Study On Mechanical Properties Of Butterfly-shaped Auxetic Honeycomb Structure

Auxetic materials are a kind of high-performance synthetic material,which shows excellent physical and mechanical properties,and has great application prospects in medicine,sensors and aerospace vehicles.Therefore,it is of great significance to design and study auxetic materials with better mechanical properties.In this thesis,based on the butterfly shaped structure and the star-shaped auxetic honeycomb structure,a novel butterfly-shaped auxetic honeycomb structure is constructed,and its mechanical properties were analyzed,and the optimization design and free vibration analysis of the novel honeycomb sandwich plate with negative Poisson's ratio were carried out.The main contents are as follows:A novel butterfly-shaped auxetic honeycomb structure model is constructed.The equivalent elastic properties under tension in two coordinate axes are calculated respectively,and its analytical solution is derived.The finite element analysis and experimental verification are carried out.Under the action of uniaxial tension,the equivalent elastic modulus and Poisson's ratio of the novel butterfly-shaped honeycomb structure are derived by energy method.The finite element analysis software ANSYS is used to simulate the tensile behavior of the structure.Furthermore,3D printing technology is used to print structural samples,which leads to carry out the experimental research.The finite element analysis results and experimental analysis results verify the correctness of the theoretical results.The relationship between structural geometric parameters and Poisson's ratio are discussed by using analytical and numerical solutions.It is found that structural length parameters have great influence on Poisson's ratio,which reveals the necessity of structural parameter optimization.Finally,the influence of structural length parameters on its equivalent elastic properties is further studied through experiments.Taking Poisson's ratio and negative relative elastic modulus of the novel butterfly-shaped honeycomb structure as optimization objectives,the Pareto solution set is obtained by using Gamultiobj multi-objective genetic algorithm.In order to obtain the optimal solution,the optimal solution is decided by entropy-weight TOPSIS method.And three optimization schemes with the greatest degree of closeness to the ideal point are selected for experimental analysis to determine the optimal solution.Compared with the re-entrant honeycomb structure and the star-shaped honeycomb structure,the negative Poisson's ratio and in-plane stiffness of butterfly-shaped honeycomb structure are increased by 7%and 25%,respectively.The results show that the novel butterfly-shaped honeycomb structure improves the stiffness of the structure while maintaining a high auxetic effect,which has certain guiding significance for the research and application of auxetic materials with high stiffness.The novel butterfly-shaped honeycomb structure is applied to sandwich plate,and the dynamic model of auxetic honeycomb sandwich plate is established.In order to obtain the nonlinear dynamic equation of honeycomb sandwich plate under free vibration,the nonlinear partial differential equation of honeycomb plate is derived by using Reddy high-order shear plate theory,Von-Karman large deformation relation and Hamilton principle.The natural frequency of the system is solved by Navier method,and the influence of different core thickness coefficient _ch/h and core structure parameters on the natural frequency of the system is studied.The results show that the natural frequency of the new auxetic honeycomb sandwich plate is higher than that of the traditional auxetic honeycomb sandwich plate,and the possibility of resonance of the sandwich plate in the application process is relatively reduced.