含压电不完美界面的压电复合材料的变分界限研究

发布时间：2018-03-03 06:37

本文选题：压电不完美界面　切入点：有效性能　出处：《西南交通大学》2015年硕士论文　论文类型：学位论文

【摘要】：随着压电复合材料在智能材料领域中起着越来越重要的作用,对于压电复合材料的整体性能的预测是在细观力学中已经成为一个重要领域。在实践应用中,压电复合材料或不均匀材料的各组分之间的界面是不完美的。在压电的范围内,已经提出了三种不完美界面模型,分别是压电弹簧型不完美界面模型、压电薄膜型不完美界面模型和压电通用不完美界面模型。其中压电弹簧界面模型规定在界面上面力和法向电位移是连续的,但位移场和电势是不连续的,并且它们在界面上的跳跃量分别正比于对应的面力和法向电位移。而与压电弹簧界面模型对偶的压电薄膜界面模型则约定在界面上位移场和电势场是连续的,但面力和法向电位移是不连续的,且分别满足与位移和电势的表面梯度成正比的广义Laplace-young方程。第三种模型是指压电通用型不完美界面模型,它是基于通过用不完美界面代替界面相的方法和渐进分析得到的,在该模型中,位移、电势、面力和法向电位移一般是不连续的。基于细观力学的方法,本文研究了含两类特殊不完美界面的压电复合材料的有效性能,推导了含不完美界面的压电复合材料的有效性能的尺寸依靠性界限。为了实现本文的研究目的,首先,基于Gu和He的工作,推导出压电弹簧不完美界面模型和压电薄膜不完美界面模型；然后,将传统的线性压电体的最小势能原理被扩展到含这两种不完美界面的压电复合材料,并且得到了该压电复合材料的广义变分原理。接着,考虑一含两类压电不完美界面且由单向圆柱形纤维嵌入基体组成的压电复合材料被施加远处反平面的力学载荷和平面内的电学载荷,通过选取简单的许可场,运用已得到变分原理,得到了该压电复合材料的电弹性模量的一阶显性界限。最后,通过数值结果说明了所求界限的尺寸依靠性。
[Abstract]:As piezoelectric composites play an increasingly important role in the field of smart materials, the prediction of the overall properties of piezoelectric composites has become an important field in micromechanics. The interface between the components of piezoelectric composites or uneven materials is not perfect. In the piezoelectric range, three kinds of imperfect interface models have been proposed, one is the piezoelectric spring type imperfect interface model, the other is the piezoelectric spring type imperfect interface model. The piezoelectric film type imperfect interface model and the piezoelectric universal imperfect interface model. The piezoelectric spring interface model stipulates that the force and normal electric displacement above the interface are continuous, but the displacement field and potential are discontinuous. And their hopping at the interface is proportional to the corresponding surface force and normal electric displacement respectively, while the piezoelectric film interface model, which is dual with the piezoelectric spring interface model, agrees that the displacement field and the potential field are continuous at the interface. However, the surface force and the normal electric displacement are discontinuous and satisfy the generalized Laplace-young equation which is proportional to the surface gradient of the displacement and potential respectively. The third model refers to the piezoelectric universal imperfect interface model. It is based on the method of replacing interface phase with imperfect interface and progressive analysis. In this model, displacement, potential, surface force and normal electric displacement are generally discontinuous. In this paper, the effective energy of piezoelectric composites with two kinds of special imperfect interfaces is studied, and the dimensional dependence limits of the effective properties of piezoelectric composites with imperfect interfaces are derived. Based on the work of Gu and he, a piezoelectric spring imperfect interface model and a piezoelectric film imperfect interface model are derived. And the generalized variational principle of the piezoelectric composite is obtained. Considering that a piezoelectric composite consisting of two kinds of piezoelectric imperfect interfaces and consisting of unidirectional cylindrical fibers embedded in matrix is subjected to the mechanical load of the far antiplane and the electrical load in the plane, a simple allowable field is selected. The first order explicit limit of the electroelastic modulus of the piezoelectric composite is obtained by using the variational principle. Finally, the size dependence of the obtained limit is illustrated by numerical results.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB33

【共引文献】