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1、华中科技大学博士学位论文复合材料的模糊可靠性及模糊稳健优化研究姓名：魏俊红申请学位级别：博士专业：固体力学指导教师：陈建桥20060401I摘 要 纤维增强复合材料（FRP）是由高强度、低密度的纤维材料与基体组成，具有很多其它材料所没有的优点或特点，广泛应用于航空、航天、造船和汽车等领域。对纤维增强复合材料的可靠度和可靠度优化的研究，是近年来备受关注的问题。现有的可靠度和可靠度优化研究主要考虑了影响因素的随机性，而忽略了模糊因素的影响。本文考虑模糊因素和设计变量的差异，对复合材料结构进行了模糊可靠性及模糊稳健设计研究，具体内容如下： 1 建立了复合材料层合板结构的模糊可靠性分析模型。在已有的复
2、合材料可靠性分析中，一般假设载荷或者强度为随机变量，失效状态为二值状态。但是在工程实际中，由于复合材料组分材料性能的分散性，复合材料/结构的复杂性，强度行为的多样性，以及载荷与环境等因素的不确定性，使得强度的准确预测非常困难，而且结构的失效判断也包含一定的模糊性，因此在复合材料的可靠性分析中不仅需要考虑随机性因素，还应考虑模糊因素的影响。基于此，本论文在复合材料的可靠性分析中做了以下研究：首先提出： （1）用模糊方法来描述强度变量，并利用隶属度函数来定量的表示强度参数。 （2）考虑安全和失效状态之间的中间过渡状态，将失效状态用模糊状态来描述。在（1）和（2）的基础上，利用模糊数学和可靠性的基本
3、理论，建立了两种模糊可靠度分析模型，并提出了其相应的数值算法。 2 研究了复合材料层合板的模糊可靠度优化。复合材料层合板的可靠度优化问题，由于既考虑设计变量的随机性，又考虑结构在满足可靠度要求的情况下达到最优， 因此成为国内外都在积极探索的前沿问题。 可靠性优化研究虽然取得较多成果，但仍处在发展过程中。已有的分析模型或方法没有考虑设计目标，设计变量和约束条件所具有的模糊性，把许多本来是模糊的量人为地当成是确定量，例如设计水平的高低，制造水平对设计的影响，结构及工艺的经济实用，安全可靠以及人文因素，如政治影响、经济政策环境条件及市场情况等。由于常规的可靠性优化忽略了模糊现象的存在，使得设计变量和
4、目标函数不能达到应有的取值范围，所以住往会漏掉II真正的优化方案，甚至会带来一些矛盾的结果。本论文在复合材料层合板的可靠度优化问题中，考虑了各种模糊因素的影响，并将其归结在设计目标和约束条件的模糊性当中，根据设计目标和约束条件的重要性的不同，建立了两种模糊可靠度优化模型，并分别研究了其相应的求解方法。 3 讨论了复合材料层合板的稳健设计。稳健性是指对因素（原因、输入）发生微小变差的不敏感性，而稳健设计是对产品性能、质量、成本作综合考虑而获得高质低价的现代设计方法。其最重要的特点就是在设计阶段就考虑了设计变量和环境变量的变差对设计结果的影响，从而提高了产品的总体质量，使产品质量对影响参量的变化保
5、持稳定。在本论文中，考虑纤维角度和单层板厚度的变差对结构性能的影响，对复合材料结构进行稳健设计。首次提出对复合材料结构进行模糊稳健设计的思想。在模糊可靠度优化的基础上，提出了模糊约束的稳健性问题，建立了复合材料的模糊稳健设计模型，通过具体算例说明了稳健设计和模糊稳健设计的可行性和必要性。 关键词关键词: 复合材料，模糊可靠度，模糊优化，模糊稳健设计 IIIABSTRACT By virtue of its excellent properties, such as the high specific strength and high specific modulus, anisotropy
6、and designability, the Fiber Reinforced Plastics （FRP） has been widely used as structure materials in aircraft, space, marine and automobile, etc. The fibrous composites strength, its reliability, and the optimum design are important subjects of research. Many achievements have been made in the reli
7、ability and reliability-based studies based on the probability theory, but little has been done considereding the fuzziness of the factors. In this paper, considereding the the fuzziness and derivation of the design variable, the fuzzy reliability and fuzzy robust design are studied and the achievem
8、ents can be listed as follows: 1 The fuzzy reliability analysis model of laminated composites is established. In a classical reliability model, some of the variables such as loads and strengths are considered as random variables and the rest deterministic ones. The binary state assumption is adopted
9、 for the structure system. That is, a system is either in function or failure state. From the view of the engineering practice, the strength behaviors of composite laminated can be greatly influenced by the properties of constitutive materials, the laminate structures, and load conditions etc, accom
10、panied by many uncertainty factors. The prediction of composites strength is a very difficult task. And the structure state cant be described fully by the binary state assumption. So the fuzziness should be introduced together with the randomness in the reliability research of composites. In this pa
11、per, the fuzzy concept is first introduced to describe the strength in the reliability computation of composite laminates. Based on the fuzzy mathematics and the conventional reliability theory, a fuzzy reliability model is constructed. The model can provide an alternative method assessing structura
12、l reliability in the case where the distribution pattern of strength parameters is hard to determine. Then, a generalized fuzzy reliability model （GFRM） is established on the basis of the fuzzy state assumption together with the probabilistic assumption, which can effectively evaluate the reliabilit
13、y IVof a system with different types of uncertainty factor. 2 A fuzzy reliability optimization method is developed. The reliability optimum design of laminated composites is an important subject and has attracted much attention in the structural optimization field. In practice engineering, there are
14、 many factors that can influence the composites reliability, such as the design philosophy, manufacturing level, material quality and working environments. These factors can be described as random or fuzzy variables. So in an optimum design model, both the probability and the fuzziness may be involv
15、ed in, resulting in the fuzzy reliability and the fuzzy optimization problem. In this paper, the fuzzy reliability and fuzzy constraint are introduced in the reliability optimum design of laminated composites. By applying the fuzzy mathematic theory and the optimum design method, two kinds of fuzzy
16、reliability optimum models are established, and the corresponding solution method is developed. 3 The fuzzy robust design problem of laminated composites is studied. For any optimization problems, generally speaking, there exist a number of uncontrollable variations （due to uncertainties, noise） that can significantly affect the stability of an optimum solution. Practically it is difficult （sometimes even impossible） to eliminate these variations, but we have to account for them in the opt
