The Research On The Optimization And Design Of Variable Stiffness Composite Material Based On The Surrogate Method

Due to excellent flexible designability and mechanical properties,Fiber reinforced composites(FRCs)are widely used in the automotive lightweight design.According to the requirements of the mechanical performance for the FRC,the design of the FRC needs to find an optimum composite laminate and fiber path to maximize the mechanical properties of the composite material under different loading conditions.The ideal composite structure is the Variable Stiffness composite with curve fiber path.However,due to the large-scale design and time-consuming computation of the curve fiber path design,the optimization design of variable stiffness composites is more difficult and complex compared with the constant stiffness composite with straight fiber path.The traditional method to deal with the optimization design of variable stiffness composite materials is meta-heuristic optimization algorithm.However,to obtain relatively reliable optimization results,this method needs thousands of sample points on the optimization design problem,which makes the optimization method time-consuming and unacceptable.Recently,the Efficient Global Optimization(EGO)algorithm based on the surrogate model is widely applied to deal with the time-consuming optimization problem.In this paper,the design of variable stiffness composites based on the EGO algorithm are studied as follows:(1)The EGO algorithm framework is established based on Expected Improvement(EI)criterion,which can extend the standard EGO algorithm to the Single-Surrogate Efficient Global Optimization(SSEGO)based on arbitrary Single surrogate model.To investigate the pefromance of SSEGO algorithm,multi-Surrogate Efficient Global Optimization(MSEGO)is introduced.Moreover,the evaluation method of SSEGO and MSEGO algorithms is established.Two performance evaluation criteria based on EGO algorithm are proposed to describe the global exploration ability and local exploitation ability of EGO algorithm in the optimization process.Compared with standard EGO algorithm and MSEGO,SSEGO can deal with more kinds of optimization problems.In addition,reasonable combination of surrogate models can effectively improve the optimization efficiency of MSEGO algorithm.To investigate the performance of SSEGO and MSEGO algorithms in practical engineering applications,an engineering test benchmark based on material inverse problem was proposed.According to the benchmark results,SSEGO algorithm has high optimization efficiency.(2)In this paper,Least Square Support Vector Regression(LSSVR)assisted EGO optimization method(LSSVR-EGO)is proposed and applied to improve the buckling load of variable-stiffness composite plate and cylinder.The optimization results demonstrate that the buckling load of the composite plate and cylinder is higher than the constant stffiness composite with straight fiber path.In addition,to verify the robustness of the optimal design of the variable stiffness composite cylinder,the optimal results of the variable stiffness composite cylinder are perturbed.The results demonstrate that the optimal design of variable stiffness composite cylinder is robust.(3)Augmented Tchebycheff Assisted Ensemble Surrogate Multi-Objective optimization method(ATAESMO)is proposed to deal with the multi-objective optimization design problem.To select surrogate model with the high accuracy in the optimization process,an accuracy assisted Tchebycheff combination method of Ensemble Surrogate method is proposed.Fristly,with the evaluation of the accuracy of multi-surrogate model,the method uses the Tchebycheff function to weights the multi-surrogate model with the accuracy and applied to the prediction of the objective function.Meanwhile,the multi-objective EI criterion based on the single objective EI criterion,also known as Expected Hypervolume Improvement(EHI),is combined with the surrogate model method and applied to the optimization method.Numerical results demonstrate that ATAESMO has high optimization efficiency,and its optimization results have good robustness.In this paper,an Elastic-Plastic Representative Volume Element(EPRVE)meso-scale finite Element model is proposed to predict the stress-strain response curve of fiber reinforced composites under cyclic loading.To obtain the material properties of EPRVE,ATAESMO algorithm is applied.Numerical results demonstrate that ATAESMO algorithm has high optimization efficiency.Moreover,ATAESMO algorithm can obtain the high accuracy stress-strain curve of fiber reinforced composites under cyclic loading.(4)A multi-scale material/structure integration optimization framework for variable stiffness composite cylinder is established,which can simultaneously optimize the fibers volume fraction in hybrid composite materials and the curve fiber path of variable stiffness composite.Firstly,a hybrid composite structure based on four fiber types is proposed.To obtain the mechanical properties of hybrid composites,a meso-scale finite element model based on RVE is introduced,and the mechanical properties of the meso-scale finite element model are obtained by using the asymptotic homogenization theory.Moreover,to improve the computational efficiency of the meso-scale finite element model,the surrogate assisted RVE(SARVE)finite element model is proposed and applied to obtain the mechanical properties of hybrid composites.Then,ATAESMO method is applied to maximize buckling load of the variable stiffness composite cylinder with the minimum material cost,which obtain the optimal material/structure design of the variable stiffness composite cylinder.Moreover,to investigate the location influence of fiber orientation angle for the curve fiber path,an exponential curve fiber path method is proposed.The optimization results demonstrate that the fiber volume fraction of hybrid composites and the curve fiber path have a significant influence on the mechanical properties of variable stiffness composite cylinders.The proposed optimization method can effectively reduce the material cost and improve the buckling load for the variable stiffness composite.