不确定凸模型近似算法的一种改进

将非概率凸模型理论与摄动理论相结合,通过有界不确定参数结构的特征值问题,对凸模型理论的一次近似算法作出一种改进．改进后的算法由于在计算中不用特征值导数,与Ｅｌｉｓｈａｋｏｆ的算法相比,不仅拓广了凸模型理论的应用范围,而且还可提高算法的计算效率．     

不确定性参数系统振动控制闭环特征值的上、下界估计

用凸模型理论讨论参数不确定性系统的振动控制问题。把不确定系统的振动控制转化为确定性问题来处理,然后讨论不确定参数对闭环特征值的影响,提出了闭环系统特征值上、下界的计算公式。     

载荷作用位置不确定条件下结构动态稳健性拓扑优化设计

研究当外载荷作用位置不确定时, 连续体结构动态稳健性拓扑优化设计. 在减小结构对简谐激励动响应的同时, 有效降低其对外载荷作用点随机扰动的敏感性. 首先基于非概率凸模型的方法, 将外激励作用位置的不确定性用有界区间变量表示. 其次通过对加载位置的导数分析, 获得了在激励位置扰动情况下结构动柔顺度的二阶泰勒展开式. 基于变密度方法, 推导出了动柔顺度对拓扑设计变量的一阶灵敏度显性表达式. 最后在材料体积约束下, 采用移动渐近优化算法并结合载荷扰动区间内灵敏度的最大绝对值, 对连续体结构进行动态稳健性拓扑优化设计, 并与传统载荷位置固定条件下的确定性优化结果进行对比, 充分展示考虑外激励作用位置扰动对结构拓扑构型设计及其动柔顺度变化的影响. 数值优化结果表明, 采用文中提出的方法所获得的结构动响应的稳健性更高, 能有效抵抗外激励作用位置的随机扰动. 只要少许增大材料的体积, 稳健性优化设计的动响应将在整个载荷扰动区域内优于确定性优化结果.     

对区间不确定性问题的可靠性度量的探讨

实际工程中大量存在不确定性因素,处理不确定性因素的可靠性逐渐成为科学和工程中一个非常重要的概念。区间不确定性是继随机性和模糊性之后被人们研究的又一种不确定性。区间不确定性一般可由区间变量或凸集合模型来描述。近年来,有些文献针对区间不确定性提出了计算非概率可靠性的方法。本文对这些方法进行比较和讨论,并和假定各区间不确定参量在允许取值区间内为具有熵最大的矩形分布,采用概率可靠度的理论来处理问题得到的结果进行了比较。     

基于区间因子法的不确定性桁架结构动力响应分析

研究了不确定性桁架结构的动力响应分析问题.在桁架结构的物理参数、几何尺寸和荷载幅值均为区间变量时,从结构响应的Dulaamel积分式出发,利用区间因子法、区间运算和振型叠加法导出了结构动力响应区间变量的表达式.通过算例考察了结构参数和作用荷载的区间分散性对结构动力响应分散性的影响,经与蒙特卡洛数值模拟结果的比较,表明文中所提出的计算模型和分析方法的合理性和可行性.     

基于代理模型的柔性机械臂区间不确定性分析

针对柔性机械臂系统中不确定参数引起的动态响应不确定性问题,给出了一种基于局部均值分解(LMD)和Chebyshev代理模型(CM)的区间不确定性分析方法.基于LMD方法将柔性机械臂的非线性响应分解为若干分量,并解析出表征信号的瞬时幅值、瞬时相位和趋势项,通过对分解后的信号构建Chebyshev代理模型进而得到柔性机械臂的完整代理模型.提出的柔性机械臂不确定性分析方法能够改善传统CM方法在长时程分析中区间边界失效的现象,以算例说明了本文方法应用于柔性机械臂系统不确定性分析的有效性和准确性.     

椭球凸模型非概率可靠性度量和区间安全系数的关系

研究了椭球凸模型非概率可靠性度量和区间模型安全系数的关系。根据基于椭球凸模型的非概率可靠性指标和非概率可靠度的定义,建立了两者之间的函数关系;按照区间模型安全系数的定义,给出了由椭球参数确定的3种区间模型安全系数,分析了它们的意义;建立了非概率可靠性指标和区间模型安全系数之间的解析关系,讨论了它们在评估结构可靠性或安全程度上的意义;通过数值算例验证了分析结果。     

结构鲁棒优化的非概率集合理论凸方法

以传统的优化理论为基础,考虑含不确定结构参数的情况,提出了非概率凸集合理论的结构优化方法. 将结构优化列式中的目标函数与约束条件所含有的不确定参数用凸集合定量化,只需知道其所在范围的边界,降低了以往处理不确定性问题概率方法需要知道不确定参数的均值、方差或概率分布密度等详细统计信息的要求. 提出的鲁棒优化方法在使目标函数达到设计要求的同时,结构还能承受结构参数在其所在范围内变化引起结构性能的变异. 通过优化问题中普遍使用的10杆平面桁架和一个72杆空间桁架实例,给出了当结构参数为名义值时结构的优化结果,以及结构参数具有不确定性时的优化结果,力求表明所介绍的方法的可行性和优越性.     

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     

一种考虑相关性的概率--区间混合不确定模型及结构可靠性分析

提出了一种考虑相关性的概率--区间混合不确定性模型及结构可靠性分析方法,能够处理变量之间具有相关性的混合可靠性分析问题.分别针对概率变量,概率区间变量及区间变量定义了相关角的概念,用以定量描述变量之间的相关性;通过仿射坐标,将相关变量转换为独立变量;给出了其可靠性分析模型,并构建了一高效求解方法获得其可靠性指标和失效概率区间;最后通过分析两个数值算例,验证了方法的有效性.     

Vertex solution theorem for the upper and lower bounds on the dynamic response of structures with uncertain-but-bounded parameters

The aim of this paper is to evaluate the effects of uncertain-but-bounded parameters on the dynamic response of structures. By combining the interval mathematics and the finite element analysis, the mass matrix, damping matrix, stiffness matrix and the external loads are represented as interval matrices and vector. With the help of the optimization theory, we present the vertex solution theorem for determining both the exact upper bounds or maximum values and the exact lower bounds or minimum values of the dynamic response of structures, in which these parameters reach their extreme values on the boundary of the interval mass, damping, stiffness matrices and the interval extemal loads vector. Three examples are used to illustrate the computational aspects of the presented vertex solution theorem.     

Interval arithmetic operations for uncertainty analysis with correlated interval variables

A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analy-sis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional par-allelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation, and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addi-tion, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.     

Wave scattering method for dynamic response analysis of structures with stochastic parameters

The wave scattering method is presented to analyze dynamic response of frameworks with stochastic parameters. First, with the uncertain physical, geometric, and loading properties in consideration, the stochastic waveguide equations containing the axial, torsional and flexural wave modes are established. Second, the stochastic wave scattering equation and wave translation matrix are derived to obtain the wave modes. Third, the methodology to extract the generalized displacements and forces from stochastic wave modes is proposed. Finally, a cantilever beam, a planar framework, and a space framework have been presented as numerical examples to illustrate the e?ciency of the proposed method. It is found that the results obtained by the proposed method with higher computational e?ciency show an excellent agreement with those by Monte Carlo simulation method. Furthermore, the influences of stochastic parameters on dynamic response are revealed.     

Interval finite difference method for steady-state temperature field prediction with interval parameters

A new numerical technique named interval finite difference method is proposed for the steady-state temperature field prediction with uncertainties in both physical parameters and boundary conditions. Interval variables are used to quantitatively describe the uncertain parameters with limited information. Based on different Taylor and Neumann series, two kinds of parameter perturbation methods are presented to approximately yield the ranges of the uncertain temperature field. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed method for solving steady-state heat conduction problem with uncertain-but-bounded parameters.     

求解轴对称结构侧向冲击响应的一种快速算法

轴对称结构在侧向冲击载荷下的动力响应分析,一般采用解析、半解析法或者直接进行有限元数值模拟,这些方法均有一定的局限性.本文依据线性动力学问题的叠加原理,提出了一种基于有限元分析和线性叠加的快速算法.该方法首先采用多条母线对载荷进行离散,然后采用有限元计算结构在单个"载荷单元"作用下的动力响应,最后采用坐标旋转和线性叠加的方法计算得到结构在复杂分布载荷作用下的响应.算例表明,本文提出的算法是正确、有效的,并且具有快速、简便、灵活的特点.     

随机结构非线性动力响应的概率密度演化分析

提出了随机结构非线性动力响应分析的概率密度演化方法．根据结构动力响应的随机状态方程,利用概率守恒原理,建立了随机结构非线性动力响应的概率密度演化方程．结合Newmark-Beta时程积分方法与Lax-Wendroff差分格式,提出了概率密度演化方程的数值分析方法．通过与Monte Carlo分析方法对比,表明所给出的概率密度演化方法具有良好的计算精度和较小的计算工作量．研究表明：随机结构非线性动力响应概率密度具有典型的演化特征,随着时间增长,概率密度曲线分布趋于复杂．     

Advanced response surface method for mechanical reliability analysis

Based on the classical response surface method (RSM), a novel RSM using improved experimental points (EPs) is presented for reliability analysis. Two novel points are included in the presented method. One is the use of linear interpolation, from which the total EPs for determining the RS are selected to be closer to the actual failure surface; the other is the application of sequential linear interpolation to control the distance between the surrounding EPs and the center EP, by which the presented method can ensure that the RS fits the actual failure surface in the region of maximum likelihood as the center EPs converge to the actual most probable point (MPP). Since the fitting precision of the RS to the actual failure surface in the vicinity of the MPP, which has significant contribution to the probability of the failure surface being exceeded, is increased by the presented method, the precision of the failure probability calculated by RS is increased as well. Numerical examples illustrate the accuracy and efficiency of the presented method.     

Non-probabilistic reliability method and reliability-based optimal LQR design for vibration control of structures with uncertain-but-bounded parameters

Uncertainty is inherent and unavoidable in almost all engineering systems. It is of essential significance to deal with uncertainties by means of reliability approach and to achieve a reasonable balance between reliability against uncertainties and system performance in the control design of uncertain systems. Nevertheless, reliability methods which can be used directly for analysis and synthesis of active control of structures in the presence of uncertainties remain to be developed, especially in non-probabilistic uncertainty situations. In the present paper, the issue of vibration con- trol of uncertain structures using linear quadratic regulator （LQR） approach is studied from the viewpoint of reliabil- ity. An efficient non-probabilistic robust reliability method for LQR-based static output feedback robust control of un- certain structures is presented by treating bounded uncertain parameters as interval variables. The optimal vibration con- troller design for uncertain structures is carried out by solv- ing a robust reliability-based optimization problem with the objective to minimize the quadratic performance index. The controller obtained may possess optimum performance un- der the condition that the controlled structure is robustly re- liable with respect to admissible uncertainties. The proposed method provides an essential basis for achieving a balance between robustness and performance in controller design ot uncertain structures. The presented formulations are in the framework of linear matrix inequality and can be carried out conveniently. Two numerical examples are provided to illustrate the effectiveness and feasibility of the present method.     

Non-linear analysis of structures using two-point method

Non-linear algebraic equations must be solved by an iterative method, the non-linear equations being linearized by evaluating the non-linear terms with the known solution from the preceding iteration. The Newton-Raphson method, which is based on the Taylor series expansion and uses the tangent stiffness matrix, has been extensively used to solve non-linear problems. In this paper, a new Newton-Raphson algorithm is developed for analyses involving non-linear behavior. Our method, here named as a two-point method, is constructed as a predictor-corrector one, most frequently taking Newton's method in the first iteration. It should be noted that our concern in this research ignores the problem of passing limit points. The presented method incorporates the known information at each stage of the loading process to determine the subsequent unknown variables. Compared with the classic Newton-Raphson algorithm, it offers a strategy that can be deployed to reduce both the number of the iterations and the computing time involved in non-linear analysis of structures.     

圆形地下连续墙场地地震反应的简化计算方法

首先将水平地震荷载作用沿环向展开为傅立叶级数,利用沿圆周法向和切向两个方向的正交性,再将水平地震荷载转化为一致横向荷载组合,使三维求解问题转变为一系列旋转子午面上二维问题的叠加,进而提出圆形地下连续墙场地地震反应的简化计算方法。之后,采用等效线性化方法来考虑土体非线性性质,进一步将非线性地震反应问题转化为线性问题求解。...