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计变量的中值和不确定性半径均可取作优化参数,所以可得到比确定性优化更多的优化信息将该方法应用于桁架结构,算例表明该方法是有效的.     

含模糊参数的随机振动

本文在抗震结构模糊随机振动的研究基础上,进一步研究含模糊参数的随机振动分析方法,为了较好地描述具有模糊性的随机干扰,首先在Zadeh定义的模糊变量的基础上,定义了含模糊参数的随机变量和含模糊参数的随机过程,并讨论了它们的概率分布和数字特征;然后将模糊随机干扰模拟为含模糊参数的随机过程,提出了在这种模糊随机干扰下振动体系的模糊随机反应分析的基本方法和数值方法;最后对于抗震结构的模糊随机振动给出了具体的分析和算例     

不确定非线性结构动力响应的区间分析方法

研究多自由度非线性不确定参数系统的动力响应问题. 以区间数学为基础,将不确定性参数用区间进行定量化,借助一阶Taylor级数,给出了近似估计非线性振动系统动力响应范围的区间分析方法. 从数学证明和数值算例两方面,将其与概率摄动有限元法进行了比较,结果显示区间分析方法对不确定参数先验信息具有要求较少、精度较高的优点.     

考虑参数不确定性的非线性梁随机振动分析

非线性系统的随机振动分析一直是结构动力学领域中的难点,已有一些研究表明基于矩等效的线性化方法在功率谱预测上会得到不恰当的分析结果;另一方面,由于不确定性在实际工程中普遍存在,如果同时考虑非线性和不确定性,更是显著增加了问题难度。本文以具有非线性非理想边界梁为研究对象,基于梁模型的动力学微分方程推导了对应的广义频响函数,并应用Volterra级数理论建立了非线性系统随机振动的谱分析方法,最后,结合蒙特卡洛抽样方法计算了具有参数不确定性非线性梁响应功率谱的均值和方差,讨论了不确定性对结构随机振动响应统计特征的影响。     

基于单元的静力区间有限元法

在许多工程问题中 ,结构参数和荷载具有某种程度的误差或不确定性。若不将它们定量化或模型化加以考虑 ,就不能作出合理的分析和设计。考虑到有限元法在科学界和工程界的广泛应用 ,本文以连续梁结构为例 ,建立了基于单元的静力区间有限元法。为了说明本方法的有效性 ,本文给出了一个数值例子 ,并把所得结果与文献 [1 2 ]进行了比较。     

基于二阶摄动法求解区间参数结构动力响应

在处理区间参数结构动力响应问题时,现有的分析方法大多局限于一阶区间分析方法. 如果参数的不确定量稍大,采用一阶区间分析方法对结构动力响应范围进行估计可能会失效,所以需要考虑二阶区间分析方法.但是采用基于区间运算的二阶区间分析方法得到的结果将会对动力响应范围过分高估. 为了克服以上缺点,首先基于二阶摄动法得到结构动力响应广义函数. 然后通过求解此动力响应函数的最大和最小值,将结构动力响应区间的问题转化为序列低维箱型约束下的二次规划问题. 最后采用DC 算法(di erence of convex functionsalgorithm) 对这些箱型约束下的二次规划问题进行求解. 这样可以在不引入过多计算量的情况下,避免了对动力响应范围的过分估计. 通过数值算例,将该方法和其他区间分析方法进行比较,验证了该方法的有效性与精确性.     

结构的宽带随机振动

结构的宽带随机振动理论是随机振动理论中一个引起兴趣的领域.这种随机振动模态数量很大,从而呈现简单的渐近趋向.本文综述该领域的一些概念和方法.讨论的重点是,具有小阻尼的均匀对称结构,在孤立点上受平稳宽带随机力激励时,其均方响应空间分布的渐近型式.     

结构随机振动响应的工程简化分析

鉴于结构随机振动响应有限元分析的复杂性,本文提出了一种工程简化分析方法,以便于工程人员应用.它可以直接利用结构模型试验数据,从而保证分析结果具有足够的精度.     

考虑参数不确定性的复合层合扇形板随机振动特性分析

复合材料结构的随机振动分析一直是结构动力学领域十分关注的问题,但现有研究均是在确定性参数的基础上进行的,未考虑参数不确定性对结构随机振动特性的影响。本文以复合层合扇形板为研究对象,考虑材料参数的区间不确定性对结构随机振动特性的影响,基于改进Kriging模型建立复合层合扇形板随机振动特性的快速分析模型,并在此基础上研究了不同不确定性参数对复合层合扇形板横向随机振动特性的影响。同时,通过与Monte Carlo模拟仿真所得结果进行对比,证明了本文方法的有效性。数值分析结果表明,复合层合扇形板的随机振动特性对不同不确定性参数的敏感程度不同,可对复合层合扇形板的横向随机振动响应产生显著差异。研究结果可为工程实际中复合层合扇形板的不确定性随机振动响应的预测提供一定的参考依据。     

区间参数振动系统的动力优化

对具有区间参数的多自由度振动系统的不确定性优化问题,提出一种新的区间优化方法．利用泰勒展开和函数的区间扩张,将区间优化问题转化为近似的确定性优化问题．该方法应用于多自由度线性扭振系统,并把区间设计变量的中值和不确定性半径取作优化参数．算例表明该方法是有效的．     

具有随机参数的动力系统随机地震响应分析

本文同时考虑地震输入的随机性和结构动力本数的随机性，在随机振动分析中引入随机有限元法，以单自由反动力系统为例，分析了不同参数变异性对随机结构动力响应的影响。     

Stochastic finite element method based on local averages of random fields

The stochastic finite element method (SFEM) based on the local, averages of random fields, which was proposed in [5], is now generalized to analyze the structures with several correlated random parameters. The covariance matrix of the local averages of a random vector field is derived. The SFEM based on the local averages of random vector fields is formulated. The numerical examples show that the generalized SFEM preserves the advantages of the original one, i. e., rapid convergence, good accuracy and insensitivity to the correlation structures of random parameters.Project supported by National Natural Science Foundation of China.     

Interval finite element method and its application on anti-slide stability analysis

The problem of interval correlation results in interval extension is discussed by the relationship of interval-valued functions and real-valued functions. The methods of reducing interval extension are given. Based on the ideas of the paper, the formulas of sub-interval perturbed finite element method based on the elements are given. The sub-interval amount is discussed and the approximate computation formula is given. At the same time, the computational precision is discussed and some measures of improving computational efficiency are given. Finally, based on sub-interval perturbed finite element method and anti-slide stability analysis method, the formula for computing the bounds of stability factor is given. It provides a basis for estimating and evaluating reasonably anti-slide stability of structures.     

Stochastic finite element analysis of local average random fields

This paper discussed the concepts underlying a new approach to representation and analysis of homogeneous random Fields. An orthogonalized isoparametric local average model of random fields is proposed, and the optimum selection of random variables is determined based on the theory of nonlinear programming. The finite element method is used to develop a methodology for random field analysis. Numerical examples showing the accuracy and efficiency of the method are studied.     

幂律全塑性罚函数随机有限元

用罚函数有限元方法解决平面应变下的体积不可压缩问题,应用摄动有限元理论发展幂律全塑性随机有限元.并以弹性模量E、泊松比μ和节点坐标等为基本随机变量,推导有限元列式,给出单板受拉、梁受弯的算例.     

Nonlinear Vibration of Plane Structures by Finite Element and Incremental Harmonic Balance Method

A nonlinear steady state vibration analysis of a wide class of planestructures is analyzed. Both the finite element method and incrementalharmonic balance method are used. The usual beam element is adopted inwhich the nonlinear effect arising from longitudinal stretching has beentaken into account. Based on the geometric nonlinear finite elementanalysis, the nonlinear dynamic equations including quadratic and cubicnonlinearities are derived. These equations are solved by theincremental harmonic balance (IHB) method. To show the effectiveness andversatility of this method, some typical examples for a wide variety ofvibration problems including fundamental resonance, super- andsub-harmonic resonance, and combination resonance of plane structuressuch as beams, shallow arches and frames are computed. Most of theseexamples have not been studied by other researchers before. Comparisonwith previous results are also made.     

A Hierarchical Finite Element for Geometrically Non-linear Vibration of Thick Plates

A p-version, hierarchical finite element for moderately thick isotropic plates is derived and free vibrations are studied. The effects of the rotatory inertia, transverse shear and geometrical non-linearity, due to moderately large displacements, are taken into account. The time domain free vibration equations of motion are obtained by applying the principle of virtual work, and are mapped into the frequency domain by the harmonic balance method. The ensuing frequency domain equations are solved by a predictor–corrector method. The convergence properties of the element, the influence of the plate's thickness and of the width to length ratio on the backbone curves and on the non-linear mode shapes are investigated. The first and higher order modes are analysed and results are compared with published results.     

Choosing the Parameters of a Mechanical System with Interval Stability

A new approach to the solution of the interval-stability problem is expounded. The approach is based on the idea of maximum extension of the initial system and on the M-matrix theory. As an example, mechanical systems with fuzzy parameters are considered