Research And Application Of Fast Reanalysis Methods For Vehicle Optimization

Reanalysis indicates that when the structure is modified during the process of design,the modified structure could be efficiently re-analyzed by using the data from initial analysis.Reanalysis methods can be calssified as approximate methods and Direct Methods(DMs).Approximate methods can be used to deal with high-rank or global modifications,but usually can only obtain approximate solutions or modified structures.On the contrary,DMs are suitable for low-rank or local modifications,but many DMs can obtain exact solutions of modified structures.Compared with full analysis,the efficiency of reanalysis is obviously enhanced.Theoritically,reanalysis methods can be used to solve different mechanical problems,incuding linear elastic analysis,dynamic analysis and nonlinear analysis,and can also be applied to many other areas,such as electromagnetism and thermology problems,which makes it potential to be applied in structural optimization design.However,the current mainstream reanalysis methods have many constraints,which severely restricts the application of reanalyhsis methods in practical engineering design.In purpose to deal with the drawbacks of reanalysis and break the bottleneck in application,this thsis makes some supplements and extensions for reanalysis,and applied it into vehicle optimization design.Optimization problems widely exist in every stage of vehicle design.In vehicle design,the objective functions and constraints are usually black-box functions.Generally,classical mathematical programming methods are not suitable for this kind of problems,because the first order derivative(gradient)and even second order derivative(Hessian matrix)are usually necessary.Therefore,heuristic algorithms are often suggested to solve these problems.However,the shortcoming is large amount of function evaluations are needed.In vehicle design,a function evaluation usually means a large scale simulation.Therefore,the efficiency of optimization can not be guaranteed.For this problem,the mainstream solutions are usually based on surrogate techniques.This strategy can significantly improve the efficiency of optimization,but will cause a fitting error of surrogate models.Moreover,these errors are usually unpredictable and uncontrollable,which means that when designers use surrogate models,they always take a risk of wrong results.Reanlaysis can be used in vehicle optimization design as an alternative solution of surrogate.Compared with surrogate models,the accuracy of reanalysis is higher,and the errors are controllable,thus the optimal results will be more reliable.This thesis aims at enhancing the feasibility of reanalysis,and researches reanalysis from thoeritial study and practical application simultaneously.The main research contents are as follows:(1)Developed modified combined approximation(CA)and multi-grad assisted reanalysis method as extension of approximate reanalysis methods.Modified Combined Approximation(CA)can reanalyze ill-conditioned equations with singular stiffness matrix by integrating Singular Value Decomposition(SVD)and CA.Multigrid assisted reanalysis method can be used to dealing with large mesh change after modification.Existing reanalysis methods generally require a high consistency between initial mesh and modified mesh.Specifically,the number and coordinates of the nodes should be unchanged after modification,except for the part related to the modification.This is difficult for CAD technique to guarantee.The multi-grid assisted reanalysis method can establish a association between initial mesh and modified mesh using transfer operators,and map the stiffness matrix from modified mesh to initial mesh.Therefore,mesh consistency is no longer necessary.(2)Developed Independent Coefficients(IC)and Indirect Factorization Updating(IFU)methods as extension of DMs.Compared with traditional reanalysis methods,the inverse of initial stiffness matrix is unnecessary for IC,thus large amount of storage can be saved for large scale problems.Moreover,only initial result are required as input information,therefore,IC can be used together with any available initial analysis method.The IFU is an exact reanalysis method,and the efficiency can be impressive while dealing with low-rank modifications.IFU provides a method to convert the local modifications into low-rank form,which can cover the shortage of current DMs research.(3)Structural optimization system based on reanalysis and CAD/CAE integration.A CAD/CAE integration strategy based on subdivision is further developed.Subdivision surfaces using triangle mesh are used for CAD modeling and CAE analysis simultaneously.Feature objects are defined on subdivision models.By constructing a data structure of ‘key points – feature lines – feature surfaces',the mesh model can be controlled by a series of geometrical parameters.Therefore,the geometrical optimization procedure becomes a closed loop.Reanalysis methods are integrated with a global optimization method,Genetic Algorithm(GA)to solve the optimization problem.The high efficiency of reanalysis and global convergence of GA are combined.Without using of popular surrogate model,the modeling errors can be avoided,and a global optimal solution can be guaranteed.To improve the analysis accuracy of triangular mesh,the Edge based Smooth Finite Element Method(ES-FEM)is employed.A graph theory based edge structure constructing strategy is suggested to construct edge structure efficiently for ES-FEM,therefore the efficiency and feasibility of ESFEM can be much enhanced.(4)Reanalysis based optimization method for variable-stiffness fiber composite.Path functions are defined based on previous researches.The contour lines of functions can be used to describe fiber paths by using new developed path function.The parameters of the path functions are used as design variables,and the optimization object is calculated using Finite Element Method(FEM).The variable-stiffness composite laminate is formulated using FEM based on Mindlin shell theory.Manufacturing constraints are considered by examining the curvature and parallelism of fiber paths defined using path functions.In order to improve the efficiency of optimization,reanalysis methods are employed to accelerate the optimization process.By using the reverse method of composite material parameters based on reanalysis,the mechanical parameters of fiber composite can be efficiently obtained from experiment data,thus the premise condition for fiber composite optimization can be prepared.