Study Of The Geometric Configuration Of The Vertex-based Hierarchical Thin-wall Structure And Their Mechanical Behaviors And Applications

Specialised energy-absorbing structures are the core technical devices for the passive safety protection of trains.With higher design standards for transport equipment,new energy-absorbing structures with better performance need to be developed.The Vertex-based Hierarchical Thin-wall structure（VHT）combines the concept of bio-hierarchical structures with traditional thin-walled structures to significantly increase the upper limit of mechanical properties of existing structures.However,most of the existing studies have been limited to the assessment of the mechanical properties of low-order VHTs,and the geometrical configuration and evolution of VHTs have not been elucidated,thus failing to reveal the evolution of their mechanical behaviour with order and limiting the design and application of such structures.To address the above issues,a combination of mechanical experiments,numerical simulations and theoretical analyses are used to study two typical types of VHT structures,Vertex-based Hierarchical Square（VHS）and Vertex-based Hierarchical Honeycomb（VHHC）,using the mathematical idea of moving from the particular to the general.The study of the geometric configuration and evolution,in-plane static properties and out-of-plane energy absorption properties of VHTs is carried out systematically to reveal the evolution and convergence of their mechanical properties and behaviour with order,and to propose ideas for the design of energy-absorbing structures based on VHTs.The main elements and innovative work are as follows:Transforming the qualitative description of VHT based on fractal geometry into a quantitative description of Euclidean geometry provides the basis for studying its mechanical properties.Based on the existing geometrical configurations of VHT,the configurations are classified into two categories based on the inner and outer circular configurations of polygons;the concepts of mathematical levels and construction ratios are introduced to characterize the infinite iterative and self-similar properties of VHT,respectively,to achieve quantitative representation of the VHT construction process and obtain its subset types and design space;the local and overall geometrical compatibility conditions of the iterative evolution of VHT are explored to quantify its construction laws;On this basis,the VHS and VHHC are deconstructed separately by the cut-and-complement method to establish the equimass-based calculations of the wall thickness and relative density of the structure,and to generalise the expressions and geometric meanings of the corresponding calculations of the VHT;the wall thickness convergence values of the VHS and VHHC of order 1 are obtained separately by using limit analysis,and the convergence conditions and convergence values of the VHS wall thickness with order are elucidated by using the D’Alembert discriminant method.A theoretical model of the in-plane static behavior of VHS and VHHC is developed,and the optimal design intervals for the relevant mechanical properties are obtained,revealing the customisable characteristics of their in-plane mechanical properties.The in-plane elasticity experiments are used to verify the accuracy of the simulation method,and then a parametric study of the in-plane elastic behaviour of VHS and VHHC based on numerical simulations is carried out to statistically derive the optimal design intervals for the equivalent mechanical parameters of VHS and VHHC based on the construction ratio.The unified theoretical equations for the in-plane equivalent of Young’s modulus and Poisson’s ratio are obtained by using the energy method;the comparison with the results of the first-order VHS considering the axial deformation of the beam confirms that the computational efficiency of this model is significantly better than that of the existing models under large constitutive ratios,and reveals the evolution mechanism of the in-plane mechanical behaviour of VHS under the influence of the constitutive ratios.The theoretical calculation is combined with numerical results to investigate the wide variation of the equivalent Young’s modulus and Poisson’s ratio in the VHS and VHHC faces concerning the constitutive ratio and order,which provides a theoretical basis for the tailoring of the relevant mechanical properties.A theoretical model is constructed to characterize the out-of-plane energy absorption characteristics of VHS and VHHC,and the optimum design intervals for the relevant mechanical properties are obtained.The influence of order on the out-of-plane energy absorption characteristics of VHS and VHHC is investigated using out-of-plane quasi-static crushing experiments,and the reliability and accuracy of the numerical simulation method are verified.On this basis,the optimal design interval and wide variation of specific energy absorption and average load of VHS and VHHC based on the constitutive ratio are found;through the classical Super Folding Element model,the theoretical equations of half-wavelength and average load of VHS and VHHC are derived by applying the idea of discretization;by combining the simulation deformation mode and the theoretical results,the three types of surface absorption of VHS and VHHC are revealed.The three out-of-plane deformation mechanisms of VHS and their causes are revealed;the simulation and theoretical analysis of a given VHS show that the convergence of its average load is determined only by the construction ratio function,while its dimensionless average load varies with the 1.67th power of the thickness.From an engineering point of view,the five-hole honeycomb end absorber for high-speed trains is used as a carrier to obtain the energy absorption performance indices through numerical simulations as reference parameters for the design of VHT-based train end absorbers;Two different design ideas for VHT energy absorption devices are proposed,and the out-of-plane energy absorption performance of the new structure is evaluated through numerical simulations;the results show that the new design of the 1^st-order VHHC achieves an overall improvement in energy absorption performance by increasing the specific energy absorption and average load by33.3%and 22.6%respectively compared to the 5-holes honeycomb,with the peak force reduced by 5%.In summary,this study normalises the geometric configuration of VHT for the first time,elucidates the relevant mechanical properties and behaviour of VHT with the evolution process of layers,reveals the optimal design interval of the mechanical properties of VHT based on the construction ratio,and proposes the design idea of VHT-based train end energy absorbers,which provides a new design concept for the development of high-performance special energy absorbing elements for trains.There are totally 170 figures,30 tables and 189 references.