Research On Spatial Mapping Algorithm Based On Reanalysis

Optimization design is a reliable design method,which is widely used in all aspects of automotive design.With the development and maturity of computer technique and numerical method,FEM-based computer simulation technology is also widely used in automotive design.Optimization design method integrated with computer simulation technology can effectively deal with many engineering design problems.However,the computational cost of evaluation in the design procedure is an essential bottleneck for simulation-based applications.To improve the efficiency of simulation,multiple strategies,such as surrogate,reanalysis,dimension reduction and others,have been developed.Space mapping(SM)is an important branch in this discipline.The idea of SM is utilized to construct the projection between fine and coarse models.During SM-based optimization,the coarse model is mainly utilized to determine the search direction while the fine model is utilized only to revise the coarse model for the next iteration.Compared with direct optimization method(without coarse models),the efficiency of SMs can be significantly improved.With the development of SM technique,the application had extended to structure optimization,crashworthiness design,sheet metal stamping and other fields gradually.Recently,more complicated problems have been solved by SMs by importing the finite element method(FEM).However,with the increase of complexity of physical models,it is still difficult for the SM to handle complicated practical problems,especially for high dimensional nonlinear problems.Therefore,in this study,an efficient computational method,reanalysis method is integrated with the SM.The reanalysis-based SM(RBSM)algorithm is suggested based on the SM algorithm,reanalysis and optimization methods,which is far more efficient and more accurate.Compared with surrogate assisted evaluation,the accuracy of reanalysis method is significantly improved due to introduction of equilibrium equations.Compared with reduced basis methods(RBMs),reanalysis methods can solve more complicated problems in multidiscipline.Generally,compared with other SM algorithms,coarse and fine spaces are based on solvers instead of models,which extends the concept of coarse and fine models.Due to the high accurate reanalysis method,the reanalysis-based SM algorithm is easier to converge.Moreover,to integrate geometry and finite element models easily,a B-rep based reanalysis method is also introduced.To verify the performance of the suggested method,two examples have been carried out by using reanalysis-based SM algorithm.According to the results,the efficiency of optimization procedure is improved significantly.For variable stiffness(VS)composite hole plate problem,it is shown that the suggested method could deal with high dimensional nonlinear problems,which makes the application of SMs more extensive.Finally,we design a Matlab/GUI-based SM optimization toolbox graphical interface,providing a simple and convenient operating platform for end users.