A NEW METHOD FOR THE UNCERTAIN RESPONSE ANALYSIS OF STRUCTURES WITH UNCERTAIN PARAMETERS

A computing method for estimating the upper and lower bounds of the response ofstructures with uncertainties is presented.The uncertain parameters are described by the convexmodel.A numerical example of the frame structure is given to illustrate the effectiveness of thismethod.     

区间参数结构的动力响应优化

讨论区间参数结构的动态响应问题的区间优化方法．利用摄动理论和函数区间扩张,将区间优化问题转化为近似的确定性优化问题．由于区间设汁变量的中值和不确定性半径均可取作优化参数,昕以可得到比确定性优化更多的优化信息．将该方法应j用于桁架结构,算例表明该方法是有效的．     

DYNAMIC OPTIMIZATION FOR UNCERTAIN STRUCTURES USING INTERVAL METHOD

An interval optimization method for the dynamic response of structures with interval parameters is presented. The matrices of structures with interval parameters are given. Combining the interval extension with the perturbation, the method for interval dynamic response analysis is derived. The interval optimization problem is transformed into a corresponding deterministic one. Because the mean values and the uncertainties of the interval parameters can be elected design variables, more information of the optimization results can be obtained by the present method than that obtained by the deterministic one. The present method is implemented for a truss structure. The numerical results show that the method is effective.     

不确定参数闭环控制系统特征值的区间分析

运用区间理论,讨论了区间参数的结构振动控制问题,给出了求解闭环系统区间特征值的一种方法．基于区间参数导出了区间刚度矩阵和质量矩阵,然后利用矩阵摄动理论和区间扩张理论,推导了复区间特征值上下界估计的算法．这些结果是从二阶系统的左右特征向量出发得到的．将该文方法应用到悬臂梁的控制问题,数值结果表明它是有效的．     

具有随机参数的含裂纹板弯曲应力强度因子的统计分析

本文首次应用随机有限元法研究了具有随机参数的含裂纹板裂纹尖端弯曲应力强度因子的统计性质。文中首先给出了杂交模式的裂纹尖端奇异单元的刚度矩阵,然后基于随机场的局部平均理论和一阶泰勒展开得到了应力强度因子均值和方差的计算公式。作为数例,详细讨论了杨氏模量、泊松比及板厚度的不确定性对应力强度因子的影响。     

一种基于证据理论的结构可靠性分析方法

提出了一种基于证据理论的结构可靠性高效求解方法. 通过构造优化问题求解极限状态方程的非概率可靠性指标及设计验算点, 并构造一辅助区域. 通过辅助区域显著减少需要进行极值分析的焦元个数, 并基于区间分析方法减少焦元上极限状态方程的计算次数, 从而有效降低计算成本. 数值算例及工程应用验证了该方法的有效性.     

基于区间的不确定多目标优化方法研究

基于非线性区间优化,提出了一种不确定多目标优化方法.基于区间序关系和区间可能度,把不确定多目标的目标函数和约束转化为确定性的目标函数和确定性的约束.对于复杂的工程优化问题,为了提高效率,采用拉丁方试验设计方法,构建响应面近似模型,并基于近似模型进行不确定多目标优化,从而形成了非线性区间优化方法与近似模型相结合的高效不确定多目标优化方法.数值算例表明了该方法的有效性和工程实用性.     

具有随机参数的含裂纹板弯曲应力强度因子的统计分析

本文首次应用随机有限元法研究了具有随机参数的含裂纹板裂纹尖端弯曲应力强度因子的统计性质。文中首先给出了杂交模式的裂纹尖端奇异单元的刚度矩阵,然后基于随机场的局部平均理论和一阶泰勒展开得到了应力强度因子均值和方差的计算公式。作为数例,详细讨论了杨氏模量、泊松比及板厚度的不确定性对应力强度因子的影响。     

随机过程激励下随机结构系统可靠度分析的一种方法

提出了随机过程荷载激励下，具有随机参数的结构系统可靠度分析的一种方法，该方法基于首次超越破坏机制，分析随机过程荷载激励下，结构参数（随机变量）取某一确定向量时的条件失效概率，采用Ｍｏｎｔｅ Ｃａｒｌｏ技术模拟结构参数的随机性，由条件失效概率给出随机结构的无条件失效概率，最后对中方法和程序作了检验，并进行了实际计算。     

不确定初始几何缺陷壳的动态屈曲分析

研究了动载作用下含有不确定初始几何缺陷壳的动态屈曲问题.给出了不确定初始几何缺陷在椭球描述和区间描述下,壳的动态响应和安全因子的界限估计.从数学证明和数值算例两方面,讨论了基于不确定性初始几何缺陷两种描述的凸模型方法和区间分析方法所得壳动态响应及安全因子的界限的关系,为判断壳的动态屈曲失效提供了依据.     

基于Taylor展式的不确定结构复特征值问题两种非概率方法比较研究

代替传统的处理不确定问题的概率统计方法,将利用区问数学和凸模型理论研究具有有界不确定参数的非比例阻尼结构复特征值所在区域问题．区间数学将有界不确定结构参数用超长方体即区问向量进行定量化,而凸模型理论则用椭球对有界不确定参数进行定量化．在不用知道不确定变量的概率统计特性的条件下,区间分析方法和凸模型理论都可以确定出有界不确定结构参数的非比例阻尼结构复特征值所在区域．通过数学证明和数值算例来说明,在凸模型理论中的椭球在由区间分析中的超长方体—区间向量来确定的条件下,由区间数学所确定出不确定结构复特征值实部和虚部的宽度要比凸模型所确定出的范围的宽度要小,而这正是工程技术人员所要求的结果。     

论不确定性结构力学的发展

结构力学是直接为工程结构设计服务的,而工程设计中包含大量不确定性因素和信息,包括随机性、模糊性和未确知性信息.由于引用统计数学方法处理随机性问题,在结构力学中产生了可靠性理论和随机振动理论.随着模糊性和未确知性问题的提出和研究,近年来在结构力学中又逐渐形成了一些新的分支,包括结构的不确定性优化设计,广义(模糊随机)可靠性理论,模糊随机振动理论和模糊地震工程学等.本文简要地介绍这四个新的分支的发展情况,主要介绍作者及其学生们的工作,并着重介绍基本概念.      

论不确定性结构力学的发展

结构力学是直接为工程结构设计服务的,而工程设计中包含大量不确定性因素和信息,包括随机性、模糊性和未确知性信息．由于引用统计数学方法处理随机性问题,在结构力学中产生了可靠性理论和随机振动理论．随着模糊性和未确知性问题的提出和研究,近年来在结构力学中又逐渐形成了一些新的分支,包括结构的不确定性优化设计,广义(模糊随机)可靠性理论,模糊随机振动理论和模糊地震工程学等．本文简要地介绍这四个新的分支的发展情况,主要介绍作者及其学生们的工作,并着重介绍基本概念．     

不确定性振动凸集理论的研究

评述了振动凸集理论的研究概况,就研究范畴、常用的概念、现有的方法和应用领域及进展情况作一全貌的介绍      

根部柔性梁的不确定性建模与确认

首先导出了包含根部挠性参数的悬臂梁动力学方程近似解,将平动和转动柔性参数作为不确定性源,根据若干预紧力矩下的模态实验结果完成了柔性参数识别,并假定其服从正态随机分布,识别了均值与标准差,进而通过回归分析建立了不确定参数随预紧力矩变化的数学模型.最后通过新的模态实验结果对所建模型进行了确认,通过确认结果,明确了该模型的使用范围.     

STUDYING THE FOCAL VALUE OF ORDINARY DIFFERENTIAL EQUATIONS BY NORMAL FORM THEORY

ＳＴＵＤＹＩＮＧＴＨＥＦＯＣＡＬＶＡＬＵＥＯＦＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＢＹＮＯＲＭＡＬＦＯＲＭＴＨＥＯＲＹＺｈａｎｇＱｉｃｈａｎｇ（张琪昌）（ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙ．Ｔｉａｎｊｉｎ３０００７２．Ｐ．Ｒ．Ｃ...     

A new approach to perturbation analysis of vibration modes with close frequencies

This paper presents a new method for perturbation analysis of vibration modes with close frequencies. The main idea of this method is to transform the perturbation analysis problem of vibration modes with close frequencies into a perturbation problem associated with repeated frequencies. A numerical example is given to demonstrate the good agreement of eigensolutions obtained by this method with the exact solutions.This project is supported by National Natural Science Foundation of China     

The numerical solution of the acoustic wave scattering from penetrable obstacles by a least-squares method

This paper documents a numerical method for a two dimensional time-harmonic wave scattering problem by penetrable obstacles. The Fourier–Bessel function combining a multipole expansion is used to give an approximation of the scattering field. This method is based on the least-squares technique. Especially, we find a simple function to control the errors, and then give the theoretical results of the presented method. The continuity across the element boundaries is enforced by minimizing a simple quadratic functional. This method does not need to truncate the domain and could obtain high accuracy by increasing the number of basis functions with even coarse mesh. At last, we give some examples to illustrate the effectiveness of the approach including the solution domain being multiple or even multi-connected.     

Application of Kalman Filter Finite Element Method and AIC

This paper presents a numerical simulation for application of the Kalman filter finite element method. The Kalman filter is employed frequently for the solution of time series analysis including observation and system noises. Applying the Kalman filter to the finite element method, the present method is capable of the estimation in time and space directions. In this method, the matrix generated by the finite element method is applied to the state transition matrix. Using the Kalman filter finite element method, the characteristics of both the Kalman filter and the finite element method can be strengthened. In this paper, the state transition matrix is based on the shallow water equations which are approximated by the finite element method. This method can estimate the tidal current not only in time but also in space directions.     

A numerical method for determining the shear stress of magnetorheological fluids using the parallel-plate measuring system

This work proposes a new numerical method for determining the shear stress, which does not need any preassumption about the exact behavior of the fluid to achieve absolute data using a parallel-plate measuring system. The ability for representing different behaviors along the entire shear-rate range makes this method particularly interesting for the study of magnetorheological (MR) fluids. In this work, the conversion factors used by the rheometer for concentric-cylinder, cone-plate, and parallel-plate measuring systems are first analyzed. This analysis shows that the software used by the rheometer is not appropriate for the quantitative characterization of non-Newtonian fluids using the parallel-plate measuring system. Therefore, a new method for conversion of the parameters measured by the rheometer to the rheological parameters of the fluid is proposed; simultaneously, this new method is compared with other correction methods proposed in the literature: the Rabinowitsch-type method and the single-point method. Finally, the proposed method is applied for the quantitative characterization of an MR fluid.