优化双圆弧拟合

本文提出一种优化双圆弧拟合的新算法，它采用的方法是用改变双圆弧联结点的切线使双圆弧与样条曲线间的法向误差达到最小（或小于允许误差），与其他双圆弧拟合方法相比较，该算法计算简单，线性，并可消除拟合曲线的不稳定性，拟合效果快速，良好。可直接应用于雕塑曲面的ＣＮＣ加工中。     

符号矩阵填充的修正增广拉格朗日乘子算法

矩阵填充问题是近年来的研究热点之一,特别地,符号矩阵填充问题在生物医学等领域有着很好的应用前景.本文以奇异值阈值方法为基础,针对符号矩阵填充提出了修正的增广Lagrange乘子法.修正算法对每步产生的阈值矩阵进行符号投影,形成新的符号矩阵,构成在符号矩阵离散集合上的迭代.同时证明了在合理条件下,当罚因子充分大时,修正算...     

基于VB的优化双圆弧拟合误差分析及其算法改进

针对数控加工的特点,分析了双圆弧拟合的方式,运用VB实现了双圆弧拟合算法并进行了误差分析;通过对误差分布的分析以及对影响误差因素的研究,探索了双圆弧曲线误差变化的规律,提出了基于步长规划来减小误差的改进拟合算法.     

基于Epsilon算法的不确定性结构二阶区间优化方法

该文提出一种求解不确定性结构模态的二阶区间优化算法,首先应用拉格朗日乘子法将带有约束条件的模态优化问题转化为非约束优化,再用区间扩展的二阶泰勒展开式近似表述不确定性结构的模态区间函数。由于其二阶常数项(海森矩阵)的计算十分繁琐,这里采用DFP方法(Davidon and Fletcher-Powell method)近似迭代计算该常数项,同时计算满足约束条件和优化目标的结构参数和参数不确定性区间。在结构重分析中采用Epsilon算法,从而在保证计算精度的同时节省了计算时间。通过算例计算进一步证明该方法对于板壳加筋不确定结构的优化是有效的。     

单曲玻璃幕墙折线拟合圆弧的实现方法及应用

日前，圆弧形、“S”形或其它类型的技术含量高、漂亮美观的单曲面玻璃幕墙越来越多，采用折线拟合圆弧法（平直玻璃）设计该类建筑幕墙，大大减低工程造价。为业主节约投资。本文就该类建筑幕墙设计的简化原则与运用、系统构造设计方法进行探讨总结，以期对同类曲面造型工程的处理作些有益的贡献。     

基于状态空间法的圆弧曲梁面内动力学分析

该文采用状态空间法研究了圆弧曲梁面内动力学特性。通过选择合适的状态变量，建立了相应的状态空间列式，并给出了固有频率和振动模态的求解过程。进一步通过引入辛内积的概念，建立了三种工程常见边界条件(简支、固支和自由)下圆弧曲梁面内振动模态关于质量和旋转惯量的正交关系式。在此基础上，运用模态叠加法给出了非齐次状态方程的解析解，并得到了圆弧曲梁在竖向移动集中荷载作用下的瞬态响应。数值算例结果表明该文方法是十分精确和可靠的。     

基于Gauss-Newton法的L1数据拟合

在数据拟合中，当个别数据存在较大测量误差时，采用Ｌ１准则对数据进行拟合要优于最小二乘准则。本文通过建立Ｌ１准则与最小二乘准则之间的关系，给出了一种基于Ｇａｕｓｓ－Ｎｅｗｔｏｎ法的Ｌ１数据拟合自满。计算结果表明，该方法易于理解，便于编程，具有一定的理论意义和现实意义。     

三点法测量圆弧半径的数据处理

介绍了在圆弧上测得任意三点的坐标值，通过建立直线方程和圆方程以及通过算得测点间的坐标距离求得圆弧半径的三种数据处理方法。     

基于投影的二阶段空间圆线拟合算法

对空间圆线精确拟合算法进行研究．线性和非线性最小二乘法是拟合规则曲线和曲面方程的常见方法．空间圆线作为规则的二次曲线,由于没有特定的曲线方程无法直接使用线性和非线性最小二乘法来进行求解．由于空间圆线可以被看作平面和球面相交形成,圆线特征值可以通过平面和球面特征值求解．提出了基于投影二阶段拟合算法完成空间圆线拟合的方法．对空间圆线拟合原理进行了介绍,通过数据验证了算法的正确性、可行性和精确程度．使用程序进行了算法实现．与贝塞尔和B样条曲线算法精度进行了比较,表明该算法在精度方面具有优势,可用于逆向工程中提高空间拟合算法的精确度．     

Topology optimization using bi-directional evolutionary structural optimization based on the element-free Galerkin method

In this article, the bi-directional evolutionary structural optimization (BESO) method based on the element-free Galerkin (EFG) method is presented for topology optimization of continuum structures. The mathematical formulation of the topology optimization is developed considering the nodal strain energy as the design variable and the minimization of compliance as the objective function. The EFG method is used to derive the shape functions using the moving least squares approximation. The essential boundary conditions are enforced by the method of Lagrange multipliers. Several topology optimization problems are presented to show the effectiveness of the proposed method. Many issues related to topology optimization of continuum structures, such as chequerboard patterns and mesh dependency, are studied in the examples.     

Frictionless 2D Contact formulations for finite deformations based on the mortar method

In this paper two different finite element formulations for frictionless large deformation contact problems with non-matching meshes are presented. Both are based on the mortar method. The first formulation introduces the contact constraints via Lagrange multipliers, the other employs the penalty method. Both formulations differ in size and the way of fulfilling the contact constraints, thus different strategies to determine the permanently changing contact area are required. Starting from the contact potential energy, the variational formulation, the linearization and finally the matrix formulation of both methods are derived. In combination with different contact detection methods the global solution algorithm is applied to different two-dimensional examples.     

基于粒子群算法的改进模态参数识别方法

针对一类多模态振动衰减信号的模态参数识别,结合奇异值分解(singular value decomposition,SVD)、解析模态分解(analytical mode decomposition,AMD)、自回归功率谱和粒子群优化(particle swarm optimization,PSO)算法,提出了一种改进...     

基于RPE算法的正弦信号测量

给出了一种同时测量正弦波参数的方法.该方法基于递推预报误差(RPE)算法,采用递推结构,具有占用内存少、易于编程、能够进行在线测量、计算精度高等特点.并给出了部分试验结果.     

A scaled boundary finite element based explicit topology optimization approach for three-dimensional structures

This article proposes an efficient approach for solving three-dimensional (3D) topology optimization problem. In this approach, the number of design variables in optimization as well as the number of degrees of freedom in structural response analysis can be reduced significantly. This is accomplished through the use of scaled boundary finite element method (SBFEM) for structural analysis under the moving morphable component (MMC)-based topology optimization framework. In the proposed method, accurate response analysis in the boundary region dictates the accuracy of the entire analysis. In this regard, an adaptive refinement scheme is developed where the refined mesh is only used in the boundary region while relating coarse mesh is used away from the boundary. Numerical examples demonstrate that the computational efficiency of 3D topology optimization can be improved effectively by the proposed approach.     

基于随机无网格伽辽金法和蚂蚁算法的结构可靠性分析

 用摄动随机无网格伽辽金法(PSEFGM)求解随机结构的响应,然后采用蚂蚁算法对结构可靠性进行了分析。摄动随机无网格伽辽金法具有不需要划分单元和精度高等特点。蚂蚁算法是一种智能型随机搜素优化算法,对目标函数没有任何可微甚至连续的要求,可有效克服经典算法易于陷入局部最优解的常见弊病。数值实例表明,在随机结构可靠性分析方面,随机无网格迦辽金法与蚂蚁算法比经典算法具有明显的优势。     

采用混合粒子群算法实现匹配追踪算法

针对匹配追踪信号稀疏分解的巨大计算量问题,在具有全局优化能力的粒子群算法基础上,提出了一种结合BFGS(Broyden、Fletcher、Goldfarb和Shanno)方法和变异操作的混合粒子群算法实现信号匹配追踪分解。利用BFGS方法增强了算法的局部开发能力,加快了信号特征提取速度;通过变异操作控制种群多样性以避免早熟收敛,增强了算法全局探测能力,提高了信号特征提取精度。通过与单一粒子群算法和遗传算法实现仿真信号匹配追踪分解的结果进行对比,证明了使用混合粒子群算法的匹配追踪分解能够快速准确提取信号特征参数。最后,将该算法应用于某内圈损伤轴承振动信号中的冲击特征提取,结果表明该算法在工程应用中具有一定的准确性和实用性。     

基于遗传算法的复合材料结构-声辐射优化研究

研究了外载荷作用下的复合材料结构振动响应和声辐射问题。在此基础上, 分析了复合材料的结构-声辐射优化设计模型, 基于遗传算法进行了对称型复合材料板结构的结构-声辐射铺层几何优化分析。数值算例表明, 复合材料板结构的铺层数、 铺层厚度和铺层角度等参数优化, 可以有效降低结构的振动和声辐射。数值算例结果验证了优化方法的有效性。     

Topology optimization of periodic cellular solids based on a superelement method

It is well known that the structural performance of lightweight cellular solids depends greatly on the design of the representative volume element (RVE). In this article, an integrated topology optimization procedure is developed for the global stiffness maximization of 2D periodic and cyclic-symmetry cellular solids. A design variable linking technique and a superelement method are applied to model the structural periodicity and to reduce the computing time. In order to prevent the numerical instabilities associated with checkerboards in the design process, the quadratic perimeter constraint is used. Finally, the topology optimization problem is solved by the dual optimization algorithm. Several numerical examples are used to test the efficiency of the optimization procedure. Results show that the optimal topology of the RVE is not unique. It greatly depends on the size of the RVE. The computing efficiency can be greatly improved by means of the superelement technique. Also, for the optimal solution, the equivalent torsional rigidity has been compared with what is in the literature, to check the structural efficiency of the obtained topology. It has been observed that the current topology solution has the strongest rigidity when the same volume fraction of solid-phase materials is used.