并进行了多个算例的数值分析。计算结果表明该模型不仅能够对多体系统进行静、动力耦合分析,而且还能够模拟多体系统的变形与应力及接触界面上的接触应力和相对运动等复杂的非线性过程。