Study of key algorithms in topology optimization

The theory of topology optimization based on the solid isotropic material with penalization model (SIMP) method is thoroughly analyzed in this paper. In order to solve complicated topology optimization problems, a hybrid solution algorithm based on the method of moving asymptotes (MMA) approach and the globally convergent version of the method of moving asymptotes (GCMMA) approach is proposed. The numerical instability, which always leads to a non-manufacturing result in topology optimization, is analyzed, along with current methods to control it. To eliminate the numerical instability of topology results, a convolution integral factor method is introduced. Meanwhile, an iteration procedure based on the hybrid solution algorithm and a method to eliminate numerical instability are developed. The proposed algorithms are verified with illustrative examples. The effect and function of the hybrid solution algorithm and the convolution radius in optimization are also discussed.     

RECONSTRUCTION STABILITY OF NEARFIELD ACOUSTIC HOLOGRAPHY

The distributed source boundary point method (DSBPM) is used as the spatial transform algorithm for realizing nearfield acoustic holography (NAH),the sensitivity of the reconstructed solution to the measurement errors is analyzed,and the regularization method is proposed to stabilize the reconstruction process,control the influence of the measurement errors and get a better approximate solution.An oscillating sphere is investigated as a numerical example,the influence of the measurement errors on the reconstruction solution is demonstrated,and the feasibility and validity of the regularization method are validated.     

子结构综合法辩识结合部的特征参数

为了获取结合部的等效刚度与 阻尼参数,采用子结构综合法来建立结合部辨识方程式,利用模型更新的方法修正已知模型,使修正的 模型与已知模型等效,并利用修正的模型来获取所需的频响函数,从而根据完备频响函数辨识出结合部参数。为了保证数值计算的稳定性,采用最小二乘原理将矛盾方程转化为定解方 程,并引入加权的概念,使得被测数据能够充分利用。最后通过两个仿真算例来验证该方法的 可行性和工程实用性。仿真结果可以看出,该方法具有较高的辨识精度。     

A dynamic boundary model for implementation of boundary conditions in lattice-Boltzmann method

Methodology of implementation of the no-slip boundary condition in the lattice-Boltzmann method affects overall accuracy of the numerical solutions as well as the stability of the solution procedure. We propose a new algorithm, i.e., the method of using a dynamic equation for establishing no-slip boundary conditions on walls. The distribution functions on the wall along each of the links across the physical boundary are assumed to be composed of equilibrium and non-equilibrium parts which inherit the idea of Guo’s extrapolation method (2002). In the proposed algorithm, we employed a dynamic equation to correct the velocity error occurring on the physical boundary. Numerical results show that the dynamic boundary model is featured with improved accuracy and simplicity. The proposed method is postulated to be useful especially in the study on microfluidic mixing.     

基于无网格Galerkin法的灵敏度分析与形状优化

结构形状优化已经在工程应用中得到重视,将无网格法与形状优化相结合能够从根本上解决优化过程中出现的有限单元扭曲或畸变问题。为此在无网格Galerkin法的基础上,利用离散导数法,提出一种基于离散型的节点位移灵敏度分析方法,其中采用了拉格朗日乘子法来施加本质边界条件。该方法的最大优势是求解过程与无网格Galerkin法的求解过程相似,容易实现。另外对形状优化的数学模型和节点位移的设计速度域进行了讨论。采用具有解析解的实例,对所提出的灵敏度分析方法进行了验证,所得结果显示两者非常吻合。利用上述所建立的形状优化算法,完成了两个工程实例的形状优化设计。     

光学系统计算机辅助装调中的一种优化算法

如何快速、准确、稳定地确定失调量是光学系统计算机辅助装调技术的一个关键部分.本文首先进行数学建模,建立了失调量与引入像差的关系式,然后提出了求解失调量的伪逆及奇异值巩固逆算法,以解决直接按最小二乘法方程组求解所带来的数值不稳定性及解的不精确性问题.最后,利用本文所建立的数值分析模型,进行了模拟计算,计算结果表明,本文的计算方法是合理可行、有效的.     

A mesh-less method to solve electrical resistance tomography forward problem using singular boundary distributed source method

This paper presents a novel mesh-less method called singular boundary distributed source (SBDS) method to solve the electrical resistance tomography (ERT) forward problem. Mesh-less methods are mathematically simple and computationally efficient i.e. same accuracy that of mesh or domain based methods can be achieved with less computation time. The domain boundary is discretized such that the source and field points coincide on the same boundary and the solution is expressed as a linear combination of fundamental solution of governing equation. The singularity appearing due to coinciding of source and field points is addressed using a hybrid approach. The coefficients corresponding to Neumann boundary are evaluated using the improved distributed source method (IBDS) while the coefficients corresponding to Dirichlet boundary conditions are evaluated using inverse interpolation technique. The hybrid SBDS with complete electrode model is formulated for ERT forward problem. The proposed SBDS method has better accuracy and convergence as compared to other mesh-less methods. Especially, the SBDS method solution is not dependent on distributed source radius therefore is stable compared to the IBDS method. The proposed SBDS method is tested with numerical experiments and the performance is compared against boundary discretization methods such as the IBDS and boundary element methods.     

Three-dimensional trajectory design for horizontal well based on optimal switching algorithms

This paper considers a three-dimensional trajectory design problem for horizontal well. The problem is formulated as an optimal control problem of switched systems with continuous state inequality constraints. Since the complexity of such constraints and the switching instants is unknown, it is difficult to solve the problem by standard optimization techniques. To overcome the difficulty, by a time-scaling transformation, a smoothing technique and a penalty function method, an efficient computational method is proposed for solving this problem. Convergence results show that, for a sufficiently large penalty parameter, any local optimal solution of the approximate problem is also a local optimal solution of the original problem. Two numerical examples are presented to illustrate the efficiency of the approach proposed.     

一种9杆巴氏桁架位置正解的超混沌改进牛顿法

提出非线性方程组全部实数解求解的超混沌改进牛顿法,完成了第33种非平面两耦合9杆巴氏桁架的位置正解问题。结合矢量法和复数法建立该机构4回路的4个约束方程,利用正、余弦三角函数关系增设4变量,建立4个补充方程,从而构造了该机构位置分析的8变量约束方程组。将超混沌序列和改进牛顿迭代法结合,应用超混沌离散系统产生迭代初始点,提出了应用超混沌序列的改进牛顿迭代法求解非线性方程组全部实数解的新方法,完成了该机构的位置分析。给出计算实例,并与其他方法进行了比较,实例表明该方法的正确性和有效性。     

Kinematic Solution of Spherical Stephenson-Ⅲ Six-bar Mechanism

A closed-form solution can be obtained for kinematic analysis of spatial mechanisms by using analytical method.However,extra solutions would occur when solving the constraint equations of mechanism kinematics unless the constraint equations are established with a proper method and the solving approach is appropriate.In order to obtain a kinematic solution of the spherical Stephenson-III six-bar mechanism,spherical analytical theory is employed to construct the constraint equations.Firstly,the mechanism is divided into a four-bar loop and a two-bar unit.On the basis of the decomposition,vectors of the mechanism nodes are derived according to spherical analytical theory and the principle of coordinate transformation.Secondly,the structural constraint equations are constructed by applying cosine formula of spherical triangles to the top platform of the mechanism.Thirdly,the constraint equations are solved by using Bezout’ s elimination method for forward analysis and Sylvester’ s resultant elimination method for inverse kinematics respectively.By the aid of computer symbolic systems,Mathematica and Maple,symbolic closed-form solution of forward and inverse displacement analysis of spherical Stephenson-III six-bar mechanism are obtained.Finally,numerical examples of forward and inverse analysis are presented to illustrate the proposed approach.The results indicate that the constraint equations established with the proposed method are much simpler than those reported by previous literature,and can be readily eliminated and solved.     

Solving topology optimization problems by the Guide-Weight method

Finding a good solution method for topology optimization problems is always paid attention to by the research field because they are subject to the large number of the design variables and to the complexity that occurs because the objective and constraint functions are usually implicit with respect to design variables. Guide-Weight method, proposed first by Chen in 1980s, was effectively and successfully used in antenna structures’ optimization. This paper makes some improvement to it so that it possesses the characteristics of both the optimality criteria methods and the mathematical programming methods. When the Guide-Weight method is applied into topology optimization, it works very well with unified and simple form, wide availability and fast convergence. The algorithm of the Guide-Weight method and the improvement on it are described; two formulations of topology optimization solved by the Guide-Weight method combining with SIMP method are presented; subsequently, three numerical examples are provided, and comparison of the Guide-Weight method with other methods is made.     

冗余仿人臂避关节物理约束的一种逆运动学问题求解方法

冗余仿人臂有无穷多组逆运动学解满足末端位姿要求,但由于其连杆机构与形状的设计仿人臂每个自由度都有关节位置物理约束。为使所求取的逆运动学解最大化地远离仿人臂关节限位,提出冗余仿人臂(8-DOF)一种几何-数值迭代相结合求解逆运动学问题方法,该方法在计算出仿人臂逆运动学解几何表达式基础上,以仿人臂的“远离限位度”指标构建适应度函数并以此为寻优目标,通过粒子群优化方法(Particle swarm optimization,PSO)搜索冗余关节角最优组合,并获得满足仿人臂末端位姿要求的最优逆运动学解。该方法不仅解决了冗余仿人臂逆运动学多解问题,而且所求关节角不存在理论误差、求解速度快及所求关节角远离关节位置限位裕量大的优点,仿真试验验证了该方法有效性。     

3-6Stewart平台的正向运动学数值求解分析

针对 Stewart平台正向运动学求解的困难 ,建立了 3- 6 Stewart平台正向运动学数学模型 ,同时采用改进的Newton- Raphson方法进行数值求解。并利用消元法进行模型简化 ,迭代初值采用先粗后细的方法选取。仿真分析表明 ,该方法提高了效率和计算稳定性。     

旋转状态下干涉配合应力分析的边界元法

本文对边界元法用于旋转状态下干涉配合的应力分析进行了讨论。根据边界局部坐标与整体坐标间的关系,推导出适用于处理干涉配合中接合面上的联接条件的二维弹性问题的边界积分方程;建立了旋转状态下干涉配合应力分析的边界元方程,并讨论了数值计算的方法。文中给出了一个算例,将边界元解与解析解进行了比较。计算表明,文中的方法对旋转状态下干涉配合的应力分析是可行的,其计算精度令人满意。     

注塑加工中冷却分析的边界元法

本文给出了一组用于注塑加工中热传导分析的边界积分公式。应用边界元法开发了一注塑模三维冷却分析系统。对影响数值模拟效率的线性方程组求解、数据内外存交换及计算机存储资源调度与管理、边界积分公式及其数值处理方法进行了较深入的研究。本文所提出的公式、线性方程组的分步迭代法求解法和计算机存储资源管理程序包,大大地减少了模具冷却分析的时间。     

One method for restoration of blurred images

A new method is proposed to reduce image distortions caused by random noise and rectilinear uniform motion of the object or recording system. The of a restoration model is based on a statistical regularization method, and the obtained system of linear equations and inequalities is solved using a multistep support vector method. An advantage of this approach is that the iterative nature of the algorithm makes it possible to take into account the a priori information on the solution represented by the inequalities. The results of numerical experiments showing the efficiency of the algorithm are given.     

Large deflection of constant curvature cantilever beam under follower load

This paper describes a method to analyze for the large deflections of curved prismatic cantilever beams with uniform curvature subjected to a follower load at the tip. The large deflection, the deflection dependent follower load and the initial curved geometry are the important features of the beam considered in this work. Shear force formulation proposed by Lee [Large deflections of cantilever beams of non-linear elastic material under a combined loading. Int J Non-Linear Mech 2002;37(3)] is used for deriving the governing equations. Using this approach, the resulting two point boundary value problem (TPBVP) can be reduced to an initial value problem (IVP). Fourth order Runge-Kutta method along with one parameter reverse shooting method is applied to the numerical solution to the problem. A novel approach presented in this paper of integrating from the free end to the fixed end of the cantilever beam simply replaces the two parameter shooting with a single parameter shooting yielding several advantages. This solution technique is demonstrated for various types of follower tip loads on curved and straight cantilever beams and is validated with existing solutions in the literature.     

基于反问题的正则化波束形成改进算法

基于反问题的正则化波束形成技术能以较高的计算效率得到稳健的声源识别结果。然而由于其正则化解中的正则化矩阵取决于低效的传统波束形成方法,使得基于反问题的正则化波束形成的声源识别结果精准度较低。为了在低信噪比环境下进一步提升其声源识别性能,基于Tikhonov正则化一般形式解提出一种双重迭代优化算法。该算法基于延时求和波束形成算法与互谱运算构造出新的正则化矩阵,并结合迭代方法对新正则化矩阵和波束输出进行优化,最终以较少的迭代步数经两次迭代运算有效提高了声源识别精度和稳定性。最后,通过数值仿真和实验算例,进一步验证了双重迭代优化算法的可行性和有效性。     

机械设备流固耦合动力分析的有效方法

提出流固耦合动力分析的新方法。该法通过结构动力学的有限元求解方程和Newmark法,导出了新的迭代公式。流场的动压力使弹性体的动态特性变为载荷非线性问题;同时,固体位移场的变形作用使流场成为可变域流场。这些问题都可用本法得以解决。文中给出算例和工程应用实例。数值解结果表明,该法收敛速度快,效率高,克服了耦合问题的求解困难。     

基于遗传算法的旋转机械转子裂纹识别的研究

转子裂纹是旋转机械中常见且危险的一种故障,转子裂纹的有效识别和定位也是故障诊断领域一直研究的课题。将转子裂纹的识别作为一反问题,从反问题的求解角度,提出了基于遗传算法的转子裂纹识别策略,该策略的基本思路是借助于有限元分析方法建立裂纹转子的有限元模型,并将转子裂纹识别问题形式化为一优化问题,进而利用遗传算法进行优化求解实现转子裂纹的识别。数值仿真研究表明,所提出的裂纹识别的反问题进化求解策略能以较好的精度和鲁棒性识别转子裂纹,是有效可行的,且适用于更广泛的无损检测和缺陷辨识等应用场合。