| Hierarchical sandwich structure is a new type of lightweight structure that combines the excellent mechanical properties of hierarchical structure and sandwich structure,with higher specific strength and specific stiffness,and has a wide application prospect in aerospace,navigation,civil engineering and vehicle engineering.As a typical structure in the hierarchical sandwich structure,the corrugated hierarchical structure with a second order core has excellent mechanical properties and various failure modes,and different failure modes will occur in different order of the structure.At present,the research on mechanical properties and failure mode,lightweight optimization design and experiment of the corrugated hierarchical structure with a second order core is not perfect,and there are many differences between the theoretical analysis results and the experimental results.Based on the theory of elastic beam,the mechanical properties and failure mode of hierarchical corrugated structure with a second order core were studied using theoretical analysis,simulation and validation experiment.The influence of geometrical parameter variation on structural failure mode is also discussed.the theoretical prediction failure model is verified and two optimal design models with different performance requirements are established for secondary hierarchical fold structures.The main conclusions of this article are shown:（1）Based on the elastic beam theory,considering the local failure defects of the structure,the mechanical analysis of the original structure system of hierarchical corrugated structure with a second order core and the structure system under local failure defects is carried out,and six possible failure modes of hierarchical corrugated structure with a second order core under local failure defects are given.According to the characteristics of each failure mode,it is divided into three types:failure of small struts,failure of the larger strut face sheets and failure of the over all structure.The formulas of nominal normal stress and nominal shear stress corresponding to each failure mode are given.（2）Through the dominant relationship among the failure modes,when t1/l1 and t/l are in the range of 10-4～10-1,the failure mechanism diagram of the structure is drawn,and the influence of the change of geometric parameters on the failure modes of the structure is analyzed.The effects of inclination angleθandθ1 on the failure mode for the original structure system and the influence of parameters l1/l,θandαon the structural failure mode under local failure defects are discussed.Combined with the finite element simulation,the correctness of the influence of geometric parameters on structural failure mode is verified,and the finite element analysis results are in good agreement with the theoretical prediction.（3）Using photosensitive resin material,the verification experimental model was made by 3D printing technology.and the correctness of the mechanical properties and failure mode of the corrugated hierarchical structure with a second order core were further verified by uniaxial compression of the experimental model.The failure modes obtained from the experiments are consistent with the theoretical prediction,and the relative error between the two ultimate bearing capacities is only 0.125%,which proves that the theoretical prediction has a good prediction accuracy.（4）Considering the characteristics of rich failure modes and special configurations of the corrugated hierarchical structure.With geometrical parameters of the structure as design variables and structural material consumption（relative density）as optimization goal,two optimization design models based on specific failure mode constraints and specific failure sequence constraints were proposed for the structure,respectively.The two optimization designs were verified by examples.The results show that the performance indexes of the structure were greatly improved after optimization design,which which provides a reference for the designers to get a relatively ideal structure model. |
