Research On The Mechanical Properties Of Grid Beetle Elytron Plate Based On The Equivalent Model Of Core Layer

Grid beetle elytron plate(GBEP)is a new type of lightweight and high-strength sandwich plate structure inspired by bionic research on the microstructure of the beetle’s forewing.Experimental studies have shown that the mechanical properties of GBEP,such as compression,shear,and energy absorption,are significantly superior to common sandwich plates such as honeycomb plates,and have great application potential.However,the current research on GBEPs is mainly based on experimental and finite element analysis,and there have been no reports on theoretical prediction and optimization.At the same time,with the deepening of research on mechanical properties,it is necessary to conduct finite element analysis on a large number of multi-scale models,resulting in an increasingly large computational workload.The efficiency of existing experimental research methods can no longer meet the requirements.In order to achieve the practical application of GBEP,a highquality structure,in many fields with huge differences,such as aerospace,shipbuilding,and building structures,it is necessary to conduct mechanical properties research on plates of various sizes,propose relatively complete and accurate mechanical properties calculation methods,and ultimately provide a simple and efficient design method for such structures based on actual engineering characteristics.In order to solve the problems of calculation difficulties and lack of theoretical studies in GBEP researches,based on previous research on sandwich panel structures such as honeycomb plates,combined with the structural characteristics of GBEPs themselves,based on discrete layer theory(also known as sandwich theory),the basic unit of GBEP core layer was selected as the research object.The mechanical properties of GBEPs were studied theoretically for the first time,and their equivalent elastic moduli,equivalent Poisson’s ratios,the equivalent shear moduli and equivalent yield strength in the core layer are used to establish an equivalent model of the GBEP core layer.The accuracy and efficiency of the equivalent model in calculating various load cases were verified using finite element and experimental methods,the mechanical properties were studied accordingly,and the method of analyzing and calculating GBEP based on its core equivalent model is finally proposed.The main conclusions are as follows:(1)The expressions for the in-plane and out-of-plane equivalent elastic moduli and Poisson’s ratios of the GBEP core layer unit are calculated and organized with dimensionless parameters(ratio of trabecula radius to wall thickness)and(the ratio of trabecula radius to the side length of the unit),which are verified by finite element simulation to have a high accuracy in a large size range.Compared with honeycomb and grid plate units,the results show that the compressive stiffness of GBEP in the core layer has a significant advantage over honeycomb plate,but is weaker than grid plate.(2)By calculating the in-plane and out-of-plane equivalent shear moduli expressions of the grid beetle elytron plate and the grid plate,the advantages of the mechanical properties of the core layer of the GBEP with a honeycomb-trabecula structure were theoretically proved.The obtained expressions have been verified by experimental and finite element results,and the calculation accuracy is good.The concept of stiffness per unit volume(SPUV,expressed by)was proposed to measure the stiffness produced by a unit volume of material.The results showed that,under the circumstance of same wall thickness,the in-plane and out-ofplane shear stiffness of the GBEP was greater than that of the grid plate,but the out-of-plane shear SPUV was slightly lower than that of the grid plate.(3)The equivalent yield strength of the GBEP under in-plane compression was calculated,and the equivalent model of the GBEP core layer was preliminarily completed.Finite element and experimental studies have shown that the equivalent model of the GBEP core layer has good computational accuracy under different size parameters,and compared to the original finite element model,the equivalent homogeneous model can greatly reduce the number of finite elements and improve computational efficiency.Based on the core layer equivalent model,the in-plane compression performance of GBEPs under lateral loads was investigated,and the optimal size parameters under this condition were determined.The feasibility of using the core layer equivalent model to study the mechanical properties of GBEPs was preliminarily verified.(4)For 43 types of GBEP models with different size parameters,the computational accuracy and efficiency of the finite element models before and after equivalence in calculating their in-plane shear and three-point bending properties were verified.It was found that the GBEP core layer equivalent model can reach good accuracy and high efficiency in calculating the multi-scale model subjected to different loads,and is a great substitute for the original model.The equivalent bending stiffness expression of GBEP core unit with upper and lower sheets is derived,and the stiffness coefficients in three-point bending mid-span are calculated in some cases.(5)In order to investigate the out-of-plane buckling behavior of GBEPs,the expressions of out-of-plane buckling loads for grid wall and trabecula were derived.In this process,the Flügge’s formula for calculating the buckling load of cylindrical shells has been modified,and a theoretical formula closer to the experimental value has been obtained.According to the buckling process,the influence of the buckling order of grid wall and trabecula on the overall buckling load is revealed,which enriches the connotation of the honeycomb-trabecula synergistic mechanism.