Study On The Fuzzy Reliability And The Robust Optimum Design For Laminated Composites

By virtue of its excellent properties, such as the high specific strength and high specific modulus, anisotropy and designability, the Fiber Reinforced Plastics (FRP) has been widely used as structure materials in aircraft, space, marine and automobile, etc. The fibrous composite's strength, its reliability, and the optimum design are important subjects of research. Many achievements have been made in the reliability 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 achievements 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 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, accompanied by many uncertainty factors. The prediction of composites'strength is a very difficult task. And the structure state can't 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 paper, 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 structural 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 reliability of 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 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 involved 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 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 optimization process to ensure that when they occur the optimum design obtained is still feasible and stable. To get an optimum design while ensuring its feasibility without eliminating the source of variations is commonly known as robust optimization.In this paper, the fuzzy robust design methodology is developed and introduced to the laminated composites for the first time. The variations of fiber angle and the ply thickness are incoperated in the model. On the basis of the fuzzy reliability optimum, the robustness of the fuzzy constraint is discussed. Examples are worked out to show the necessity of the robust design and fuzzy robust design.