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A Study of Rapid Structural Design Method Based on Reduced-basis Method and Its Application

Author: SunJun
Tutor: HuDeAn
School: Hunan University
Course: Mechanical Engineering
Keywords: Reduced-basis method structure design rapid design Finite elementmethod
CLC: O242.1
Type: Master's thesis
Year: 2012
Downloads: 13
Quote: 0
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Numerical simulation is an essential modern design methods. It’s very obvious thatnumerical simulation is able to improve the quality of products while it can alsoreduce the design period, due to which the numerical simulation is the dominant toolfor technicians to handle with the complicated problems of structure design.Nevertheless if the scale of the model become large, the calculation of structure istime-consuming a lot. When combining those structure calculation with optimization,the mentioned problem would be much more worse. Promoting the effectivity ofcalculation at the premise of keeping a enough accuracy is meaningful a lot forstructure design. At this background, lots of abroad and domestic scholars have comeup with several rapid calculation methods, one of which is the hybrid methodconsisted of finite element and reduced-basis method. Several researchs showed thatthis algorithm is robust, but till now nearly all the profit related to this hybrid methodis theorecal, which means there are still lots of work to do to make the method’sapplication into structure design come ture. This paper illustrated two applications ofthe hybrid algorithm. The main work is as follows:1. A method of rapid design was suggested to improve the efficiency of large scaleproblem design. The reduced-basis method and Finite element method werecombined to form a hybrid algorithm, which can calculate different typical cases.The hybrid method reduced the original large scale problem into a smaller one byconstructing a reasonable reduced space, which can reduce computation time andkeep the necessary accuracy. Based on the reduced model, optimal design was carriedout on the structure. Applying the rapid design method that have been illustratedabove into the3D-frame structure. Take the racing car’ body as the model.Combining with optimization algorithm, the reduced-basis method is able to obtainthe content results of design rapidly.2. There is one weakness of The hybrid method, the application of hybrid methodinto a large scale problem will cause too many large scale matrix without parameters,which would require too much memory and bring down the effectivity ofcomputation. Towards this problem, the hybrid method based on sensitivity analysiswas suggested to Bring the hybrid method into the large scale structure consistedwith triangle and quadrangle shell. which is able to testfy the application protentialof the hybrid method. The method improve the usage effectivity of compute memoryand its computation effectivity by partially and explicitly expressing the parameters.The final result shows the hybrid method based on sensitivity analysis is able toobtain the acceptable result for engineering problem. All the work that contained in this paper indicates this hybrid algorithm is suitablefor structure optimization. It is able to calculate various typical cases to improve theeffectivity. When the algorithm is applied towards large scale problem, sensitivityanalysis should be taken to control the total number of matrix without parameters,which would improve the effectivity of calculation a lot. The final result shows thehybrid algorithm’s protential of application into structure design.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Mathematical modeling, approximate calculation > Mathematical modeling
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