子结构灵敏度综合在结构动力重分析中的应用

提出了一种利用子结构灵敏度综合进行基于灵敏度分析的结构动力重分析的新方法.通过固定界面子结构模态综合技术,有效减少了自由度数目,达到了减少计算量的目的.同时,还给出了利用子结构灵敏度综合求解结构n阶特征灵敏度的一般表达式.所提出的结构动力重分析方法操作简单,易于实现,适用于大型复杂结构的结构动力重分析.     

|x|在加密Newman结点的有理插值

有理逼近是逼近论中重要的和具有很强生命力的课题.本文研究Newman型有理算子逼近非光滑函数|x|,在Newman构造结点组的零点附近[0,e~(-n~(1/2))]增加n个结点.首先,简单介绍|x|的有理插值的一些主要成果.然后,对Newman不等式进行改善,由原来的e~(-n~(1/2))提高到8e~(-2n~(1/2)).由此得到Newman型有理算子逼近|x|的逼近阶为O(e~(-2n~(1/2))),这个结果优于Newman的经典结果.     

分数阶导数系统非平稳随机振动灵敏度分析的时域显式方法EI北大核心CSCD

分数阶导数模型是描述黏弹性材料本构关系的理想模型。进行了分数阶导数线性系统非平稳随机振动的灵敏度分析。建立分数阶导数系统动力响应的时域显式表达式;采用灵敏度分析的直接求导法或伴随变量法,推导系统动力响应灵敏度的时域显式表达式;提出分数阶导数系统响应统计矩灵敏度高效计算的时域显式方法。所提出的基于直接求导法和伴随变量法的时域显式方法,分别适用于少设计变量和多设计变量两种情况下的响应统计矩灵敏度分析。以非平稳地震激励下设置分数阶导数黏弹性阻尼器的层剪切结构为数值算例,验证了所提方法的计算精度和计算效率。     

有理插值算子对连续函数的逼近

本文给出了有理插值算子当1＜S＜Z及S＞2时的Timan型逼近阶，从而推广了已有的S＞3的结果．     

向量值函数的最佳Lp逼近

本文主要讨论向量值函数空间L,(μ,x)内的元素用凸子集逼近时最佳逼近的特征。并指出它在联合最佳逼近上应用。     

基于单位分解法的实体壳广义单元模型

基于单位分解的广义有限元法的逼近空间由单位分解函数和局部覆盖函数构成,采用传统有限元形函数作为单位分解函数,其局部覆盖函数的定义不依赖于有限元网格.以十六结点六面体等参单元形函数作为单位分解函数,采用一阶多项式局部覆盖函数建立了十六结点六面体广义单元.在此基础上利用广义有限元法可以灵活构造各向异性逼近空间的特点,根据薄壳的变形特性,对壳体法向挠度和切向位移分别采用一阶和零阶多项式局部覆盖函数,构造了实体薄壳广义单元.计算结果表明:十六结点六面体广义单元和实体薄壳广义单元用于板壳结构分析时具有比相应的常规实体单元更高的收敛性和求解效率,且实体薄壳广义单元比十六结点六面体广义单元具有更高的求解效率.     

应用动力单元法进行空间索网结构自由振动分析

索网结构具有成型跨度大而结构重量轻的优点,因此在空间航天领域得到了广泛应用。目前对索网结构的动力学分析主要是采用集中质量法或有限单元法进行低阶模态的分析,这些方法得到的较高阶频率和模态,其精度和实用性都不理想。动力单元法采用含有固有频率的动态形函数作为动力学分析离散单元中的插值函数,该形函数由单元动力学控制微分方程导出,因此能给出比有限元法更高的求解精度。在总结研究动力单元法理论的基础上,推导了张紧索单元的动力单元矩阵。采用动力单元法对几个典型的空间张紧索网结构进行动力学特性的分析,并将分析结果与传统有限元分析结果进行比较。     

基于一元对称幂基的等距曲面有理逼近算法

给出了基于一元对称幂基的等距曲面蒙面逼近新算法。利用一元对称幂基逼近张量积Bézier曲面u向曲线的等距曲线,得到一组等距逼近曲线,取固定的v值,得到一组数据点,用反算控制顶点的方法得到过这组数据点的v向曲线。对这两组曲线用蒙面算法得到逼近的有理等距曲面。该算法计算简单,将二元等距曲面有理逼近转化为一元曲线有理逼近,同时方便地解决了整体误差问题,随着对称幂基阶数的升高,可以得到较理想的逼近效果。     

一类基于有理混合函数的插值曲面

从多项式混型合函数出必，通过数学变换，构造了一类混合函数－混合函数类，进一步研究了[n/n]型有理混合函数，在此基础上讨论了多种插值条件下曲面的生成方法，并且给出了可视化结果。     

Sobol''''法在非线性隔振系统灵敏度分析中的应用研究

将基于方差的全局灵敏度分析方法——Sobol’法引用到结构动力分析中。Sobol’方法利用积分将函数f(x)分解成递增项之和，通过采样计算f(x)总方差及各项偏方差，从而求得灵敏度。与目前结构动力学广泛应用的局部灵敏度分析方法相比，该方法具有能考虑参数的随机分布、适用于参数不同的变化范围及参数同时变化情况等特点。以线性阻尼、立方刚度的非线性被动隔振体为对象，用Sobol’法计算了传递率对结构参数的一阶及总灵敏度，得出了软、硬弹簧和线性阻尼对传递率的影响规律．其结果为系统的优化设计提供了依据。     

Least squares stochastic Boundary Element Method

The main issue in this paper is mathematical formulation and computational implementation of the stochastic Boundary Element Method based on the generalized stochastic perturbation technique. The key feature is a replacement of the given order polynomial response function with the least squares method leading to a numerical determination of this response function. This new approach minimizes the approximation error during the recovery of the structural response indexed with the random input parameter, which is a decisive factor for the entire stochastic method accuracy; contrary to some lower order techniques, numerical implementation of up to the fourth order probabilistic moments is displayed. Computational experiments obey both analyses for the homogeneous and heterogeneous structures with Gaussian random material parameters and also some comparison against the Monte-Carlo simulation and analytical results.     

模糊结构有限元分析的一种新方法

本文利用信息熵的概念,将模糊变量转变为随机变量,将模糊结构视为随机结构进行处理,从而提出了模糊结构有限元分析的一种新方法。当模糊结构转换的随机变量处于小扰动情况下,利用摄动法得到有限元递归方程组,解之可以得到响应量的均值和方差。     

Optimization of discrete event systems via simultaneous perturbation stochastic approximation

We investigate the use of simultaneous perturbation stochastic approximation for the optimization of discrete-event systems via simulation. Application of stochastic approximation to simulation optimization is basically a gradient-based method, so much recent research has focused on obtaining direct gradients. However, such procedures are still not as universally applicable as finite-difference methods. On the other hand, traditional finite-difference-based stochastic approximation schemes require a large number of simulation replications when the number of parameters of interest is large, whereas the simultaneous perturbation method is a finite-difference-like method that requires only two simulations per gradient estimate, regardless of the number of parameters of interest. This can result in substantial computational savings for large-dimensional systems. We report simulation experiments conducted on a variety of discrete-event systems: a single-server queue, a queueing network, and a bus transit network. For the single-server queue, we also compare our work with algorithms based on finite differences and perturbation analysis.     

Numerical stabilization of Biot's consolidation model by a perturbation on the flow equation

In this paper a stabilized finite element scheme for the poroelasticity equations is proposed. This method, based on the perturbation of the flow equation, allows us to use continuous piecewise linear approximation spaces for both displacements and pressure, obtaining solutions without oscillations independently of the chosen discretization parameters. The perturbation term depends on a parameter which is established in terms of the mesh size and the properties of the material. In the one‐dimensional case, this parameter is shown to be optimal. Some numerical experiments are presented indicating the efficiency of the proposed stabilization technique. Copyright © 2008 John Wiley & Sons, Ltd.     

一类弱非线性振动方程的变分迭代算法

本文提出了一种求解非线性方程的迭代算法,这种方法是先给方程一个带待定函数的试函数作为初始近似解,然后用拉氏乘子法构造一个迭代公式,而拉氏乘子可用变分的概念最佳确定。应用这种方法不会出现长期项,其结果比传统的摄动方法要好得多。     

Random matrix eigenvalue problems in structural dynamics

Natural frequencies and mode shapes play a fundamental role in the dynamic characteristics of linear structural systems. Considering that the system parameters are known only probabilistically, we obtain the moments and the probability density functions of the eigenvalues of discrete linear stochastic dynamic systems. Current methods to deal with such problems are dominated by mean‐centred perturbation‐based methods. Here two new approaches are proposed. The first approach is based on a perturbation expansion of the eigenvalues about an optimal point which is ‘best’ in some sense. The second approach is based on an asymptotic approximation of multidimensional integrals. A closed‐form expression is derived for a general rth‐order moment of the eigenvalues. Two approaches are presented to obtain the probability density functions of the eigenvalues. The first is based on the maximum entropy method and the second is based on a chi‐square distribution. Both approaches result in simple closed‐form expressions which can be easily calculated. The proposed methods are applied to two problems and the analytical results are compared with Monte Carlo simulations. It is expected that the ‘small randomness’ assumption usually employed in mean‐centred‐perturbation‐based methods can be relaxed considerably using these methods. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust design of tuned mass dampers installed on multi-degree-of-freedom structures subjected to seismic action

This study deals with robust optimum design of tuned mass dampers installed on multi-degree-of-freedom systems subjected to stochastic seismic actions, assuming the structural and seismic model parameters to be uncertain. A new global performance index for evaluating the efficiency of protection systems is proposed, as an alternative to commonly used local performance indices such as the maximum interstorey drift. The latter can be considered a good estimator of seismic damage, but it does not measure the whole structural integrity. The direct perturbation method based on first order approximation is adopted to evaluate the effects of uncertainties on the response. The robust design is formulated as a multi-objective optimization problem, in which both the mean and the standard deviation of the performance index are simultaneously minimized. A comparison of the effectiveness and robustness of tuned mass dampers designed using local or global performance indices is carried out, considering different levels of uncertainty.     

An alternative approach to shape design sensitivity analysis

A novel method is presented in this paper for calculating shape design sensitivity, which is based on the finite difference method (FDM). By analysing the numerical procedure of the FDM, the perturbation of the geometry is replaced by a perturbation load which can be calculated once the stress field of the initial problem and the design boundary perturbation are known. The final shape design sensitivity is obtained by solving the perturbation problem which has the same geometry and the kinematical boundary condition as the initial problem, but under the perturbation loads. Therefore the new method does not require the calculation of the matrices of the perturbed structure, and is independent of the perturbation step. A numerical implementation of the finite difference load method (FDLM) is described in which the boundary element method is used to evaluate the structural response. The numerical examples demonstrate that this new method for shape design sensitivity analysis is very accurate.