周期分布压电纤维复合材料平面问题研究
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作者:
作者单位:

1.南京航空航天大学机械结构力学及控制国家重点实验室,南京210016;2.江苏科技大学船舶与海洋工程学院,镇江212003

通讯作者:

高存法,教授,博士生导师,E-mail:cfgao@nuaa.edu.cn。

中图分类号:

O343.1

基金项目:

国家自然科学基金面上(11872203)资助项目。


Study on Plane Problem of Periodic Piezoelectric Fibrous Composites
Author:
Affiliation:

1.State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China;2.School of Naval Architecture & Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China

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    摘要:

    为了探索压电纤维复合材料中局部应力场的分布规律和准确预测其有效刚度,基于复变函数理论和线性压电理论,得到了含周期分布压电纤维复合材料平面问题的半解析解。根据单胞内基体和夹杂所占区域的几何特点,分别给出复势函数的级数形式,这些复势函数在基体与夹杂的相邻界面上应满足连续性条件,在单胞的外边界应满足周期性边界条件和远场加载条件,从而确定复势函数中的待定系数,进而确定局部场,最后根据平均场理论给出了复合材料有效刚度和等效压电常数。结果表明:当基体模量大于压电夹杂模量时,电载荷对夹杂周围的局部应力场的影响是显著的,施加沿压电夹杂极化方向的正向电载荷有可能使基体与夹杂相邻界面上的最大等效应力位置相对于无电载或施加反向电载荷时发生90°改变;反之,电载荷对局部应力场几乎没有影响。由于微观结构的对称性,使得复合材料宏观上沿两个对称轴方向具有相同的刚度。同时还发现等效压电系数对基体模量非常敏感。

    Abstract:

    Based on the complex variable techniques and linear piezoelectric theory, we derive a semi-analytical solution for the plane problem of a periodic piezoelectric fibrous composite to explore the distribution of the local stress field and predict the effective stiffness of the composites. Specific series with unknown coefficients are introduced to describe the complex potential functions of the representative unit cell of the composites. The unknown coefficients are determined from the continuity conditions on the interface and the periodic boundary conditions imposed on the edge of the unit cell. Once the complex potential functions are determined, the effective stiffness and effective piezoelectric constant of the composites are obtained according to the average-field theory. The numerical results show that when the modulus of the matrix is larger than that of the piezoelectric inclusion, the influence of the electric loading on the local stress field around the inclusion is significant. The positive electric loading along the polarization direction of the piezoelectric inclusion may induce the orientation of the maximum equivalent stress on the interface of the matrix and the inclusion to change 90° relative to the case of non-electric loading or negative electric loading. On the contrary, the electric loading has little effect on the local stress field. Because of the symmetry of the microstructure, the composite shows the same stiffness along the two symmetrical axes. It is also found that the effective piezoelectric constant is sensitive to the modulus of the matrix.

    图1 含周期分布压电夹杂的二维弹性体及其正方形单胞Fig.1 Elastomer with periodic piezoelectric inclusions and the corresponding square unit cell
    图2 作用在二维连续体边界上的外力Fig.2 External force acting on the boundary of a two-dimensional continuum
    图3 本文结果与已知解的比较Fig.3 Comparison between our solutions and previous solutions
    图4 体积分数和电载荷不同时软夹杂周围环向应力场Fig.4 Hoop stress around a soft inclusion under different volume fractions of the inclusion and electrical loadings
    图5 电载荷不同时硬夹杂周围环向应力场Fig.5 Hoop stress around a hard inclusion under different electrical loadings
    图7 复合材料有效刚度中非零值量随软夹杂体积分数变化情况Fig.7 Nonzero effective stiffness of the composites with varying volume fractions of soft inclusions
    图8 软夹杂体积分数不同时计算得到的复合材料有效刚度中的零值量Fig.8 Zero effective stiffness of the composites calculated by this method under different volume fractions of soft inclusions
    图9 复合材料有效刚度中非零值量随硬夹杂体积分数变化情况Fig.9 Nonzero effective stiffness of the composites with varying volume fractions of hard inclusions
    图10 硬夹杂体积分数不同时计算得到的复合材料有效刚度中的零值量Fig.10 Zero effective stiffness of the composites calculated by this method under different volume fractions of hard inclusions
    图11 等效压电应变常数随夹杂体积分数的变化情况Fig.11 Effective piezoelectric strain coefficient with varying volume fractions of the inclusions
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引用本文

杨绘峰,高存法.周期分布压电纤维复合材料平面问题研究[J].南京航空航天大学学报,2021,53(1):116-124

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  • 收稿日期:2020-04-17
  • 最后修改日期:2020-05-17
  • 在线发布日期: 2021-02-05
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