The Research On Isogeometric Topology Optimization Based On Deep Learning

The rapid development of science and technology in recent years,not only make machine learning,especially deep learning technology,be applied to real life,but also expanded the entire scope of artificial intelligence(AI).These technologies also pro-moted the development of society,and at the same time provided new methods for prob-lems in the engineering field.Topology optimization(TO)is a mathematical method that optimizes the material distribution in the design domain under specified load con-ditions,constraints and performance indicators.Topology optimization is widely used in aerospace,automobile manufacturing,marine engineering,bridge construction and other engineering fields,and it plays an important role in these fields.The research of traditional topology optimization methods is mainly based on the analysis of finite ele-ment method,thus there are still many problems in topology optimization,such as low efficiency,checkerboard phenomenon,grid dependence,etc.,which restrict the devel-opment of the topology optimization field.Therefore,this thesis mainly focuses on the above-mentioned problems in topology optimization,and proposes a new isogeometric topology optimization algorithm based on deep learning.The isogeometric topology optimization methods based on deep learning proposed in this thesis adopt the combination of DenseNet and UNet in its network architectures,while having the advantages of both networks.In addition,unlike the other deep learn-ing based methods,the density distributions in the design domain are represented in the B-spline space.Training related parameters of B-spline through neural networks speed up the whole process,and reduces time consumption.In this thesis,the numeri-cal experiments show that the algorithm is effective in the two-dimensional and three-dimensional cases.In the two-dimensional case,it is compared with the SIMP method in topology optimization,and the accuracy on the test set is more than 97%;in the three-dimensional case,compared with the isogeometric topology optimization method,the accuracy on the test set is more than 98%.At the same time,the method proposed in this thesis can greatly improve efficiency,saving more than 95%of the time in both 2D and 3D situations.The most important thing is that the isogeometric topology optimization method we proposed can eliminate the checkerboard phenomenon.We also discussed the universal applicability of isogeometric topology optimiza-tion methods based on deep learning.In this thesis,the universality is based on the idea that the density distribution parameterization of the B-spline is independent of the dis-crete design domain,thus the B-spline coefficients of the same size can be used under different design domain sizes.In the two-dimensional case,we used samples with de-sign domain sizes of 40×40,60×60,and 80×80 for neural network model training.The results of different design domain sizes show that the accuracy rate exceeds 96%compared with the SIMP method,but other results still need to be improved.In the three-dimensional situation,we obtained samples with the design domain size of 30×30×8,30×30×12 and 40×40×8 in the isogeometric method.The results of three different design domain sizes show that the accuracy rate exceeds 97%compared with the isogeometric topology optimization method,and it also has other excellent perfor-mances.At the end of the thesis,two other examples of different design domain sizes(40×40×12 and 50×30×10)are used to verify the universality of the method.In addition,we analyze the input methods of the neural network model,which verifies the necessity of adding additional information to the input methods of different neural network models.