Research On Topology Optimization Methods Of Continuum Structure Based On Element Exchange Method

The structural optimization is the crucial technology in product designing, which helps the designer to reach the goal that with fewer materials cost but much better property fulfill the requirements got. The most important and challenging point in structural optimization is topological optimization, during the conceptual design period; most of the improvements of the structural property and the decrease of cost are based on the structural topological optimization. The topological optimization is acknowledged as the most effective way in improving designing efficiency, and become the hottest issue in the field. Because of the complexity of the topological optimization modeling, many theoretical, modeling and algorithmic studies are immature in practical engineering use, especially to some complex models, the solving efficiency is unacceptable. Thus, in order to find a much more effective and wider application range, topological optimization is certainly becomes the most important and hottest issue nowadays.Through the overall observation of domestic and abroad, based on the study of the topological problems in model solving, this thesis addresses a topology optimization method based on Exchange element method (EEMTO), EEMTO is much quicker in solving than the OC methods. Aimed at the mathematical instability of the SIMP model solving, the Exchange Element Filter method could eliminate the checkerboard numerical instability phenomenon effectively. And several application examples have proved the validity and superiority of the EEMTO and the Exchange Element Filter Method.First, the continual topological optimization process is given based on the EEM method. Based on the variable density method, set up the continual rigidity optimization model for solving, with the constrain of the optimization criterions, with the help of EEM's concept, improved the iterate operator present the EEMTO method, and carry out the algorithm with Matlab codes. The results have showed that the EEMTO could make the function to convergent and find the best solution much quicker, improved the quality and efficiency of solving and optimizing.Secondly, aimed at the numerical instability in the topological optimization, addressed the Exchange Element Filter Method with the EEM method concept. The structure in each iteraction, use the Checker Control and the Exchange Element operation to refresh the element information, reduced the steps of filter, improved the efficiency, and improved the property of structural production.At last, through some practical examples, the validity and superiority of the EEMTO and the Exchange Element Filter Method has been demonstrated. The superiority of the Exchange Element Filter Method also has been proved by several engineering practical examples.