Research On Real-time Computation Method In Structural Analysis

Due to increasingly fierce competition, it is very important to shorten the design cycles of product. With the increasing of complexity, more parameters should be involved. Thus, the computation cost is also increased correspondingly. It is difficult to satisfy the efficiency demand of the engineering problems by improving the computer techniques. In order to develop the efficiency of complicated structural problems, real-time algorithms are needed to be studied. For optimization design, repeated computations need to be implemented at each iteration. Thus, the real-time algorithm is especially important in optimization designs. In the nearly two decades, many researches were carried out to develop an effective real-time algorithm to solve practical engineering problems. Although a lot of achievements were obtained, many problems in this field weren't solved yet. In this paper, a real-time algorithm—reduced basis method (RBM) is deeply studied. Two improved methods are suggested: inversion reduced basis method (IRBM) and coefficient reduced basis method (CRBM). Furthermore, the two methods are also applied to the structural optimization design.The main innovations of this paper are listed as follows:1. Inversion reduced basis methodFor traditional reduced basis method, the design parameters should be separated from the linear elastic operator. Furthermore, the linear elastic operators of the practical engineering problems can't be expressed explicitly by design parameters. In view of the above mentioned shortcomings of reduced basis method, IRBM is suggested. No matter what the linear elastic operator can or not be expressed explicitly by the design parameters, IRBM can work well. Additionaly, many existing real-time algorithms can't estimate error bounds of the results, which make the accuracy of the results indefinite. On the contrary, the proposed IRBM can predict error bounds. Thus, the intervals of the results of high dimensional problems can be estimated. Finally, IRBM is used to analyze the static and undamped free vibration problems in this study.2. Coefficient reduced basis methodForreduced basis method, it is time-consuming to separate design parameters from the linear elastic operators. The above IRBM can simplify the process, while after the matrix inversion items independent of the design parameters are demanded, which hence makes the computation complex. Therefore, CRBM is developed, which can be used to analyze the structures expressed explicitly by the design parameters. It can also be applied to analyze the structures with elements which are unable to be expressed in an explicit form of the design parameters. In the CRBM, an error estimation method is also provided. CRBM is used to analyze the static and undamped free vibration problems.3. The rapid structural optimization algorithms based on the improved reduced basis methodsAfter variation of parameters, computation of forward problem is needed to carry on in the optimization process. When the structure is complex, it takes a long time to carry out a single analysis procedure. Accordingly the optimization design is difficult to perform. By combining the improved reduced basis methods with optimization techniques, the rapid optimization algorithms of structure are developed. With the variation of the design parameters, the above two real-time algorithms are adopted to construct to improve the computation efficiency.