Structural Topology Optimization Of Boxing Girders Based On Variable-density Method

Engineering structure optimization design is regard as an efficient design tool forimproving service life, reducing parts manufacturing costs and energy consumption. It hasbecoming the focus of the research on industrial design. It is significant for product designespecially in the initial stage. As the main theoretical algorithm for topology optimizationdesign, variable-density method turned to be the fundamentals of algorithmics in topologyoptimization of mainstream finite element software, and widely used in lightweight designof automotive and machinery industries. Researching on its theory and improving theadvantages and disadvantages are always research hotspot for optimization designers.The main contents of this dissertation are as followed.(1) It has provided an overview of the development of structural optimization, thedomestic and foreign development present situation and current problems. The necessityand feasibility for topology optimization design of boxing girder based on variable-densitymethod have been put forward.(2) It has described that the basic concepts, mathematical models, level, classificationand technology roadmap of structural topology optimization problems.The research on thebasic principles and characteristics of each common optimization algorithm for continuumstructural topology optimization was carried on. The analysis of numerical instability intopology optimization iterative was made.(3) On the basis of the research on the theory of variable-density method, Iterativeformula and mathematical models of topology optimization based on variable-densitymethod were derived. For numerical instability, the theoretical formulas of interpolation models were brought up, and a typical example was given.(4) Based on the research of static analysis and results of boxing grider structure, alarge number of low-stress units on girder were found. The application of topologyoptimization iteration formulas and mathematical models based on variable density methodhas made for optimizing the webs of girder. The numerical instability were handled and thefinal results of the topology optimization was obtained by the theory and formulas ofinterpolation models. Compared with analytical results of the original model, the border ofthe final results was so clear to meet the actual processing needs.