Research On Buckling Analysis And Optimization Methods Of Hierarchical Cylindrical Shells Based On Multi-fidelity Modeling

Due to the high specific stiffness and strength,thin-walled cylindrical shell structures have been widely used in main load-carryling structures of launch vehicles such as fuel tanks and inter-stages.In comparsion to traditional cylindrical shell structures,hierarchical cylindrical shell structures developed based on biologic inspirations possess multiple structural or material hierarchies,which contributes to increasing the load-carrying capacity and reducing the material cost of cylindrical shell structures.However,the increase of structural or material hierarchies would result in low buckling analysis efficiency and weak global optimizing ability for hierarchical cylindrical shell structures.To solve these problems,research on buckling analysis and optimization methods was performed for hierarchical cylindrical shell structures including hybrid fiber composite shells and hierarchical stiffened shells in this paper.First,linear buckling analysis and optimization methods were developed for hybrid fiber composite shells based on POD model reduction method,which could increase the computational efficiency of linear buckling analysis and optimization for hybrid fiber composite shells with stiffness mutation.Then,linear buckling analysis and optimization methods were developed for hierarchical stiffened shells based on the NIAH equivalent method,which could increase the computational efficiency of linear buckling analysis for hierarchical stiffened shells.Furthermore,the post-buckling optimization method was developed for hierarchical stiffened shells based on the adaptive equivalent strategy,which could increase the computational efficiency of post-buckling optimization for hierarchical stiffened shells.Moreover,the evaluation method for the prediction accuracy of buckling modes and the model updating method were developed for the equivalent models of stiffened shells.Based on these methods,the optimization framework of fast prediction of the knockdown factor of stiffened shells was established.Finally,the surrogate-based post-buckling optimization method was proposed based on the multi-fidelity competitive sampling method,which could contribute to improving the global optimizing ability of the surrogate-based post-buckling optimization for hierarchical cylindrical shell structures.The main content of this thesis is as follows:(1)With respect to hybrid fiber composite shells with stiffness mutation,linear buckling analysis and optimization methods were developed based on POD method.First,the reduced-order eigenvalue buckling formula were derived based on POD method.Next,the effective assembly method and the update strategy of POD bases were proposed,and then the POD buckling analysis and optimization framework was established with offline-online-update steps.Illustrative examples of the low-cost and ply angle optimizations of hybrid fiber composite shells were carried out.In comparison to the detailed finite element method,the high prediction accuracy of the proposed method in buckling load and buckling mode was validated,and the high prediction efficiency of the proposed method for the linear buckling analysis and optimization of hybrid fiber composite shells with stiffness mutation was demonstrated.(2)With respect to hierarchical stiffened shells with complicated geometrical configurations and multiple buckling modes,an efficient,stable and widely applicable linear buckling method was developed based on NIAH method and Rayleigh-Ritz method,which could fast predict the linear buckling load and buckling mode for hierarchical stiffened shells.The proposed method has overcome the shortcomings of SSM that the prediction accuracy is relatively low and the applicability is relatively weak.(3)In order to increase the computational efficiency of the post-buckling analysis method based on the explicit dynamics method,an efficient post-buckling analysis method was developed for hierarchical stiffened shells based on the adaptive equivalent method by means of NSSM,which could provide reasonable eqivalent concepts for the post-buckling analysis model of hierarchical stiffened shells.Furthermore,a surrogate-based post-buckling optimization framework was established for hierarchical stiffened shells based on the fixed-point method.By comparison against the traditional optimization method,the proposed optimization method had outstanding convergence speed,optimization efficiency and global optimizing ability.(4)With respect to the high computational cost of the surrogate-based optimization for the knockdown factor prediction of stiffened shells,an optimization framework of fast prediction of the knockdown factor of stiffened shells was developed based on the model updating method.First.Modal Assurance Criterion(MAC)coefficients were defined for stiffened shells,in order to evaluate the prediction accuracy of buckling modes.On the basis of MAC coefficients,the model updating method was developed for the equivalent model of stiffened shells,in order to increase the prediction accuracy of the equivalent model in buckling load and buckling mode effectively.Finally,an optimization framework of fast prediction of the knockdown factor of stiffened shells was established.In comparison to the traditional method,the proposed method could reduce the computational time greatly.(5)With respect to the post-buckling optimization problem of hierarchical cylindrical shell structures with multiple variables,multimodal and multiple constraints,the surrogate-based post-buckling optimization method was established based on the multi-fidelity competitive sampling method,by combining the high efficiency of equivalent models or reduced-order models and the high accuracy of detailed models.In comparison to the traditional optimization method based on Latin hypercube sampling,the proposed method could reduce the design space reasonably,avoid the blind sampling and guarantee the competitiveness of each sampling point based on the high-fidelity model.And the outstanding global optimizing ability of the proposed method was also demonstrated.