不同载荷边界典型负泊松比结构等效力学建模

Equivalent mechanics modeling of typical negative Poisson’s ratiostructure under different load boundaries

为探索不同载荷边界下典型负泊松比结构(内凹六边形结构)的力学行为,基于Euler梁理论建立了不同变形特点的弹性等效力学理论模型,并通过有限元分析揭示了变形过程、验证了理论解的准确性。结果表明,不同载荷边界下结构的变形模式不同,体现为:均布载荷作用下横梁和侧壁都发生弯曲变形,平板载荷作用时仅侧壁发生变形,集中载荷作用时弯曲变形由横梁主导。有限元分析指出,3种载荷边界下内凹六边形结构发生塑性大变形后都能实现压缩-收缩的负泊松比效应,且平板加载时结构的负泊松比效应最佳。等效泊松比的理论预测值与有限元分析结果具有较好的吻合度,弹性范围内等效泊松比在均布载荷条件下为正值、在平板载荷条件下有最大的负值、在集中载荷条件下接近于零。本研究为固体火箭等高轻量化需求装备提供了潜在方案。

To explore the mechanical behavior of typical negative Poisson’s ratio structure(concave hexagonal structure)under different load boundaries,the theoretical model of elastic equivalent mechanics with different deformation characteristics was established based on the Euler beam theory,and the deformation process and the accuracy of the theoretical solution were verified through the finite element analysis.The results show that the deformation mode of the structure is different under different load boundaries,which are reflected as:the cross beam and the side walls occur the bending deformation under the uniform load;only the side walls deform during the plate load;the bending deformation is dominated by the cross beam during the concentrated load.The finite element analysis points out that the negative Poisson’s ratio effect with compression-contraction can be realized after a large plastic deformation under the three load boundaries,and the negative Poisson’s ratio effect is the best during plate loading.The theoretical predicted value of the equivalent Poisson’s ratio is in good agreement with the finite element analysis results.The equivalent Poisson’s ratio in the elastic range is positive under uniform load,and has the largest negative value under plate load,and is near zero under concentrated load.This study provides potential solutions for the equipment such as solid rockets with the high lightweight demand.