脱层板固有频率的有限元方法分析

结合弹性材料修正后的H-R(Hellinger-Reissner)变分原理和二次插值函数,建立了平面坐标系下Hamilton正则方程推导了八节点等参元列式.考虑到脱层板的连接界面上应力和位移的连续性,将脱层板离散成上下两层,采用"分离合并"技术,建立脱层情况下板的控制方程.本文具体研究了脱层结构的固有频率问题,数值实例证明了本文方法的正确性.八节点等参元的使用不仅减少了节点数,同时也大大提高了计算效率.     

基于MATLAB的B样条小波程序的实现

MATLAB是一种建立在向量、数组、矩阵基础上,面向科学和工程计算的高级语言,为科学研究和工程计算提供了一个方便有效的工具。该文简要介绍了B样条和B样条小波的构成,并利用MATLAB语言编写了绘制任意阶B样条和B样条小波图形的程序。     

基于B样条小波的彩色印刷扫描图像逆半调

彩色印刷是一种利用黄、品红、青、黑四色油墨叠印产生彩色图像的技术,逆半调是将半色调图像转换成连续调图像的过程,主要应用在电子出版和印刷图像电子化方面。选取LAB颜色空间作为逆半调处理的颜色空间,选择三阶B样条小波作为小波基,遵循小波分解、小波系数调整、小波重构的小波变换算法,对彩色印刷扫描图像进行逆半调处理,得到逆半调图像。实验结果表明,该算法避免了破坏彩色图像红、绿、蓝颜色通道的颜色相关性,对彩色印刷扫描图像的重建和印刷加网图像的恢复具有一定的理论意义和应用价值。     

小波方法光顺的B样条模糊系统及其应用

为了减少不准确数据对模糊系统的影响, 本文利用准均匀B样条小波方法光顺了B样条模糊系统. 首先将B样条模糊系统的多分辨率表示转化为准均匀B样条函数的多分辨率表示, 接着利用准均匀B样条小波分解方法对相应的准均匀B样条函数进行分解就得到了一系列光顺性逐渐增强、规则个数逐渐减少的模糊系统, 即基于小波方法的光顺B样条模糊系统. 最后, 仿真结果表明, 小波方法光顺的B样条模糊系统构造的模糊控制器在改善原来B样条模糊系统构造的模糊控制器性能的同时, 大大提高了原来控制器的运行效率.     

有理B样条曲线的区间隐式化

研究有理B样条曲线的区间隐式化问题,即对给定的一条有理B样条曲线,寻求低次的区间隐式B样条包含给定的曲线,要求区间隐式B样条曲线的宽度尽量小,并且尽量避免多余分支的出现．将该问题分为求解近似隐式曲线和边界曲线两步,并将问题转化为求解局部的线性最优化问题．最后给出几个算例．     

基于非均匀B样条小波的图像水印算法

提出了一种基于非均匀B样条小波变换的数字水印嵌入与提取算法,并通过实验分析了其鲁棒性。由于利用非均匀B样条小波对图像进行分解可以得到小于原图的任意大小的低分辨子图,因而利用方法可以方便地嵌入小于载体图像的任意大小的二值水印,并可以盲提取。实验结果表明,该算法具有较强的抗各种常见攻击的鲁棒性。     

有理B样条曲面的区间隐式化

提出有理B样条曲面的区间隐式化方法,即对一个有理B样条曲面,寻求包含给定的曲面的区间隐式B样条曲面,使得区间隐式B样条曲面的"厚度"尽量小,同时尽量避免出现多余分支.该问题等价于求区间隐式B样条曲面的2个边界曲面.针对该问题建立一个最优化模型并求解.     

柱坐标系下正则方程的八节点等参元列式

结合弹性材料修正后的H-R变分原理和二次插值函数,为柱坐标系下Hamilton正则方程建立了八节点等参元列式.首先简要地介绍了弹性材料修正后的H-R变分原理,然后采用二次插值函数表达壳的平面外应力和位移函数,详细地推导了柱坐标系下Hamilton正则方程的八节点等参元列式.数值实例的分析结果证明了本文八节点等参元列式的正确性.     

恒载效应对拱结构自振频率的影响分析

提出用样条有限点法分析拱的自振频率,采用3次B样条函数的线性组合作为位移振型函数,以曲杆变形理论为基础,根据Hamilton原理建立了考虑恒载效应影响时拱的振动频率方程.计算分析了恒载效应对拱结构自振频率的影响.结果表明恒载效应会使拱结构自振频率减小;影响大小与结构自身刚度有关;拱结构截面刚度一定时,拱矢跨比、径厚比越大,恒载效应对自振频率的影响越大.     

Mixed least-squares finite element model for the static analysis of laminated composite plates

This paper presents a mixed finite element model for the static analysis of laminated composite plates. The formulation is based on the least-squares variational principle, which is an alternative approach to the mixed weak form finite element models. The mixed least-squares finite element model considers the first-order shear deformation theory with generalized displacements and stress resultants as independent variables. Specifically, the mixed model is developed using equal-order C⁰ Lagrange interpolation functions of high p-levels along with full integration. This mixed least-squares-based discrete model yields a symmetric and positive-definite system of algebraic equations. The predictive capability of the proposed model is demonstrated by numerical examples of the static analysis of four laminated composite plates, with different boundary conditions and various side-to-thickness ratios. Particularly, the mixed least-squares model with high-order interpolation functions is shown to be insensitive to shear-locking.     

基于Kane方法的Stewart传感器动力学及固有频率分析

通过线性化动力学方程并应用Kane方法,研究了Stewart传感器的固有频率．将Stewart传感器的上平台、上连杆、敏感元件及下连杆作为独立的子结构分别处理,依据矢量和张量理论对其运动学方程和动力学方程进行系统的推导,并经过简化导出Stewart传感器简洁的固有频率方程形式．为验证Kane方法的有效性,提供了MATHEMATICA数值算例．相比于传统的牛顿一欧拉方法及拉格朗日方法,Kane方法既简洁又高效,特别适合于计算机计算．     

Large deflection analyses of skew plates using hybrid/mixed finite element method

A new hybrid/mixed shell element is developed using oblique coordinate systems to analyze the large deflection behavior of skew plate with various skew angles, length to width ratios, thicknesses and supported edges under uniformly distributed and concentrated loads. The results obtained from the new element are compared with available theoretical and numerical solutions. An excellent agreement is achieved even for coarse meshes. The accuracy and efficiency of the proposed element are demonstrated.     

Collocation method using quintic B-spline and sinc functions for solving a model of squeezing flow between two infinite plates

An axisymmetric viscous flow, generated by two large parallel plates slowly approaching each other is investigated. The steady nonlinear governing equations are converted into a fourth-order nonlinear differential equation using integrability condition. The resulting nonlinear boundary value problem is solved using quintic B-spline collocation and sinc-collocation methods. The approach consists of reducing the problem to a set of algebraic equations. Numerical examples are included to demonstrate the validity and applicability of the techniques and a comparison is made with existing results in the literature.     

A split least-squares characteristic mixed finite element method for Sobolev equations with convection term

In this paper, a split least-squares characteristic mixed finite element method for a kind of Sobolev equation with convection term is proposed, in which the characteristic method is based on the approximation of the material derivative term, that is, the time derivative term plus the convection term. The resulting least-squares procedure can be split into two independent symmetric positive definite sub-schemes and does not need to solve a coupled system of equations. Theory analysis shows that the method yields the approximate solutions with optimal accuracy in L²(Ω) norm for the primal unknown and in H(div;Ω) norm for the unknown flux, respectively. Numerical examples in one dimension, which are consistent with the theoretical results, are provided to demonstrate the characteristic behavior of this approach.