Second-order Approximation Dynamic Optimization For 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 interval analysis 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. 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 thatΔK ,Δf are pre-selected in the equation K (α)U= f(α) andΔK ,ΔM are also pre-selected in the equation K (α)U=λM(α). In general,ΔK ,ΔM andΔf 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. Wu jie have presented first-order dynamic optimization of structures with interval parameters in engineering based on interval analysis. However , there are few paper about second-order dynamic optimization of structures with interval parameters in engineering based on interval analysis. Hence, it is necessary to develop an more effective and more accurate second-order method to solve the dynamic optimal problems of structures with interval parameters. This paper presents a second-order interval optimization method based on the interval analysis.In this paper, on the basis of the work of Yang Xiaowei, Lian Huadong and Wu jie, the second-order approximation optimal problems are discussed: 1. In chapter 4, the background of the second-order optimizal method is presented.2. In chapter 5, a second-order dynamic interval optimization method for structures with interval parameters is presented.3. In chapter 6, the impletement of CAD/CAE/CAM software are presented and the core commands and modules of the I-DEAS open solution are discussed.