正交各向异性弹塑性摩擦接触问题的数值求解

采用正交各向异性摩擦定律对三维弹塑性摩擦接触问题进行分析,基于参变量变分原理,经过有限元离散,将问题化为线性互补问题模型,之后给出一个求解互补问题的非内点光滑化算法．对三维接触问题,滑动方向的确定一直是个难点,为此,该文采用作者提出的组合规划法和迭代法对各向异性摩擦本构模型进行分析,数值结果说明了模型与算法的正确性。     

钢制弹丸冲击混凝土时绝热剪切局部化的数值计算

为描述弹丸材料冲击混凝土时的绝热剪切过程,根据冲击条件下绝热剪切局部化的一维分析结果,给出冲击混凝土弹丸材料的绝热剪切局部化模型并引入到数值分析中。为了既能描述混凝土的非线性变形及断裂特性又要保持分析过程中材料界面的清晰,混凝土划分成光滑粒子并使用无网格光滑粒子动力学算法,而弹体划分成有限元网格并使用有限元算法。结果显示,利用本文中给出的绝热剪切局部化模型计算得到的弹丸内绝热剪切局部化区域与实验中的破坏位置一致。     

光滑边域连续-非连续细胞自动机在裂纹开裂扩展中的应用

针对岩石裂纹开裂扩展问题，将应变光滑技术与连续-非连续细胞自动机方法相结合，构建了非连续裂纹贯穿单元和裂纹尖端单元光滑应变场，提出快速自适应光滑边域连续-非连续细胞自动机方法.构建了裂纹面位移非连续精细表征的非连续增强形函数，建立了裂纹贯穿单元和裂纹尖端单元的光滑应变矩阵求解方法，利用高斯散度定理将单元的区域积分转换为光滑域边界线积分，推导给出了光滑边域连续-非连续细胞自动机应变矩阵计算表达式，并提出了快速自适应更新方法，建立了加速因子随元胞更新而同步更新的自适应加速算法，基于此，最佳加速因子随更新自动获得，收敛速度较传统细胞自动机方法得到极大提高.利用C++编制了分析计算程序，针对多裂纹开裂扩展过程进行了模拟，并与扩展有限元进行了比较.研究发现，光滑边域连续-非连续细胞自动机方法在解的精确性、稳定性和收敛性上较扩展有限元有显著优势.     

接触力优化设计的熵正则化方法

包含单侧接触的机械和结构系统中,接触面间的局部接触力很大时,容易导致结构局部磨损和破坏。利用结构优化的手段极小化接触面上的最大接触力是调整接触面上接触力分布的一个有效途径。然而在数学上,目标函数的不可微和约束中的接触条件导致该结构优化问题属于非光滑和非凸优化问题,因而常用优化算法的优化结果是不可靠的。为此,本文提出接触力优化的一个熵正则化模型,并利用基于正则化过程的序列二次结构优化算法求解。所提的方法在数值上避免了处理不可微问题,而且正则化参数的调整还有助于获得更小的局部最优解。以离散结构为例的数值算例验证了本文的模型和算法。     

蚁群算法求解二维拉压不同模量反问题

利用光滑函数技术对二维拉压不同模量本构关系进行光滑化处理,采用初应力方法求解二维拉压不同模量正问题的有限元方程。在此基础上,建立了基于连续域蚁群算法的二维拉压不同模量反问题的数值求解模型,考虑了区域非均质的影响,实现了对拉压弹性模量和泊松比的单一/组合识别。通过两个数值算例,对所提算法进行了数值验证,分别探讨了蚁群算法相关参数、测点分布和数据噪音等对识别结果的影响。数值验证表明,所提算法可有效地求解二维拉压不同模量反问题,并具有较好的计算精度。     

一类多线程并行四面体网格优化算法

提出了一类多线程并行、组合了光滑化与局部重连操作的四面体网格优化算法。采用传统的基于拓扑的数据分解策略实现了并行光滑化算法,利用图染色算法将待光滑化的点分解成多个独立点集。同时提出将一类基于几何的数据分解策略应用于局部重连操作的并行化,在每个局部重连操作涉及的几何区域中定义一个特征点,然后沿希尔伯特(Hilbert)曲线对特征点进行排序,曲线的均匀分解对应局部重连操作在各线程的分配。这一分配策略的优点是使并行执行局部重连操作时重连区域相互干涉的情形极少出现。因此,当干涉情形出现时,可选择放弃产生干涉的操作,并行优化效率和效果并无明显的负面影响。最后,数值实验验证了本文算法的效率和有效性。     

非光滑多体系统动力学数值算法的研究进展

非光滑多体系统动力学数值计算方法是多体系统动力学研究的重要内容之一. 本文介绍了近年来含摩擦与碰撞的非光滑多体系统动力学数值算法方面的研究进展. 首先, 讨论了库仑摩擦模型和修正的库仑摩擦模型, 以及具有单边和双边约束的多体系统中法向约束力的特点. 其次, 回顾了基于连续模型和非连续模型的多体系统动力学方程的数值计算方法, 详细介绍了基于互补概念的非光滑多体系统动力学的事件驱动法和时间步进法, 分析比较了相关的数值算法. 最后, 指出了一些需要进一步研究的问题.     

关于弹体冲击和贯穿混凝土的三维数值模拟

利用FEM和SPH算法相结合给出弹体冲击和贯穿混凝土的三维数值模拟。将弹体划分为四面体有限元网格,混凝土划分为光滑粒子。为形成单元方便,将弹体划分成三个独立的模块并且这三个独立的模块具有拼凑功能。给出光滑粒子-有限元界面的滑移面算法。为了提高计算效率,在程序的前处理中预设界面的从属点和每个光滑粒子的关联点。计算结果与实验结果对比表明,FEM和SPH算法相结合及编制的程序能有效模拟弹体对混凝土的三维冲击和贯穿过程。同时给出在垂直冲击中二维计算与三维计算的差别。     

基于敏度分析的拉压不同模量桁架问题的数值分析

利用光滑函数技术,提出光滑化的拉压不同弹性模量问题的应力应变关系,与有限元方法相结合,建立了拉压不同模量一维连续体与桁架结构的数值求解模型,推导了敏度计算公式,采用Newton-Raphson算法进行求解.数值结果表明,本文算法具有较高的计算精度和收敛速度.     

极限分析的无搜索数学规划算法

本文研究理想刚塑性介质极限载荷因子的计算方法。根据极限分权理论的上限定理,建立了计算极限载荷因子的一般数学规划有限元格式。针对这种格式的特点,提出了一个求解极限载荷因子的无搜索迭代算法。这个算法中采用逐步识别刚性、塑性分区,不断修正目标函数的方案,克服了目标函数非光滑所导致的困难。本文提出的算法建立于位移模式有限元基础上,有较广的适用范围,且具有计算效率高,稳定性好,格式简单易于程序实现等优点。     

NON-INTERIOR SMOOTHING ALGORITHM FOR FRICTIONAL CONTACT PROBLEMS

A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.     

非光滑优化的双层规划模型及内点算法

对于包含接触约束的非光滑结构优化问题,其非光滑性体现在状态函数并不是处处可微的,针对含有应力约束及接触约束的非光滑结构优化问题,建立了一种双层规划模型,避免了求解时非光滑性所带来的问题,同时提出了一种迭代算法,用对偶内点二次规划进行分析,线性规划进行优化,算例表明这种方法十分有效。     

Model reference adaptive control of a nonsmooth dynamical system

In this paper a modified model reference adaptive control (MRAC) technique is presented which can be used to control systems with nonsmooth characteristics. Using unmodified MRAC on (noisy) nonsmooth systems leads to destabilization of the controller. A localized analysis is presented which shows that the mechanism behind this behavior is the presence of a time invariant zero eigenvalue in the system. The modified algorithm is designed to eliminate this zero eigenvalue, making all the system eigenvalues stable. Both the modified and unmodified strategies are applied to an experimental system with a nonsmooth deadzone characteristic. As expected the unmodified algorithm cannot control the system, whereas the modified algorithm gives stable robust control, which has significantly improved performance over linear fixed gain control.     

Nonlinear Krylov subspace methods for solving nonsmooth equations

IntroductionConsider the nonsmooth equationsF(y)=0,(1)whereF:D Rn→Rn.In1993,Qi and Sun[1]proposed the generalized Newton method forsolving Eq.(1)yk 1=yk-Vk-1F(yk),(2)whereVk∈F(yk)is the generalized Jacobi matrixofF[2],F(y)=Co{lyii→myyi∈DF F(yi)},andpr…     

Fixed-interval smoothing of an aeroelastic airfoil model with cubic or free-play nonlinearity in incompressible flow

Fixed-interval smoothing, as one of the most important types of state estimation, has been concerned in many practical problems especially in the analysis of flight test data. However, the existing sequential filters and smoothers usually cannot deal with nonlinear or high-dimensional systems well. A state-of-the-art technique is employed in this study to explore the fixed-interval smoothing problem of a conceptual two-dimensional airfoil model in incompressible flow from noisy measurement data. Therein, the governing equations of the airfoil model are assumed to be known or only partially known. A single objective optimization problem is constructed with the classical Runge–Kutta scheme, and then estimations of the system states, the measurement noise and even the unknown parameters are obtained simultaneously through minimizing the objective function. Effectiveness and feasibility of the method are examined under several simulated measurement data corrupted by different measurement noises. All the obtained results indicate that the introduced algorithm is applicable for the airfoil model with cubic or free-play structural nonlinearity and leads to accurate state and parameter estimations. Besides, it is highly robust to Gaussian white and even more complex heavy-tailed measurement noises. It should be emphasized that the employed algorithm is still effective to high-dimensional nonlinear aeroelastic systems.

     

FULLY SYMBOLIC GENERATION OF COMPLEX MULTIBODY MODELS*

Abstract

In this paper, a quasistatic finite element model of a spur gear pair is developed. A node-to-target contact formulation is given, where calculations of initial gaps are based upon the actual geometry of the gear flanks rather than upon a contact node and a facet or a line segment. By using a special contact search algorithm, profile modifications and mounting errors are easily incorporated in the analysis. The problem, which also includes friction, is solved by using a nonsmooth Newton method. The static transmission error can be calculated with accuracy with a relatively small number of nodes along the gear flanks. Several examples are given in order to demonstrate the model.     

舰船平台上一种改进的传递对准方案设计与仿真

为了提高舰船惯性导航系统在动基座下的传递对准的精度和快速性,针对舰船平台的应用特点,采用卡尔曼滤波器对主、子惯导的"速度加角速率"参数的误差量进行滤波估计并进行了算法设计。运用卡尔曼滤波器的平滑算法改善传递对准的精度。针对卡尔曼滤波器平滑算法会降低对准速度的缺点,在只损失一小部分精度的前提下,创新性的采用卡尔曼滤波器的降阶算法提高了对准速度。通过Matlab软件对卡尔曼滤波器算法、卡尔曼滤波器平滑算法和卡尔曼滤波器平滑加降阶算法的速度误差和姿态误差分别进行了仿真。仿真结果表明,"速度加角速率"匹配传递对准改进算法具有稳健的对准精度和快速性,有一定工程应用参考价值。     

Effect of regularized functions on the dynamic response of a clutch system using a high-order algorithm

The main objective of this work is to propose some regularization techniques for modeling contact actions in a clutch system and to solve the obtained nonlinear dynamic problem by a high-order algorithm. This device is modeled by a discrete mechanical system with eleven degrees of freedom. In several works, the discontinuous models of the contact actions are replaced by the smoothed functions using the hyperbolic tangent. We propose, in this work, to replace the discontinuous model by a regularized model with new continuous functions that permit us to search the solution under Taylor series expansion. This regularized model approaches better the discontinuous model than the model based on the smoothing functions, especially in the vicinity of the zone of singularities. To solve the equations of motion of discrete mechanical systems, we propose to use a high-order algorithm combining a time discretization, a change of variable based on the previous time, a homotopy transformation and Taylor series expansion in the continuation process. The results obtained by this modeling are compared with those computed by the Newton–Raphson algorithm.     

任意平面区域三角形网格的全自动生成算法

本文基于波前法提出了一种对任意平面区域生成三角形网格自动生成算法。算法具有区域适应性强,边界网格质量高,自动化程度高的优点。算法还包括了网格的拓扑优化,光滑及加密处理。此外,初边值条件的自动给定大大减少了数值计算中数据输入和避免了边界搜索计算。大量算例显示了算法的可靠性和适用性。