基于区间的土体参数敏感性分析方法研究

将一种新的工程结构不确定性分析方法——区间分析方法溶入工程参数的敏感性分析之中,获得了一种新的工程参数敏感性分析方法,进一步拓宽了区间分析方法理论的应用领域．给出了土体参数敏感性因子矩阵求解的区间分析过程,依据区间分析给出了参数区间和决策目标区间的确定方法．基于MARC软件进行了二次开发,实现了Duncan-Chang非线性弹性模型以及与Fortran程序的相互调用功能．通过工程算例验证了该方法的合理可行性,并与文献的结果进行了对比．     

模糊随机桁架结构的动力特性双因子分析法

针对模糊随机桁架结构的动力特性分析,提出了一种新的模糊随机有限元方法．当结构的物理参数和几何尺寸同时具有模糊随机性时,利用模糊因子法和随机因子法建立了结构刚度矩阵和质量矩阵;从结构振动的Rayleigh商表达式出发,利用区间运算推导出结构动力特性模糊随机变量的计算表达式;之后利用随机变量的矩法和代数综合法,推导出结构特征值的数字特征的计算式．通过算例分析了模糊随机桁架结构参数的模糊随机性对其动力特性的影响．该方法的优点是能准确反映结构某一参数的模糊随机性对结构特征值及其数字特征的影响．     

Sturm-Liouville特征值问题的多区域Legendre-Galerkin-Chebyshev配置法

提出了求解Sturm-Liouville特征值问题的多区域Legendre-Galerkin-Chebyshev的配置方法.该方法将问题的求解区间分成若干小区间,在小区间上运用Legendre-Galerkin-Chebyshev的配置方法求解,结合了Legendre-Galerkin方法和Chebyshev配置法的优点.数值算例显示了该方法的有效性.     

区间运算和静力区间有限元

用均值和离差两参数表征区间变量的不确定性,根据区间运算规则,论证了区间变量的运算特性.将区间分析和有限元方法相结合,提出了非概率不确定结构的一种区间有限元分析方法.将区间有限元静力控制方程中n自由度不确定位移场特征参数的求解归结为求解一2n阶线性方程组.实例分析表明文中方法是有效和可行的.     

一维不定参数结构系统振动特征问题的摄动传递矩阵法

基于Riccati传递矩阵法，给出了一维不确定参数结构系统振动特征问题的二阶摄动计算方法，该方法适用于一般的一维结构系统的实数和复数特征问题的分析，并给出了结构振动特征的灵敏度计算公式．算例对转子的陀螺特征值问题进行了摄动分析，摄动结果和精确计算结果吻合良好．     

一类Jacobi矩阵广义特征值反问题

称为n阶Jacobi矩阵,振动反问题讨论由特征值（频率）和特征向量（模态）数据确定振动系统的物理参数,其研究对结构设计和结构物理参数识别具有重要意义,弹簧-质点系统的振动反问题归结为Jacobi矩阵的特征值反问题,这类问题已被许多学者研究[1-3]．     

非线性特征值问题的二次近似方法

本文研究求解非线性特征值问题的数值方法.基于矩阵值函数的二次近似,将非线性特征值问题转化为二次特征值问题,提出了求解非线性特征值问题的逐次二次近似方法,分析了该方法的收敛性.结合求解二次特征值问题的Arnoldi方法和Jacobi-Davidson方法,给出求解非线性特征值问题的一些二次近似方法.数值结果表明本文所给算法是有效的.     

基于最小参数区间集的不确定结构响应分析

考虑到实际工程问题中普遍存在不确定性,完成了针对工程结构从定量化到传播的完整不确定性分析过程．通过建立包含全部有限样本点的最小区间/超立方体域来描述不确定参数的变化范围;借助于最小区间参数集,开展了不确定结构传播分析的研究工作以确定其最有利/不利响应．此外,进一步就给出的区间分析方法同经典概率方法的相容性进行了分析和探究．采用2个数值算例很好地论证了所述方法的正确性和可行性．     

结构动力学逆特征值问题的同伦解法

将结构动力学反问题视为拟乘法逆特征值问题,利用求解非线性方程组的同伦方法来解决结构动力学逆特征值问题,这种方法由于沿同伦路径求解,对初值的选取没有本质的要求,算例说明了这种方法是可行的．     

集值线性规划及其满意解

对目标函数和约束条件均为集值的不确定线性规划问题，利用集合的λ-截点把集值线性规划问题转化为确定型的一般参数规划问题来解决，并证明了这种求解方法是区间线性规划基于满意度求解方法的推广，为决策分析复杂的不确定性线性规划问题提供了一种有效的思路和方法。     

Computation of bounds for eigenvalues of structures with interval parameters

In this paper, the computation of eigenvalue bounds for generalized interval eigenvalue problem is considered. Two algorithms based on the properties of continuous functions are developed for evaluating upper and lower eigenvalue bounds of structures with interval parameters. The method can provide the tightest bounds within a given precision. Numerical examples illustrate the effectiveness of the proposed method.     

Exact bounds for the sensitivity analysis of structures with uncertain-but-bounded parameters

Based on interval mathematical theory, the interval analysis method for the sensitivity analysis of the structure is advanced in this paper. The interval analysis method deals with the upper and lower bounds on eigenvalues of structures with uncertain-but-bounded (or interval) parameters. The stiffness matrix and the mass matrix of the structure, whose elements have the initial errors, are unknown except for the fact that they belong to given bounded matrix sets. The set of possible matrices can be described by the interval matrix. In terms of structural parameters, the stiffness matrix and the mass matrix take the non-negative decomposition. By means of interval extension, the generalized interval eigenvalue problem of structures with uncertain-but-bounded parameters can be divided into two generalized eigenvalue problems of a pair of real symmetric matrix pair by the real analysis method. Unlike normal sensitivity analysis method, the interval analysis method obtains informations on the response of structures with structural parameters (or design variables) changing and without any partial differential operation. Low computational effort and wide application rang are the characteristic of the proposed method. Two illustrative numerical examples illustrate the efficiency of the interval analysis.     

Predicting stochastic characteristics of generalized eigenvalues via a novel sensitivity-based probability density evolution method

This paper proposes a novel numerical method for predicting the probability density function of generalized eigenvalues in the mechanical vibration system with consideration of uncertainties in structural parameters. The eigenproblem of structural vibration is presented by first and the sensitivity of generalized eigenvalues with respect to structural parameters can be derived. The probability density evolution method is then developed to capture the probability density function of generalized eigenvalues considering uncertain material properties. Within the proposed method, the probability density evolution equation for the generalized eigenvalue problem is established accounting for the sensitivity of generalized eigenvalues with respect to structural parameters. A new variable which connects generalized eigenvalues to structural parameters is then introduced to simplify the original probability density evolution equation. Next, the simplified probability density evolution equation is solved by using the finite difference method with total variation diminishing schemes. Finally, the probability density function as well as the second-order statistical quantities of generalized eigenvalues can be predicted. Numerical examples demonstrate that the proposed method yields results consistent with Monte-Carlo simulation method within significantly less computation time and the coefficients of variation of uncertain parameters as well as the total number of them have remarkable effects on stochastic characteristics of generalized eigenvalues.     

Natural frequencies of structures with uncertain but nonrandom parameters

In this paper, we present a method for computing upper and lower bounds of the natural frequencies of a structure with parameters which are unknown, except for the fact that they belong to given intervals. These parameters are uncertain, yet they are not treated as being random, since no information is available on their probabilistic characteristics. The set of possible states of the system is described by interval matrices. By solving the generalized interval eigenvalue problem, the bounds on the natural frequencies of the structure with interval parameters are evaluated. Numerical results show that the proposed method is extremely effective.The research reported in this paper has been supported by the PRC National Natural Science Foundation and by the USA National Science Foundation Grant MSM-9215698 (Program Director Dr. K. P. Chong).     

Time dependent uncertain free vibration analysis of composite CFST structure with spatially dependent creep effects

In this study, the time dependent free vibration analysis of composite concrete-filled steel tubular (CFST) arches with various uncertainties is thoroughly investigated within a non-stochastic framework. From the practical inspiration, both uncertain material properties and mercurial creep effect associated with such composite materials are simultaneously incorporated. Unlike traditional non-probabilistic schemes, both spatially independent (i.e., conventional interval models) and dependent (i.e., interval fields) interval system parameters can be comprised within a unified uncertain free vibration analysis framework for CFST arches. For the purpose of achieving a robust framework of the time-dependent uncertain free vibration analysis, a new computational approach, which has been developed within the scheme of the finite element method (FEM), has been proposed for determining the extreme bounds of the natural frequencies of practically motivated CFST arches. Consequently, by successfully solving two eigenvalue problems, the upper and lower bounds of the natural frequencies of such composite structures with various uncertainties can be rigorously secured. The unique advantage of the proposed approach is that it can be effectively integrated within commercial FEM software with preserved sharp bounds on natural frequencies for any interval field discretisation. The competence of the proposed computational analysis framework has been thoroughly demonstrated through investigations on both 2D and3D engineering structures.     

Time response of structure with interval and random parameters using a new hybrid uncertain analysis method

Practical structures often operate with some degree of uncertainties, and the uncertainties are often modelled as random parameters or interval parameters. For realistic predictions of the structures behaviour and performance, structure models should account for these uncertainties. This paper deals with time responses of engineering structures in the presence of random and/or interval uncertainties. Three uncertain structure models are introduced. The first one is random uncertain structure model with only random variables. The generalized polynomial chaos (PC) theory is applied to solve the random uncertain structure model. The second one is interval uncertain structure model with only interval variables. The Legendre metamodel (LM) method is presented to solve the interval uncertain structure model. The LM is based on Legendre polynomial expansion. The third one is hybrid uncertain structure model with both random and interval variables. The polynomial-chaos-Legendre-metamodel (PCLM) method is presented to solve the hybrid uncertain structure model. The PCLM is a combination of PC and LM. Three engineering examples are employed to demonstrate the effectiveness of the proposed methods. The uncertainties resulting from geometrical size, material properties or external loads are studied.     

Interval modal superposition method for impulsive response of structures with uncertain-but-bounded external loads

This paper is concerned with the problem of the dynamic response of structures with uncertain-but-bounded external loads. Based on the theory of complex modal analysis, and interval mathematics, a new non-probabilistic method-interval modal superposition method is proposed to find the least favorable impulsive response and the most favorable impulsive response of structures. Through mathematical analysis and numerical calculation, comparisons between interval modal superposition method and probabilistic approach are made. Instead of probabilistic density distribution or statistical quantities, in the presented method, only the bounds on uncertain parameters are needed, Numerical examples indicate that the width of the region of the dynamic response yielded by the interval modal superposition method is larger than those produced by probabilistic approach while the interval modal superposition method will required less computation effort.     

Eigenvalue analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

When the uncertainties in interval parameters are fairly large, the current analysis methods, which are usually based on the information of the first-order partial derivatives of eigenvalues, may not work well for the structural eigenvalue problem with interval parameters. To overcome this drawback, in this work, the structural eigenvalue problem with interval parameters is modeled as a series of QB (quadratic programming with box constrains) problems by taking advantage of the information of the second-order partial derivatives of eigenvalues. Then the series of QB problems would be solved by using the DCA (difference of convex functions algorithm) which is turn out be very effective for the QB problem. The specific examples, a concrete frame with sixty bars and a plate discretized with 300 finite elements, are given to show the effectiveness and feasibility of the proposed method compared with other methods.