柔性双稳态结构分岔跳跃模式的探讨

Snap-through Bifurcation Analysis of Compliant Bistable Structures

针对柔性双稳态结构跳跃路径不唯一及其力位移曲线存在不连续点(即尖点)的问题,基于有限元大变形理论建立了双稳态柔性结构的跳跃控制方程,采用多步位移载荷循环加载/卸载的方法数值模拟了跳跃过程中存在的可能屈曲模态及其变换方式,得到了其对称跳跃分岔的完整解。分析了双稳态结构参数对跳跃不连续点(尖点)和跳跃路径的影响关系,提出将结构品质因数作为双稳态跳跃"尖点"判据的方法,得到了具有稳定单一跳跃路径的双稳态结构。采用热成型方法研制了类余弦梁双稳态结构,考虑残余应力、夹持边界条件及载荷加载方式的影响,仿真预测的屈曲模态转换过程与实验结果基本一致,为双稳态跳跃特征的精确设计与控制提供理论依据。

The discontinuity of the force-displacement curve(also named sharp point)and multiple snap-through pathways significantly affect the engineering practicability of compliant bistable structures.Hence,the snap-through controlling equation for compliant bistable structures is established according to the large deflection finite element theory.By using the multistep displacement loading method,the possible buckling modes and their transforming procedure are numerically obtained,which interprets reasonably the discontinuity of the force curve.Furthermore,the influence of the structure parameters on the sharp point and snap-through pathway is numerically analyzed,and meanwhile,the structural quality factor is introduced to judge the occurrence of the sharp point.Finally,the bistability design method for achieving stable bistable mechanics with single snapping pathway is proposed.For further validation,a thermal formed bistable beam structure with quasi-cosine shape is manufactured,and the simulated mode transforming process is nearly consistent with that from experiments considering the influences of residual stress,clamping status and loading conditions,thus providing a theoretical basis to design and control the bistable snapping characteristics of compliant structures.