The Dynamic Optimization For Uncertain Structures With Interval Parameters

In many practical engineering problems, the structural parameters are uncertain, for example, the inaccuracy of measurements, errors in manufacture, etc. Therefore, the concept of uncertainty plays an important role in the investigation of various engineering problems.The most common approach to uncertain problems is to model the structural parameters as random variables or fields. In this case, all information about the structural parameters is provided by the joint probability density function(or distribution function) of them. Unfortunately, the probabilistic modeling is not the only way we can use to describe the uncertainty, and uncertainty is not tantamount to randomness. In many cases, the uncertainty phenomena do not have a stochastic nature. The reason why many researchers studying uncertain problems utilize stochastic modeling is that this randomization is the result of an established scientific stereotype. Indeed, probabilistic approaches are not able to deliver reliable results without sufficient experiment data.Since the mid-1960's, a new method called the intervalanalysis has appeared. Moore and his co-workers, Alefeld andHerzberger have done the pioneering work. Mathematically, the linear interval equations and nonlinear interval equations have been resolved. But because of the complexity of the algorithm, it is difficult to apply these results to practical engineering problems. Recently, Chen, Qiu ,etc. have used interval method in the study of the static response and eigenvalue problems of structures with bounded uncertain parameters. In their studies, several important results have been obtained, using interval analysis and matrix perturbation techniques. However, these results are based on the assumption that K, f are pre-selected in the equation K(a)U = f(a) and K, M are also pre-selected in the equation K(a)U = M(a). In general, K , M and Af are functions of the structural parameters, so they must can be calculated according to the uncertainties of the structural parameters. Yang Xiaowei and Lian Huadong have presented some effective interval methods for structures with interval parameters. Hansen in his book discussed the global optimization using interval analysis. Because of the complexity of the interval algorithm, it is difficult to deal with practical engineering problems. Recently, the interval analysis method has been used to deal with the static displacement and eigenvalue analysis of the uncertain structures with interval parameters. However, few papers can be found about the optimization of structures with interval parameters in engineering. Hence, it is necessary to develop an effectivemethod to solve the optimal problems of structures with interval parameters. This paper presents an interval optimization method based on the interval analysis.In this paper, on the basis of the work of Yang Xiaowei and Lian Huadong, some problems are discussed:1. In chapter 4, a dynamic interval optimization method for discrete systems with interval parameters is presented.2. In chapter 5, a dynamic interval optimization method for continuous systems with interval parameters is presented.3. In chapter 6, an interval optimization method of dynamic response for uncertain structures with natural frequency constraints is presented.4. In chapter 7, an interval dynamic optimization method for uncertain structures using the improved 1st-order Taylor expansion is presented.