Research And Application Of Simulated Annealing Algorithm For Structural Optimization

By means of structural optimization, not only the weight of structures can be reduced, but also the strength, stiffness, vibration behavior, buckling stability, and other performances of structures can be improved efficiently. Structural optimization is an important research direction in the computational mechanics and modern design field.The research work in the dissertation consists of two major parts. The first part proposes several improved measures on SA based on the analysis of the SA's theory and recent research of SA according to special property and requirements of structural optimization problems. The second part describes application of improved SA in some types of structural optimization problems. The numerical test and algorithmic comparison show that improved measures on S A are feasible and efficient.The research work will be introduced as follows:In chapter 1, the research developments of SA are surveyed, which include the questions for discussion of background and signification summarized in the first section, and then the history of development and characteristic for SA, research of the theory, a survey of internal and external research and the trend of development, the main contents of the research in this dissertation are presented in the last section.In chapter 2, the process and fundament of simple SA are introduced. The basic of physics are presented firstly. Then the process and the basic mathematics of SA are given. Finally, implementation of SA in a limit time and the principle of choosing parameter in SA are described.In chapter 3, improvements on SA are investigated, which is important substantial about academic algorithm of the dissertation. An improved SA is proposed by several methods being put forward. By introducing a method of adaptive conversion function, the determination of initial temperature, usually a difficult problem in SA has been solved and becomes independent to the practical problems solved. A memory is set up in order to becoming a memorial SA. Combined with the success-failure method and the variable metric method, the conception of effective shift-increment is proposed to improve the method generating new solutions. On the basis of the newly defined relative precision, a termination criterion is proposed to make better balance between the computational efficiency and the solution accuracy, and then, enhance the efficiency and robustness of the SA algorithm. Joined up optimization of continuous variable and discrete variable, the difficult was solved by using the idea of multi-objections.The contents of the following chapter show that the improvements in this dissertation are feasible and effective by some kinds of typical examples.In chapter 4, SA is applied to sizing optimization of truss with continuous, discrete variables and configuration optimization of truss with mixed variables. In sizing optimization of truss with continuous variables, solutions among SA, GA and the traditional methods are compared, which reveals that satisfying solutions are achieved, and that improved SA are feasible and effective, better computational efficiency and solution accuracy achieved. In sizing optimization of truss with discrete variables, joined up optimization of continuous variable and discrete variable, the idea of multi-objections is used. In configuration optimization of truss with mixed variables, the method generating new solutions is improved.The numerical examples show that the improved SA in the dissertation are feasible and effective.In chapter 5, the main contributions of the dissertation are summarized and the further work is suggested.The research of this dissertation is supported by the Special Funds for National Key Basic Research of China (No. G1999032805) and the Special Funds for National Key Research of China in natural science (No. G10032030).