结构动力分析自适应有限元方法综述

结构动力分析自适应有限元方法主要研究有限元动力分析的误差估计理论,建立适用于复杂结构动力分析的有限元网格自适应过程．介绍了结构动力问题自适应有限元方法的重要发展,包括固有振动和动响应分析的误差估计及相应的自适应策略;且简要介绍了几种现有的网格生成技术及其特点．最后指出这种方法存在的问题和今后的研究方向．     

改进的Z~2应力恢复过程与h型自适应有限元分析

建议了一种较为精确的边界应力求解方法，并用于改进Ｚｉｅｎｋｉｅｗｉｃｚ－Ｚｈｕ（Ｚ２）应力恢复过程。改进过程增加的计算量不大，但可有效地改善后验误差估计精度。ｈ型自适应有限元分析结果表明，改进过程更有利于最优网格寻求工作     

数值流形单元法数学网格自适应

基于数值流形方法和有限覆盖技术,将有限元法的后验误差估计理论及h型网格自适应技术推广应用到数值流形单元法中,提出了数值流形单元法的后验误差估计方法和数学网格自适应技术,并编制了相应的程序。数值算例表明,经过网格自适应,可以在粗糙的初始网格基础上得到质量比较理想的网格,计算结果可达到用户要求的精度。     

自适应有限元方法及其工程应用

自适应有限元方法是一种能通过自适应分析自动调整算法以改进求解过程的数值方法．它以常规有限元法为基础，以误差估计和自适应网格改进技术为核心，是一种效率高、可靠性高的计算方法．文中简要介绍并综述了自适应有限元方法的重要发展及应用情况．并对其发展前景作了概要的预测     

有限元分析中的最优离散化在弹性接触问题中的应用

本文提供了一种可作为弹性接触问题有限元分析后处理过程的误差估计方法.这种方法是应用应力平滑过程,通过能量模的形式而建立的.在这种误差估计方法的基础上,实现了有限元网格的自适应局部加密.数值分析实例表明,借助于这种最优离散化过程,可使计算误差平均分配于各个单元,并使总体计算误差降低.     

多尺度材料模拟的自适应有限元方法研究

研究了材料模拟中一类新型耦合多尺度的自适应有限元方法. 采用 微观分子动力学耦合宏观有限元的桥尺度方法来模拟材料破坏的前期行为，其中宏观有限元 计算推广到了一般非结构三角形网格. 材料破坏形成后，停止微观尺度的计算，它的进一步 发展和演化通过一个宏观模型来描述，采用自适应有限元方法来求解这一宏观模型. 其中， 后验误差估计的基础是变分多尺度理论，即自适应网格加密是基于粗尺度上残差分布和细尺 度上单元Green's函数. 计算中采用了破坏准则来模拟材料的断裂. 数值实验表明了 方法的有效性.     

改进的Z^2应力恢复过程与h型自适应有限元分析

建议了一种较为精确的边界应力求解方法，并用于改进Ｚｉｅｎｋｉｅｗｉｃｚ－Ｚｈｕ（Ｚ＾２）应力恢复过程。改进过程增加的计算量不大，但可有效地改善后验误估计精度。ｈ型自适应有限元分析结果表明，改进过程更有利于最优网格寻求工作。     

基于蒙特卡罗法的弹道导弹落点密集度验前估计

为获得弹道导弹落点密集度的验前估计,应用蒙特卡罗法设计了一种基于制导工具误差的模拟打靶试验统计方法。建立了由制导工具误差到导弹飞行主动段终点偏差的误差传递方程,推导出18项参数的环境函数矩阵,然后利用椭圆弹道理论将主动段终点偏差折算落点偏差,完成了由靶场验前测试数据到落点密集度的统计试验估计模型。实现了伪随机数的产生和抽样,并对其进行了参数检验、均匀性检验和随机性检验。利用某型弹道导弹靶场单元测试数据进行模拟打靶试验,统计试验结果得到落点CEP和密集度的估计值和置信区间。飞行试验结果证实了该方法的可行性。     

基于结构动力学的框架结构固有频率估算方法

对框架结构的一阶固有频率与单门框的一阶固有频率的关系进行了推导,找出一种通过部件模态参数估算整体系统的模态参数的方法．通过ANSYS有限元分析对该估算方法进行了验证,并在石油钻机井架底座的有限元模态分析中应用该方法对系统固有频率进行了估计,误差均不超过1％．结论表明,该方法对于框架串联结构的固有频率估算是方便且可行的．     

模态参数不确定性分析的贝叶斯方法研究

在结构损伤诊断和参数识别中,实测结构模态参数不可避免地存在误差。本文将模态参数视为随机变量,采用贝叶斯方法对模态参数的不确定性进行分析。分析中选用高斯联合概率密度函数作为先验密度函数,通过多次独立的模态参数测试,得到传递函数的条件概率密度函数和模态参数的后验估计表达式,再利用拉普拉斯渐近方法求解边缘概率密度函数,得到模态参数的最大后验估计。在钢筋混凝土框架结构的模态试验中,利用本文方法给出了结构模态参数的估计值,结果表明,本文方法具有良好的收敛性。     

具有外观测误差的INS传递对准的性能分析

对于给定的传递对准的误差模型，针对常值外观测速度、位置误差和随机外观测速、位置度误差两种情况，分别对惯导系统的传递对准误差模型的解算偏差和Kalman滤波器的估计偏差进行了仿真分析。结果表明，外观测误差引起的INS传递对准的估计偏差不能忽视，为采用更优的估计方法提供了依据。     

ENRICHED GOAL-ORIENTED ERROR ESTIMATION APPLIED TO FRACTURE MECHANICS PROBLEMS SOLVED BY XFEM

Based on the concept of constitutive relation error along with the residual of both origin and dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed in this paper. It leads to high quality local error bounds in the problem of fracture mechanics simulation with extended finite element method (XFEM), which involves enrichment to solve a stress singularity in the crack. Since goal-oriented error estimation with enriched degrees of freedom gives us a chance to evaluate the XFEM simulation, the stress intensity factor calculated by two kinds of XFEM programs developed by ourselves and by commercial code ABAQUS are compared in this work. By comparing the reliability of the stress intensity factor calculation, the accuracy of two programs in different cases is evaluated and the source of error is discussed. A 2-dimensional XFEM example is given to illustrate the computational procedure.     

Almost sure state estimation for nonlinear stochastic systems with Markovian switching

In this paper, the almost sure asymptotic stability is investigated for the state estimation problem of a general class of nonlinear stochastic systems with Markovian switching. A nonlinear state estimator with Markovian switching is first proposed, and then, a sufficient condition is given, which guarantees the almost sure asymptotic stability of the dynamics of the estimation error. Based on this condition, some simplified criteria are deduced by taking special forms of Lyapunov functions. Subsequently, an easy-to-verify procedure is put forward for the state estimation problem of the linear stochastic system with Markovian switching. Finally, two numerical examples are used to illustrate the effectiveness of the main results.     

Synchronization error bound of chaotic delayed neural networks

Synchronization of master–slave chaotic neural networks are well studied through asymptotic and exponential stability of error dynamics. Besides qualitative properties of error dynamics, there is a need to quantify the error in real-time experiments especially in secure communication system. In this article, we focused on quantitative analysis of error dynamics by finding the exact analytical error bound for the synchronization of delayed neural networks. Using the Halanay inequality, the error bound is going to be obtained in terms of exponential of given system parameters and delay. The time-varying coupling delay has been considered in the neural networks which does not require any restrictive condition on the derivative of the delay. The proposed method can also be applied to find error bound for state estimation problem. The analytical synchronization bound has been corroborated by two examples.     

不完全测量系统鲁棒SGQKF的传递对准滤波器设计和稳定性分析

针对复杂环境下运载体观测信息不完全测量并且存在随机干扰不确定的传递对准问题,研究了不完全测量随机不确定系统的鲁棒稀疏网格求积分(H_∞-SGQKF)的高斯逼近滤波算法。基于非线性离散系统的最优贝叶斯滤波框架和间断观测滤波算法以及不确定性扰动噪声下的H_∞范数的鲁棒SGQKF算法,给出了不完全测量的稀疏网格求积分的高斯逼近滤波算法;通过非线性系统随机稳定性理论,分析并给出了系统估计误差和估计误差方差有界的充分条件,同时给出了系统稳定的不完全测量时的丢包率临界值,证明间断观测条件下的不完全测量H_∞-SGQKF算法是稳定的。通过传递对准仿真试验和某型激光捷联式惯性导航系统的跑车试验对该算法进行了验证。结果表明,该方法比未采用鲁棒的不完全测量的稀疏网格求积分滤波的传递对准精度有所提高,说明不完全测量的鲁棒稀疏网格求积分滤波算法是正确的、稳定的,并且具有鲁棒性能。     

Determination of the size of the representative volume element for random composites: statistical and numerical approach

The representative volume element (RVE) plays a central role in the mechanics and physics of random heterogeneous materials with a view to predicting their effective properties. A quantitative definition of its size is proposed in this work. A RVE size can be associated with a given precision of the estimation of the wanted overall property and the number of realizations of a given volume V of microstructure that one is able to consider. It is shown to depend on the investigated morphological or physical property, the contrast in the properties of the constituents, and their volume fractions. The methodology is applied to a specific random microstructure, namely a two-phase three-dimensional Voronoı̈ mosaic. Finite element simulations of volumes of different sizes are performed in the case of linear elasticity and thermal conductivity. The volumes are subjected to homogeneous strain, stress or periodic boundary conditions. The effective properties can be determined for large volumes and a small number of realizations. Conversely, smaller volumes can be used providing that a sufficient number of realizations are considered. A bias in the estimation of the effective properties is observed for too small volumes for all types of boundary conditions. The variance of computed apparent properties for each volume size is used to define the precision of the estimation. The key-notion of integral range is introduced to relate this error estimation and the definition of the RVE size. For given wanted precision and number of realizations, one is able to provide a minimal volume size for the computation of effective properties. The results can also be used to predict the minimal number of realizations that must be considered for a given volume size in order to estimate the effective property for a given precision. The RVE sizes found for elastic and thermal properties, but also for a geometrical property like volume fraction, are compared.     

自然单元法的自适应研究

自然单元法(NEM)是一种新兴的无网格数值计算方法,具有前处理简单和易于准确施加本质边界条件等优点.本文基于Z-Z后验误差估计方法,给出了一种自然单元法的误差估计因子和自适应分析细化方案.采用结点处的光滑应变计算相应的恢复应力,并用于构造全域上的恢复应力场.通过结点Voronoi单胞内的能量范数相对误差指示需要进行结点...     

BOUNDARY ELEMENT METHOD FOR BUCKLING EIGENVALUE PROBLEM AND ITS CONVERGENCE ANALYSIS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｂｕｃｋｌｉｎｇｅｉｇｅｎｖａｌｕｅｐｒｏｂｌｅｍｈａｓｉｍｐｏｒｔａｎｔｓｉｇｎｉｆｉｃａｎｃｅｉｎｔｈｅｓｔａｂｉｌｉｔｙａｎａｌｙｓｉｓｏｆｅｎｇｉｎｅｅｒｉｎｇｓｔｒｕｃｔｕｒｅ.Ｈｅｎｃｅｔｈｅｎｕｍｅｒｉｃａｌｃａｌｃｕｌａｔｉｏｎｆｏｒｔｈｅｓｅｐｒｏｂｌｅｍｓｉｓｅｘｔｒｅｍｅｌｙｍｅａｎｉｎｇｆｕｌｉｎｃｏｍｐｕｔａｔｉｏｎａｌｍｅｃｈａｎｉｃｓ.ＴｈｅｐｒｅｓｅｎｔｃｏｍｐｕｔａｔｉｏｎａｌｍｅｔｈｏｄｓｆｏｃｕｓｏｎＦＥＭ ,ｄｉｆｆｅｒｅｎｃｅｍ…     

Efficient reconstruction of local heat fluxes in pool boiling experiments by goal-oriented adaptive mesh refinement

In this paper, we consider the efficient estimation of local boiling heat fluxes from transient temperature measurements in the heater close to the heater surface. For accurate prediction, heat flux estimation is formulated as a transient three-dimensional (3D) inverse heat conduction problem (IHCP). This inverse problem is ill-posed and cannot be treated straightforwardly by established numerical methods. In order to obtain a regularized stable solution, a large-scale time-dependent PDE-constrained optimization problem has to be solved and an appropriate stopping criterion for the termination of the iterative solution process has to be chosen. Since the boiling heat flux is non-uniformly distributed on the heater surface due to the strong local activity of the boiling process, the use of a fixed uniform spatial discretization is not efficient. Instead, an adaptive mesh refinement strategy can be used to obtain an appropriate discretization which significantly reduces the total computational effort. In this work, we present an automatic algorithm incorporating an adaptive mesh refinement via a heat flux-based a-posteriori error estimation technique. The suggested algorithm can cope with both spatially point-wise or highly resolved temperature observations efficiently. It is applied to real measurement data obtained from two different types of pool boiling experiments. The numerical results show that the computational effort can be reduced significantly for given estimation quality. This adaptive IHCP solution technique can be also viewed as an efficient soft sensor to deduce unmeasurable local boiling heat fluxes.     

A deterministic vortex method for solving the Navier-Stokes equations

In this paper, a new 2-D vortex method is developed, which treats the vorticity diffusion in a deterministical way. The Laplacian operator, which describes vorticity diffusion, is approximated by a contour integral. The numerical results of two model problems show that this method has a good accuracy. A primary error estimation is given, and the self-adaptive vortex blob and the boundary conditions are discussed. The project supported by the National Natural Science Foundation of China