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．     

基于Bregman距离函数的可靠性分析

针对概率结构可靠性问题,引入Bregman距离函数,建立了基于同伦算法(HM)的可靠性分析模型.利用极限状态方程,将可靠性指标求解转化为一个非线性约束优化问题.结合同伦思想的基本理论和Bregman距离函数,构造同伦方程组,采用路径跟踪算法对该方程组进行求解.通过相应的数值算例探讨了不同函数形式以及不同程度非线性问题的可靠性计算,并与其他方法计算结果进行了对比,分析结果表明该模型能够有效求解概率结构可靠性问题.     

地下结构和岩土介质弹塑性耦合分析的摄动半解析法*

本文研究了一个用于物理非线性相互作用分析的有效的数值方法。结构和介质耦合分析的弹塑性问题可用摄动法转化为几个线性问题,然后对相应的线性问题分别用有限条和有限层法分析地下结构和岩土介质以达到简化计算的目的。这种方法用了两次半解析技术——摄动和半解析解函数——将三维非线性耦合问题化为一维的数值问题。此外,本法是半解析法结合解析的摄动法应用于非线性问题的新进展,同时也是近年来发展的摄动数值法的一个分支。     

有限变形弹性理论随机变量变分原理及有限元法

本文将材料、载荷、结构几何形状、力和位移边界条件的随机性,直接引入有限变形弹性理论的泛函变分表达式中,应用小参数摄动法,建立了统一的随机变量变分原理及非线性随机有限元法,并将其应用于结构可靠性分析。算例表明,应用此方法处理随机变量的力学问题,具有使程序实施简便,计算效率高等优点。     

有界噪声参激一类三维系统的矩Liapunov指数

对于一类三维中心流形上受有界噪声参激的余维2分岔系统,计算了它的矩Liapunov指数．根据随机动力系统理论,首先建立了系统矩Liapunov指数求解的特征值问题,然后由奇异摄动法,得到了弱噪声展开的矩Liapunov指数的二阶渐近解析表达式和数值结果．接着进一步研究了有界噪声和系统参数对矩Liapunov指数和稳定指标的影响．结果表明:系统的随机稳定性有被有界噪声加强的可能性．     

分析结构非线性问题的杂交可变基Galerkin方法

基于渐近摄动理论和Galer-kin方法,本文提出分析结构非线性问题的杂交可变基Galer-kin方法。本文方法首次引入可变基函数的概念,可大幅度降低计算量,而且在有限元法等数值方法中易于推广应用,在解决非线性问题领域有广泛应用前景。最后本文分析圆板大挠度问题和扁球壳大挠度问题,以验证本文方法的有效性。     

非Gauss随机特性下的结构首次失效时间研究

提出了一个基于结构响应矩的解析方法, 用来计算具有非Gauss特性结构的首次失效时间．在该方法中,首先采用其系数可通过结构反应矩（偏态系数和峰度系数等）计算的幂级数,将非Gauss结构反应变换为标准Gauss过程．然后,利用变换的标准Gauss过程计算原结构反应过程关于某临界界限的平均超越率、平均群超尺度和初始超越概率．最后,在修正超越率为独立的假定下,建立了首次超越时间的计算公式．Gauss过程激励下非线性单自由度振动系统的分析,不仅说明了该方法的应用过程,也通过与Monte Carlo模拟和传统Gauss模型方法的对比分析,证明了该方法的精确性和效率．     

非线性自治振动系统同宿解的广义双曲函数摄动法

提出广义的双曲函数摄动法,用于求解强非线性自治振子的同宿解,克服一般摄动步骤中派生方程须存在显式精确同宿解的限制．以广义双曲函数作为摄动步骤的基本函数,拓展了基于双曲函数的摄动法的适用范围．对同时含2,3次和含4次强非线性项的系统进行求解分析,验证了方法的有效性和精度．     

静力分析的一般随机摄动法

本文对向量值和矩阵值函数的不确定结构的静力响应和可靠性进行了研究。基于Ｋｒｏｎｅｃｋｅｒ代数和摄动理论导出了随机结构的有限元分析方法，随机变量和系统导数很方便地排列到２Ｄ矩阵中，给出了一般的数学表达式．     

区间有限元方法及其在抗滑稳定性分析中的应用

通过区间值函数和实值函数的关系探讨了区间相关性导致的区间扩张的问题,给出了保证区间计算获得足够精度的计算方法;提出了基于单元的子区间摄动有限元计算方法,并给出了提高计算效率的一些方法和获得较好计算精度时的子区间数目的近似计算公式．结合工程实例,基于单元的子区间有限元方法和抗滑稳定性分析方法给出了稳定性的区间范围,为更合理地估计和评价结构的抗滑稳定性提供一定的依据．     

Structural design optimization based on hybrid time-variant reliability measure under non-probabilistic convex uncertainties

Structural safety assessment issue, considering the influence of uncertain factors, is widely concerned currently. However, uncertain parameters present time-variant characteristics during the entire structural design procedure. Considering materials aging, loads varying and damage accumulation, the current reliability-based design optimization (RBDO) strategy that combines the static/time-invariant assumption with the random theory will be inapplicable when tackling with the optimal design issues for lifecycle mechanical problems. In light of this, a new study on non-probabilistic time-dependent reliability assessment and design under time-variant and time-invariant convex mixed variables is investigated in this paper. The hybrid reliability measure is first given by the first-passage methodology, and the solution aspects should depend on the regulation treatment and the convex theorem. To guarantee the rationality and efficiency of the optimization task, the improved GA algorithm is involved. Two numerical examples are discussed to demonstrate the validity and usage of the presented methodology.     

Novel reliability-based optimization method for thermal structure with hybrid random,interval and fuzzy parameters

In this paper, novel reliability-based optimization model and method are proposed for thermal structure design with random, interval and fuzzy uncertainties in material properties, external loads and boundary conditions. Random variables are used to quantify the probabilistic uncertainty with sufficient sample data; whereas, interval variables and fuzzy variables are adopted to model the non-probabilistic uncertainty associated with objective limited information and subjective expert opinions, respectively. Using the interval ranking strategy, the level-cut limit state function is precisely quantified to represent the safety state. The eventual safety possibility is derived based on multiple integral, where the cut levels of different fuzzy variables are considered to be independent. Then a hybrid reliability-based optimization model is established with considerable computational cost caused by three-layer nested loop. To improve the computational efficiency, a subinterval vertex method is presented to replace the inner-loop and middle-loop. Comparing numerical results with traditional reliability model, a mono-objective example and a multi-objective example are provided to demonstrate the feasibility of proposed method for hybrid reliability analysis and optimization in practical engineering.     

Efficient Reliability Sensitivity Estimation for Optimization Under Uncertainty

In this contribution, an efficient framework for performing reliability-based optimization is presented. Key issues of the proposed approach are the decoupling of optimization and reliability estimation and efficient reliability sensitivity estimation. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An introduction to nonlinear problems with random parameters by the Stochastic perturbation-based FEM

The main aim of this paper is to present an algorithm and the solution to the nonlinear problems with random parameters. The methodology is based on the generalized nth order stochastic perturbation method and, on the other hand, on the Finite Element Method adjacent to the physical and geometrical nonlinearities. The perturbation approach resulting from the Taylor series expansion with uncertain parameters is proposed in two different ways – thanks to the straightforward differentiation of the initial incremental equation and, separately, using the modified Response Function Method. This approach is illustrated with the analysis of the simply supported elastoplastic beam loaded centrally with the concentrated force, where the probabilistic moments for the limit load and the reliability indices are determined via the stochastic symbolic computations. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling redundancy allocation for a fuzzy random parallel-series system

Due to subjective judgment, imprecise human knowledge and perception in capturing statistical data, the real data of lifetimes in many systems are both random and fuzzy in nature. Based on the fuzzy random variables that are used to characterize the lifetimes, this paper studies the redundancy allocation problems to a fuzzy random parallel-series system.Two fuzzy random redundancy allocation models (FR-RAM) are developed through reliability maximization and cost minimization, respectively. Some properties of the FR-RAM are obtained, in which an analytical formula of reliability with convex lifetimes is derived and the sensitivity of the reliability is discussed. To solve the FR-RAMs, we first address the computation of reliability. A random simulation method based on the derived analytical formula is proposed to compute the reliability with convex lifetimes. As for the reliability with nonconvex lifetimes, the technique of fuzzy random simulation together with the discretization method of fuzzy random variable is employed to compute the reliability, and a convergence theorem of the fuzzy random simulation is proved. Subsequently, we integrate the computation approaches of the reliability and genetic algorithm (GA) to search for the approximately optimal redundancy allocation of the models. Finally, some numerical examples are provided to illustrate the feasibility of the solution algorithm and quantify its effectiveness.     

An efficient strategy for reliability-based multidisciplinary design optimization of twin-web disk with non-probabilistic model

The twin-web disk holds big promise for increasing efficiency of the aircraft engine. Its reliability-based multidisciplinary design optimization involves several disciplines including fluid mechanics, heat transfer, structural strength, and vibration. The solution to this optimization problem requires three-loop calculations including loops for optimization, reliability, and interdisciplinary consistence often making its computational cost unacceptably high. The lack of sufficient amount of probabilistic data, especially for this brand-new turbine disk, makes matters worse. In this paper, the non-probabilistic uncertain variables are described by an evidence theory-based fuzzy set method, which we extend to general structure of uncertain data. We also propose two modifications of the active learning kriging model: one of them for the purpose of optimization with respect to the distance from the optimum point and another one for the purpose of assessing reliability by introducing the importance concept. Applications of these two modifications are demonstrated in this paper. Finally, a multi-adaptive learning kriging strategy for non-probabilistic reliability-based multidisciplinary design optimization of twin-web disk is proposed to improve its power efficiency and reliability in a computationally effective way.     

Decoupled reliability-based geotechnical design of deep excavations of soil with spatial variability

This paper presents a general decoupled method for reliability-based geotechnical design that takes into account the spatial variability of soil properties. In this method, reliability analyses that require a lot of computational resources are decoupled from the optimization procedure by approximating the failure probability function globally. Failure samples are iteratively generated over the entire design space so that their global distribution information can be extracted to construct the failure probability function. The method is computationally efficient, is flexible to implement, and is well suited for geotechnical problems that may involve sophisticated models. A design example of two-dimensional deep excavation against basal heave is discussed for Singapore marine clay where the density and normalized undrained shear strength of soil mass are modeled as random fields. Results demonstrate that the proposed method works well in practice and is advantageous over the coupled or locally decoupled reliability-based geotechnical design methods.     

Augmented line sampling for approximation of failure probability function in reliability-based analysis

An efficient approach, called augmented line sampling, is proposed to locally evaluate the failure probability function (FPF) in structural reliability-based design by using only one reliability analysis run of line sampling. The novelty of this approach is that it re-uses the information of a single line sampling analysis to construct the FPF estimation, repeated evaluations of the failure probabilities can be avoided. It is shown that, when design parameters are the distribution parameters of basic random variables, the desired information about FPF can be extracted through a single implementation of line sampling. Line sampling is a highly efficient and widely used reliability analysis method. The proposed method extends the traditional line sampling for the failure probability estimation to the evaluation of the FPF which is a challenge task. The required computational effort is neither relatively sensitive to the number of uncertain parameters, nor grows with the number of design parameters. Numerical examples are given to show the advantages of the approach.     

随机结构系统基于可靠性的优化设计

提出了以梁板（薄板）为基体的随机结构系统（即结构元件的面积、长度、弹性模量和强度等均为随机变量）在随机载荷作用下,基于可靠性的优化设计方法．给出了随机结构系统安全余量和系统可靠性指标的敏度表达式;给出最佳矢量型算法．首先是用改进的一次二阶矩和随机有限元法求出安全余量的可靠性指标的表达式,然后用概率网络估算(PNET)法求出系统失效概率的公式,对该式两边求导得出了系统可靠性指标的敏度表达式,进而用最佳矢量型算法进行优化设计．在优化迭代过程中,采用梯度步和最佳矢量步相结合的方法进行计算．最后给出了一个算例,说明该方法计算效率高,收敛稳定,适合工程应用．