层合机敏结构的变形传递和层间应力分析

Analyses of Interlayer Stresses and Strain Transfer in Smart Laminated Structures

建立了一种承受弯矩及正应力加载下结构材料与压电陶瓷传感 执行器的应力应变传递关系模型 ,获得了位移、应力、应变等场量方程。模拟了压电陶瓷作为传感器时结构的变形传递及作为执行器时的应力分布和变形传递 ,并与实验和有限元分析结果进行了比较。结果显示 :模型得出的理论值与试验和有限元结果较为接近 ;当本体材料两面贴压电陶瓷并加同向电压 (即只受纵向载荷作用 ) ,本模型与已有的一些模型模拟结果近似 ,但此模型能同时分析承受弯曲加载的智能结构情况 ;压电陶瓷作为执行器时 ,层间正应力和层间剪应力在中间都比较平缓 ,到接近边缘处有一应力集中 ,实际制作时应加强此处粘接强度 。

A new model is proposed to analyze the strain/stress transfer relation between host materials and piezoceramic sensors/actuators under bending and axial stress loading. The finite thickness of the adhesive is taken into account. The physical layers of the piezoceramic, adhesive and structure material are further subdivided into thinner layers as fine as necessary in order to improve the accuracy of stress analysis. In each thin layer the in-plane stresses are assumed to vary linearly across the thickness. By satisfying equilibrium equations, constitutive equations and displacement-strain relations, all components of stress, strain and displacement can be expressed as functions of the in-plane forces and the moments of the thin layers. The differential equations governing the in-plane forces and the moments are obtained. Then, this analytical model is used to predict strain transfer from the structure material to the sensor. It is found, both experimentally and theoretically, that the axial strain of the host material is considerably larger than the strain of the sensor, which is directly related to the output voltage. By introducing the so-called strain transfer factor, a relationship between the output voltage of the sensor and the strain of the measured material is derived. The model is used to predict interlayer stress distributions and strain transfer, which are induced by actuator strain. The result was compared with existing experiments and FEM. There is stress concentration between the actuator and adhesive around the edge of the smart structures, which may cause debonding under high stress loading.