FUZZY RELIABILITY-BASED OPTIMUM DESIGN OF LAMINATED COMPOSITES

In conventional reliability-based optimum design of structures, the reliability is computed based on the probability assumption, and the design objective and constraint are considered as deterministic ones. In many cases, however, there exist some fuzzy factors in the design objective and constraint functions. In this paper, the fuzzy reliability and fuzzy constraint are introduced to establish the fuzzy reliability-based optimum model for laminated composites. The examples show that the method developed in this paper can give consideration to both the reliability demand and the economic aspect of a structure. Since the fuzzy reliability-based optimum design is a 'soft' design, the present results provide a new methodology for the effective evaluation of structural reliability and bring us an alternative optimum design idea.     

DYNAMIC CHARACTERISTIC ANALYSIS OF FUZZY- STOCHASTIC TRUSS STRUCTURES BASED ON FUZZY FACTOR METHOD AND RANDOM FACTOR METHOD

A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented. Considering the fuzzy randomness of the structural physical parameters and geometric dimensions simultaneously, the structural stiffness and mass matrices are constructed based on the fuzzy factor method and random factor method; from the Rayleigh's quotient of structural vibration, the structural fuzzy random dynamic characteristic is obtained by means of the interval arithmetic; the fuzzy numeric characteristics of dynamic characteristic are then derived by using the random variable's moment function method and algebra synthesis method. Two examples are used to illustrate the validity and rationality of the method given. The advantage of this method is that the effect of the fuzzy randomness of one of the structural parameters on the fuzzy randomness of the dynamic characteristic can be reflected expediently and objectively.     

DAMAGE DETECTION BASED ON OPTIMIZED INCOMPLETE MODE SHAPE AND FREQUENCY

For the purpose of structural health monitoring, a damage detection method combined with optimum sensor placement is proposed in this paper. The back sequential sensor placement(BSSP) algorithm is introduced to optimize the sensor locations with the aim of maximizing the 2-norm of information matrix, since the EI method is not suitable for optimum sensor placement based on eigenvector sensitivity analysis. Structural damage detection is carried out based on the respective advantages of mode shape and frequency. The optimized incomplete mode shapes yielded from the optimal sensor locations are used to localize structural damage. After the potential damage elements have been preliminarily identified, an iteration scheme is adopted to estimate the damage extent of the potential damage elements based on the changes in the frequency. The effectiveness of this method is demonstrated using a numerical example of a 31-bar truss structure.     

A structural topological optimization method for multi-displacement constraints and any initial topology configuration

In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multidisplacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.     

Optimum design of hierarchical stiffened shells for low imperfection sensitivity

A concept of hierarchical stiffened shell is proposed in this study, aiming at reducing the imperfection sen- sitivity without adding additional weight. Hierarchical stiffened shell is composed of major stiffeners and minor stiff- eners, and the minor stiffeners are generally distributed between adjacent major stiffeners. For various types of geo- metric imperfections, e.g., eigenmode-shape imperfections, hierarchical stiffened shell shows significantly low imper- fection sensitivity compared to traditional stiffened shell. Furthermore, a surrogate-based optimization framework is proposed to search for the hierarchical optimum design. Then, two optimum designs based on two different opti- mization objectives （including the critical buckling load and the weighted sum of collapse loads of geometrically imperfect shells with small- and large-amplitude imperfections） are compared and discussed in detail. The illustrative example demonstrates the inherent superiority of hierarchical stiffened shells in resisting imperfections and the effectiveness of the proposed framework. Moreover, the decrease of imperfection sensitivity can finally be converted into a decrease of structural weight, which is particularly important in the development of large-diameter launch vehicles.     

ENERGY ABSORPTION CONTROL CHARACTERISTICS OF AL THIN-WALLED TUBES UNDER IMPACT LOAD

An experimental investigation was carried out to study the energy absorption characteristics of thin-walled square tubes subjected to dynamic crushing by impact loading to develop the optimum structural members. Here, the controller is introduced to improve and control the absorbed energy of thin-walled square tubes in this paper. When the controller were used, the experimental results of crushing of square tubes controlled by the controller＇s elements showed a good candidate for a controllable energy absorption capability in impact crushing.     

APPROACH FOR LAYOUT OPTIMIZATION OF TRUSS STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS, DISPLACEMENT AND STABILITY CONSTRAINTS

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.     

STUDY ON PARAMETERS FOR TOPOLOGICAL VARIABLES FIELD INTERPOLATED BY MOVING LEAST SQUARE APPROXIMATION

This paper presents a new approach to the structural topology optimization of continuum structures. Material-point independent variables are presented to illustrate the existence condition,or inexistence of the material points and their vicinity instead of elements or nodes in popular topology optimization methods. Topological variables field is constructed by moving least square approximation which is used as a shape function in the meshless method. Combined with finite element analyses,not only checkerboard patterns and mesh-dependence phenomena are overcome by this continuous and smooth topological variables field,but also the locations and numbers of topological variables can be arbitrary. Parameters including the number of quadrature points,scaling parameter,weight function and so on upon optimum topological configurations are discussed. Two classic topology optimization problems are solved successfully by the proposed method. The method is found robust and no numerical instabilities are found with proper parameters.     

Multi-resonator coupled metamaterials for broadband vibration suppression

In this study,multi-resonator coupled metamaterials(MRCMs)with local resonators are proposed to obtain the multiple and wide band gaps.Kinetic models of the MRCMs are established,and the boundary conditions of the unit cell are obtained with Bloch's theorem.The effects of structural parameters,including the mass of the resonator and the spring stiffness,on the distributions of the band gaps are studied.Furthermore,the frequency domain responses and the time domain responses are calculated for analyzing the structural vibration characteristics and the effects of damping on structural vibration.The results show that the frequency domain response can accurately express the distributions of the band gaps of the MRCMs,and we can increase the number and the width of the band gaps by using the MRCMs for the superior vibration suppression capability.     

AN ASYMPTOTIC METHOD FOR ANALYZING THE STRESS IN A FUNCTIONALLY GRADIENT MATERIAL LAYER ON A SURFACE OF A STRUCTURAL COMPONENT

A simple and effective method for analyzing the stress distribution in a FunctionallyGradient Material(FGM)layer on the surface of a structural component is proposed in this paper.Generally,the FGM layer is very thin compared with the characteristic length of the structural compo-nent,and the nonhomogeneity exists only in the thin layer.Based on these features,by choosing asmall parameter λ which characterizes the stiffness of the layer relative to the component,and expand-ing the stresses and displacements on the two sides of the interface according to the parameter λ,thenasymptotically using the continuity conditions of the stresses and displacements on the interface,a de-coupling computing process of the coupling control equations of the layer and the structural componentis realized.Finally.two examples are given to illustrate the application of the method proposed.     

Frequency Reliability-Based Robust Design of the Suspension Device of a Jarring Machine with Arbitrary Distribution Parameters

The frequency reliability with arbitrary distribution parameters in the stochastic dynamic structure system of practical engineering and its related theories were studied deeply in the paper. The frequency reliability method of avoiding resonance was proposed by mechanical dynamics, stochastic finite element method, and reliability theory. Then the frequency reliability formula with arbitrary distribution parameters was deduced through Edgeworth series method. Furthermore, the frequency reliability sensitivity method was presented based on the frequency reliability research, which provided a preliminary efficient way to analyze how each random parameter contributed to the system reliability. Moreover, the frequency reliability-based robust design method of the stochastic dynamic structure system was obtained by robust and optimization technology on the basis of frequency reliability and sensitivity method, which helped designers to establish acceptable parameter values and to determine the fluctuations of the parameters for the safe operations. Meanwhile, a numerical example of the suspension device of a jarring machine with arbitrary distribution parameters was provided and studied, the numerical results were in agreement with practice, which demonstrated the efficiency and accuracy of the proposed methods.     

火工品可靠性的感度参数设计法

提出一种能同时满足火工品发火可靠性和安全可靠性的设计方法,把火工品可靠性指标转换成感度分布参数的取值范围,通过对感度的调节使产品满足发火可靠性和安全可靠性要求,为火工品可靠性设计提供了一条新思路。推导出了常见火工品感度在正态分布、逻辑斯谛分布、对数正态分布和对数逻辑斯谛分布等常见分布条件下把可靠性指标转换为感度分布参数的表达式,实例证明这种方法对火工品研制有指导作用。     

离散变量框架结构的可靠性优化

以框架结构系统的可靠性分析为基础,给出离散变量框架结构可靠性优化的相对差商方法及迭代格式,并用算例证明了该法的有效性及实用性。     

动态结构系统可靠性的频率灵敏度分析

基于频率可靠性理论提出了动态结构系统的频率可靠性灵敏度的计算方法. 根据动态结构系统的固有频率与激振频率差的绝对值不超过规定值的关系准则,定义了随机结构振动问题的可靠性模式和系统的可靠度,进而提出了频率可靠性灵敏度分析方法,应用随机摄动技术、可靠性理论和灵敏度方法,推导出参数为正态随机变量时的准失效概率灵敏度的表达公式,对动态结构系统共振问题的可靠性灵敏度分析方法进行了探索. 并在此基础上,以一简化的车身-车轮-路面关系的系统模型为例,由可靠性灵敏度矩阵可以看出,各随机参数的变化对动态结构系统的可靠性及失效性的影响程度也不同,其计算结果与通常的定性分析结果完全一致,验证了所提方法的有效性. 该方法为动态结构系统的优化和设计提供了依据.      

随机参数多自由度体系在平稳随机反应下的系统动力可靠性

对具有随机参数的多自由度体系,提出了求解其系统动力可靠度上、下限的一种计算方法。考虑结构的物理和几何参数具有随机性,从结构随机响应的频域表达式出发,利用求解随机变量数字特征的代数综合法和矩法,导出了随机参数多自由度体系在平稳随机激励下的平稳随机反应均方值的数字特征,再由动力可靠性的Poisson公式导出了随机参数结构的动力可靠度的计算公式,然后根据系统可靠性分析方法,分析了随机参数多自由度体系的系统动力可靠性,最后给出了系统动力可靠度上、下限的计算公式,并给出一个算例。     

考虑空间变异性的框架结构可靠度分析方法

空间变异性是结构参数的固有属性，对于工程结构的随机响应和可靠度分析具有重要影响。结合随机场离散的局部平均理论和随机响应分析的摄动随机有限元法，提出一种考虑参数空间变异性的平面框架结构可靠度分析方法，并定量分析了参数空间变异性对结构可靠度的影响规律。首先，考虑随机因素的空间变异性，采用二维线性随机场离散的局部平均理论将平面框架结构的连续随机场离散为一组随机变量，并通过理论推导建立了随机场局部平均间协方差矩阵的二重积分表达式；然后，采用摄动随机有限元法分析结构随机响应及其对基本随机变量的梯度向量，并利用可靠度分析的梯度优化法计算结构可靠指标，从而提出了一种考虑参数空间变异性的平面框架结构可靠度分析方法。分析表明，该方法具有较高的计算精度和计算效率；随机场离散的局部平均理论对相关结构类型不敏感；随着随机场相关偏度和变异性的增大，框架结构的可靠指标逐渐减小，说明结构参数的空间变异性对结构可靠度的影响不容忽视。     

多层非线性抗震钢结构的损失估计与优化设计

本文通过结构的动力可靠性分析和损失估计建立了以动力可靠性为约束的非线性抗震结构双目标(造价与损失期望)优化设计模型,提出了具体实现这种优化设计思想的实际可行的方法。文中将地震地面运动模拟为平稳过滤有色噪声,建立了以破坏指数刻划的结构体系的模糊震害等级,提出了结构模糊动力可靠性分析和损失估计的具体方法,从而使优化设计模型中各有关量的分析和计算得以具体地实现。     

动态结构系统的频率可靠性稳健设计研究

针对随机动态结构系统振动问题进行研究,提出了系统避免共振的频率可靠性分析方法;在此基础上,推导出频率可靠性灵敏度计算公式,研究设计参数的改变对随机动态结构系统频率可靠性的影响,给出各随机参数可靠性灵敏度的变化规律;并将频率可靠性及其灵敏度分析方法与可靠性优化设计方法相结合,提出了频率可靠性稳健优化设计方法,同时以一简化的两自由度的车身-车轮-路面关系的1/4离散系统模型为例,对该模型进行了频率可靠性稳健设计的研究,其理论计算结果与工程实际情况完全一致,也说明了所提方法的有效性和实用性,为随机动态结构系统的设计、制造、使用和评估提供了合理和必要的理论依据。     

基底滞后隔震层对建筑结构随机地震反应的控制

本文应用随机最优控制理论提出了用基底滞后隔震层把大震烈度下多层剪切型结构的地震反应控制在弹性范围内的设计计算方法.文中在建立了基底设置隔震层建筑结构计算模型的基础上,确定了它随机地震反应最优控制的评价函数和可靠性约束;并在应用最优控制论导得基底等价线性耗能器的最优反馈增益的前提下,最终得到了把大震烈度下结构地震反应控制在弹性范围内的基底滞后隔震层最优设计参数的计算公式.     

大型结构可靠性优化设计的大系统方法

首先回顾了基于可靠性的结构设计方法并对其进行了简要的评述;其次介绍了目前正处于热点的大系统设计方法,并提出了应用大系统方法进行大型结构可靠性设计的策略．该策略的主要思路是从结构方案阶段即考虑结构可靠度指标及重量指标的最优分配．一个大型结构可以分解成一系列子系统,而该系统中的每一个又可以分解成一系列二级子系统,直至最基本的子系统．建议对于大型复杂结构,最基本的子系统并非结构元件,而应是能用有限元模型进行基于可靠性优化设计的子结构．