Isogeometric thickness stretchable shell: Efficient formulation for nonlinear dynamic problems

An isogeometric shell element with through-thickness stretch is introduced and applied to quasi-static and dynamic problems. The shell element supports full three-dimensional constitutive laws, ie, the plane stress assumption is not required. An updated Lagrangian rate formulation is adopted, and biquadratic spline-based interpolation functions are used for in-plane interpolation. The concept of fiber mass scaling is proposed to lower the highest eigenfrequencies to improve the performance of the formulation. Clamped and unclamped knot vectors are compared, and the advantages of using unclamped knot vectors are demonstrated. The shell element is validated using several benchmark tests, which indicate good performance of the proposed formulation.     

The solitary wave solution of the two-dimensional regularized long-wave equation in fluids and plasmas

This paper investigates the solitary wave solutions of the two-dimensional regularized long-wave equation which is arising in the investigation of the Rossby waves in rotating flows and the drift waves in plasmas. The main idea behind the numerical solution is to use a combination of boundary knot method and the analog equation method. The boundary knot method is a meshless boundary-type radial basis function collocation technique. In contrast with the method of fundamental solution, the boundary knot method uses the non-singular general solution instead of the singular fundamental solution to obtain the homogeneous solution. Similar to method of fundamental solution, the radial basis function is employed to approximate the particular solution via the dual reciprocity principle. In the current paper, we applied the idea of analog equation method. According to the analog equation method, the nonlinear governing operator is replaced by an equivalent nonhomogeneous linear one with known fundamental solution and under the same boundary conditions. Furthermore, in order to show the efficiency and accuracy of the proposed method, the present work is compared with finite difference scheme. The new method is analyzed for the local truncation error and the conservation properties. The results of several numerical experiments are given for both the single and double-soliton waves.     

INVESTIGATION OF THE THERMAL PROPERTIES OF OPTICAL MICROFIBER KNOT RESONATORS

The dependence of optical microfiber knot resonators (MKRs) thermal properties on the geometry parameters is theoretically and experimentally investigated in this article. According to the simulated and experimental results, the thermal properties of MKRs are synthetically determined by the microfiber diameter, refractive index, and thermo-optic coefficients of the external medium. Also, the rules for reinforcing or suppressing the thermal effects of MKRs and MKR-based devices by selecting matched configuration parameters are presented. A good agreement between the simulated and experimental results is obtained. The conclusions derived from our work would provide helpful guidelines in designing MKR-based devices with desired thermal properties to satisfy different requirements in applications.     

非参数自回归函数的有限元估计及其收敛速度

针对局部方法不能给出所拟合模型的简单的显式表达式,而且拟合和预报的计算量较大,本文考虑一种估计非参数自回归函数的全局有限元方法。该方法不但能克服上述局部方法之不足,而且在一定情形下优于多项式样条方法。在α-混合条件下得出了非参数自回归函数有限元估计的收敛速度,同时给出了利用AIC准则自动选择结点个数的数据追赶法,模拟算例说明了有限元估计方法的可行性。     

改进的Seifert算法的纽结可视化

纽结或链环的Seifert曲面是可定向曲面,关于该曲面的原理图可以在纽结理论的教材上查阅到,但是仅知道这些,想要去了解它们的形状和结构,仍然是很困难的.将讨论纽结和链环的可视化算法,包括Seifert算法和基于编织命名法的可视化算法,最后,给出了改进后的Seifert算法,另外,对纽结和链环生成的可定向闭曲面的亏格也做了进一步地研究.     

典型结艺产品三维结构快速设计方法

中国传统结艺产品结构复杂、设计方法原始,需要数字化设计技术的辅助来提高设计效率并增强创新.为此,提出了基于编织结构建模技术的结艺产品三维快速设计方法,以平面矢量曲线设计稿为蓝本,自动转化生成三维模型结构.该方法利用交叉点挑压状态的自动识别,配合用户交互修正得到正确的结构形式,从而回避了复杂交织结构的数学建模;针对典型结艺产品的囊状与翼状结构组合,利用平面矢量图分割、锁边连接和牵连连接来实现复杂三维结构的快速生成.实验结果表明,文中方法通过连接模式的自动识别和交互修正降低了对设计者的技术要求,简化了设计过程的复杂性.     

B-spline surface fitting based on adaptive knot placement using dominant columns

By expanding the idea of B-spline curve fitting using dominant points (Park and Lee 2007 [13]), we propose a new approach to B-spline surface fitting to rectangular grid points, which is based on adaptive knot placement using dominant columns along u- and v-directions. The approach basically takes approximate B-spline surface lofting which performs adaptive multiple B-spline curve fitting along and across rows of the grid points to construct a resulting B-spline surface. In multiple B-spline curve fitting, rows of points are fitted by compatible B-spline curves with a common knot vector whose knots are computed by averaging the parameter values of dominant columns selected from the points. We address how to select dominant columns which play a key role in realizing adaptive knot placement and thereby yielding better surface fitting. Some examples demonstrate the usefulness and quality of the proposed approach.     

传统纹样在藤制家具设计中的应用

目的 探究传统纹样在藤制家具设计中的应用策略。方法 基于当前的时代背景,结合藤制家具设计的实际情况,根据传统纹样在家具设计中的应用部位和作用,如结构装饰部件、面层编织、中国结饰、框体缠扎等部位,分析了传统纹样在藤制家具设计中的应用细节,从直接引用、变形重组、美好寓意和协调一致四个方面展开,并以具体的传统纹样为例,深入剖析了藤制家具的设计理念及方法。结论 传统纹样与藤制家具的结合不是简单地照搬照抄,而是要根据家具自身的特色进行合理简化、提炼,达到与家具整体风格的统一。传统纹样在藤制家具设计中的应用,不但为设计者提供了广泛的设计灵感和创作题材,而且增强了藤制家具中民族属性的审美特征,完成了对传统艺术文化的回归,为人们日常生活增添了情趣,旨在为藤制家具设计提供有价值的参考。     

广义B样条曲线节点插入算法及其应用

通过研究二阶常系数微分算子的零空间及其初值问题解的唯一性,引入了广义B样条曲线的概念,给出了B样条曲线的一种统一表示形式,介绍了该样条的求值算法及节点插入算法,并以多项式B样条为例,将样条曲线的求值算法和节点插入算法推广到曲面。最后给出了相应算例。数值实验表明,求值算法和节点插入算法对样条曲线和样条曲面均准确、有效。利用广义B样条曲线在2个方向上取不同类型的样条曲线,构造了特殊曲面。     

基于B样条曲线的植物叶片几何建模

针对基于图像的植物叶片真实感建模进行了研究, 提出对植物叶片图像的轮廓特征点进行三次均匀B样条曲线插值的算法。该方法提取出标本叶片图像的角点作为特征点, 采用三次均匀B样条曲线进行初步插值拟合, 并根据拟合误差采用改进的节点插入算法进行反复迭代, 直到达到要求的拟合精度。与传统方法相比, 该方法能够更快地达到逼近精度, 并且具有良好的模拟效果, 有一定的实际应用价值。