Research On Several Key Issues Of Mechanical And Structural Reliability-Based Robust Design

The reliability and safe of mechanical structures is one of the major objectives of mechanical structures design. Parameter uncertainty of mechanical structures is inherent in most engineering problems, and loads that are applied to the mechanical structures are same random. Thus, the random structure systems with random parameters subjected to random loads are appeared. The research on reliability of the uncertain systems is very important for design purposes. The reliability analysis of mechanical structures can help the designer to establish acceptable tolerances on mechanical structures and govern the fluctuations of the system parameters for safe operations. In the end, the reasonable mechanical structures could be designed with enough reliability and little cost. Due to design parameters and structural parameters are uncertain, current mechanical structures design practice tends to account for the uncertainties, which include geometry parameters, material properties, loadings, etc. Reliability-based design, reliability-based optimization design and robust design are very advanced ideas. They have extensive application prospects on account of significance in improving product quality and making performance stability. Reliability-based design and reliability-based optimization design utilize reliability theory to deal with uncertainties, and robust design attempts to make the variations of mechanical structures are insensitive to variations of design variables. In practical engineering, the aforementioned methods are very effective to improve engineering design with the consideration of the uncertainties. Unfortunately, these methods usually have been used separately in different design stages for different purposes. Therefore, it is essential to combine the reliability-based optimization theory, the reliability sensitivity analysis technique and the robust design method and to develop a reliability-based robust design approach. The objective of this dissertation is to extend the concept of reliability-based optimization through the use of reliability sensitivity coupled to a reliability-based robust design method for making the reliability of mechanical structures insensitive to the variations of the design variables. In this dissertation, on the basis of summarizing reliability-based design theory, reliability-based optimization design method and idea of robust design in the world, the reliability-based optimization design with arbitrary distribution parameters is solved, the computational method of reliability sensitivity is given, and the reliability-based robust method is presented using the perturbation method, the Edgeworth series, the reliability-based optimization theory, the reliability sensitivity technique and the robust design approach. This dissertation is divided into 6 Chapters and the main productions obtained from this paper are following as: Chapter 1: Introduction. We explicate the engineering background, the aim and meaning of the research; introduce the rise, the concept, the development of reliability-based design theory; narrate briefly advances in reliability-based optimization method and the tendency of the reliability-based optimization approach development, and set forth the significant meaning of the study on the theory & method of robust design. Chapter 2: Mathematics background and basic theory of reliability. First, mathematics theories and methods used by this dissertation are briefly introduced, and then the details of reliability-based theory and reliability-based optimization methods are described in Chapter 2. Chapter 3: Reliability-based optimization design with arbitrary distribution parameters. A practical and effective numerical method of reliability-based optimization design with arbitrary distribution parameters is proposed in Chapter 3. Techniques from the perturbation method, the Edgeworth series, the reliability-based design theory and the optimization technique are employed to present an approach for the reliability-based optimization with arbitrary distribution parameters on the condition of first four moments of original random variables known. The theoretical formulae of reliability-based optimization method with arbitrary distribution parameters are obtained. The approach is appliedto develop the reliability-based optimization design theory with arbitrary distribution parameters. Chapter 4: Reliability sensitivity design. It is very important to research reliability sensitivity of mechanical structures due to difference effects of change in random parameters on the reliability of mechanical structures. In Chapter 4, on the basis of the reliability-based design theory and sensitivity analysis method, a useful and efficient approach of reliability sensitivity is presented, change laws of the reliability sensitivity are given, the influences of design parametric changes on reliability of mechanical structures are studied and theoretic foundation are provided for reliability-based design of mechanical structures. At present, SFEM is very a practical and effective numerical approach for solving reliability of the random structures. Based on SFEM and the reliability sensitivity design method, the reliability sensitivity design approach of complex mechanical structures is proposed. The basic ideal of reliability sensitivity is to ensure quality control at the design stage by minimizing reliability sensitivity of mechanical structures to uncertain variables by proper selection of design variables. Reliability sensitivity is a way to evaluate the performance of mechanical structures when the reliability is under the influences of design parametric changes. Chapter 5: Reliability-based robust design. In Chapter 5, on the basis of the reliability-based optimization design theory, the reliability sensitivity analysis technique and the robust design method, the reliability-based robust design of mechanical structures is discussed and a practical and effective numerical approach of reliability-based robust design for mechanical structures is presented. The theoretical formula for reliability-based robust design is obtained. The reliability sensitivity is added to the reliability-based optimization design model and the reliability-based robust design is described as a multi-objection optimization, in which the minimum of the weight of mechanical structures and the minimum of the reliability sensitivity with respect to the mean value of design variables are taken as objective functions, while including a series of reliability constrains and geometry constrains etc.. The stiffness reliability-based robust design method of mechanical structure is proposed and the application field of reliability-based robust design is developed well in Chapter 5. The stiffness reliability-based robust design attempts to make the...