用压电材料进行损伤鉴别的理论与数值分析

对压电材料用于损伤监测的理论和数值分析做了一些研究。首先，设计了一种用压电材料进行损伤监测的模型。然后，对这个模型进行分析，找出简单有效的解答办法，将求解过程分解为断裂力学分析和压电分析两部分，并通过适当的假设，进行了详细的理论推导。通过正电有限元程序进行仿真计算，将数值计算结果与理论解进行比较以验证提出理论的正确性，并分析得到了裂纹参数与压电层表面电势变化之间的关系和普通弹性材料泊松比对波峰参数的影响。最后，用提出的方法验算了两个例题。从结果来看，理论结果和数值结果非常接近。

THEORETICAL AND NUMERICAL INVESTIGATION ON CRACK IDENTIFICATION USING PIEZOELECTRIC MATERIAL-EMBEDDED STRUCTURES

Theoretical and numerical investigation on crack identification using piezoelectric materials embedded in structures are presented in this paper. First, a crack estimation model, which is a laminated beam composed of piezoelectric materials bonded on the upper and lower surface of a normal elastic body with a crack in it under axial force, was designed to investigate the effect of the crack on the piezoelectric materials. Because the piezoelectric layers are not thicker than one hundredth of the normal elastic layer, and the stiffness of the piezoelectric materials is much less than that of normal engineering materials, a hypothesis named MLTNM (Most Load Taken by Normal Material) is employed to simplify the analysis. Using this supposition, the problem of the crack estimation can be separated into two subproblems: one is about the fracture mechanics analysis of a normal elastic body with a crack in it and the other is about the piezoelectric analysis of the piezoelectric films bonded on the elastic body. Using complex analysis method, one kind of Airy stress functions is chosen to get the stress and strain distributions in the elastic body with a crack in it. Supposing the strains are constant throughout the thickness direction, we could obtain the potential distribution of the piezoelectric material with given strain on one side of it. By means of these two analysis steps, the effect of the crack on the potential distribution can be obtained considering the strain continuity condition between the elastic body and piezoelectric materials. The results of the theoretical analysis and numerical results using finite element program were compared. Good consistency is found in them, that means the correctness of the theoretical analysis in this paper. The theory presented in this paper was also used to find the relationship between the crack parameters and the potential distribution and the influence of the Poisson ration of normal elastic body on the peaks' parameters. At last, according to the theoretical method in this paper, numerical simulations of the use of piezoelectric materials to crack identification were made.