含界面圆孔压电介质动力反平面行为的数值模拟
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摘要
由于压电材料本身的力电耦合特性,压电材料已被广泛应用于现代化科学技术,如声纳传感器、力电耦合执行器、压电电源补给装置及位置调节器等。这些装置均是在力电耦合场共同作用下进行工作,故材料本身的缺陷,如位错、裂纹、夹杂等对其工作特性及力电耦合特性产生很大影响。因此,研究在力电耦合场共同作用下含有缺陷的压电材料的力学性能具有重要意义。
本文采用有限元法研究压电介质中近场圆形孔洞对瞬态SH波的散射和动应力集中问题。有限元法原理在数学上是将偏微分方程的初边值问题划归一组常微分方程的初值问题或一组规则代数方程。然后,采用直接积分法进行求解,得到各节点和单元的位移、应力的时程解。用有限元模拟波动问题,首先要解决人工边界的设置问题,由于要从无限域中截取有限区域来模拟无限域,所以要引入人工边界。其次是解决时空离散带来的各种不利影响,以减少误差。还要考虑荷载的施加问题以及模型大小对解题的影响问题。本文对要解决的问题建立了有限元模型,并用通用有限元分析软件ANSYS进行了计算,给出了部分节点的位移、应力时程解和孔边动应力集中系数,并对结果进行了讨论。本文的具体工作如下：
研究了瞬态SH波入射到压电介质中界面附近多个圆孔引起散射时,讨论了两圆孔距离不同时对应力、位移和动应力集中系数影响；并且研究了瞬态SH波入射到双相压电介质界面上圆孔引起散射时,讨论了在上部压电介质不同时对应力、位移和动应力集中系数影响。
Due to this intrinsic coupling behavior, piezoelectric materials are widely used in modern technology such as high power sonar transducers, electro-mechanical actuator, piezoelectric power supplies and micro-positioner. These devices are designed to work under combined electro-mechanical loads. The presence of various defects, such as dislocations, cracks and inclusions, can greatly influence their characteristics and coupled behavior. Therefore, it is of vital importance to study the electro-elastic fields as a result of the presence of defects.
The present thesis investigates the scattering problems and the dynamic stress concentration problems of SH-wave by circular cavities in near field of piezeoelectric medium by the method of FEM. The FEM is a method of which transform the partial differential-coefficient equation's initial and boundary value issue to ordinary differential-coefficient equation's initial and boundary value problem or a set of regular algebra equation. Then, use the direct integral calculus method of NEWMARK to solve solution, and get each node and element's displacement and stress solution vs. time. There are two problems in simulating SH-wave issue by finite element method. The first is establishing artificial boundary problem, because of simulating the infinite field from the finite field in which intercept from the infinite field, so we introduce artificial boundary. The second is solving all kinds of disadvantageous influence in space-time dispersing to reduce error. In additional, the problems of load's infliction and model's size should be considered. In this article, we found the finite element model in allusion to the problem above, solved the equation by the general finite element analysis software ANSYS, gave some node's displacement and stress solution vs. time and the dynamic stress concentration at the edge of cavity, discussed the result. Our analytic works in concrete are mainly as follows:
Scattering of transient SH-wave and dynamic stress conceatration problem are investigated by two circular cavities under interface in piezeoelectric media.The influence on stress and displacement and dynamic stress concentration of different distance of zhe two cavteties are discussed. Then,Scattering of transient SH-wave and dynamic stress conceatration problem are investigated by an interface circular cavity in two dissimilar piezeoelectric media.The influence on stress and displacement and dynamic stress concentration of different piezeoelectric media is discussed.
本文采用有限元法研究压电介质中近场圆形孔洞对瞬态SH波的散射和动应力集中问题。有限元法原理在数学上是将偏微分方程的初边值问题划归一组常微分方程的初值问题或一组规则代数方程。然后,采用直接积分法进行求解,得到各节点和单元的位移、应力的时程解。用有限元模拟波动问题,首先要解决人工边界的设置问题,由于要从无限域中截取有限区域来模拟无限域,所以要引入人工边界。其次是解决时空离散带来的各种不利影响,以减少误差。还要考虑荷载的施加问题以及模型大小对解题的影响问题。本文对要解决的问题建立了有限元模型,并用通用有限元分析软件ANSYS进行了计算,给出了部分节点的位移、应力时程解和孔边动应力集中系数,并对结果进行了讨论。本文的具体工作如下：
研究了瞬态SH波入射到压电介质中界面附近多个圆孔引起散射时,讨论了两圆孔距离不同时对应力、位移和动应力集中系数影响；并且研究了瞬态SH波入射到双相压电介质界面上圆孔引起散射时,讨论了在上部压电介质不同时对应力、位移和动应力集中系数影响。
Due to this intrinsic coupling behavior, piezoelectric materials are widely used in modern technology such as high power sonar transducers, electro-mechanical actuator, piezoelectric power supplies and micro-positioner. These devices are designed to work under combined electro-mechanical loads. The presence of various defects, such as dislocations, cracks and inclusions, can greatly influence their characteristics and coupled behavior. Therefore, it is of vital importance to study the electro-elastic fields as a result of the presence of defects.
The present thesis investigates the scattering problems and the dynamic stress concentration problems of SH-wave by circular cavities in near field of piezeoelectric medium by the method of FEM. The FEM is a method of which transform the partial differential-coefficient equation's initial and boundary value issue to ordinary differential-coefficient equation's initial and boundary value problem or a set of regular algebra equation. Then, use the direct integral calculus method of NEWMARK to solve solution, and get each node and element's displacement and stress solution vs. time. There are two problems in simulating SH-wave issue by finite element method. The first is establishing artificial boundary problem, because of simulating the infinite field from the finite field in which intercept from the infinite field, so we introduce artificial boundary. The second is solving all kinds of disadvantageous influence in space-time dispersing to reduce error. In additional, the problems of load's infliction and model's size should be considered. In this article, we found the finite element model in allusion to the problem above, solved the equation by the general finite element analysis software ANSYS, gave some node's displacement and stress solution vs. time and the dynamic stress concentration at the edge of cavity, discussed the result. Our analytic works in concrete are mainly as follows:
Scattering of transient SH-wave and dynamic stress conceatration problem are investigated by two circular cavities under interface in piezeoelectric media.The influence on stress and displacement and dynamic stress concentration of different distance of zhe two cavteties are discussed. Then,Scattering of transient SH-wave and dynamic stress conceatration problem are investigated by an interface circular cavity in two dissimilar piezeoelectric media.The influence on stress and displacement and dynamic stress concentration of different piezeoelectric media is discussed.
引文
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[2]Shen Mand Bever M B.1972.Gradient in polymeric materials. J. Mater. Sci.,7,741,746.
[3]王保林.压电材料及其结构的断裂力学.国防工业出版社,2003：3-46
[4]杨大智.智能材料与智能系统.天津大学出版社,2000：183-242
[5]Rogers C A. Intelligent materials system-the dawn of new materials age. J. Inter. Mater. Syst. Struct,1993:4-12
[6]Xu Yuhuan. Ferroelectric materials and their applications. New York:Elsevier
[7]宋天舒、刘殿魁、于新华。SH波在压电材料中的散射和动应力集中,哈尔滨工程大学学报2002(1)：120-123
[8]Pak, Y. E.,. Crack extension force in a piezoelectric materials. ASME Trans. J. Appl. Mech.1990,57:647-653
[9]Park, S. B., Sun, C. T., Effect of electric field on fracture of piezoelectric ceramic. Int. J. Fract.1995,70:203-216
[10]Park, S. B., Sun, C. T., Fracture criteria for piezoelectric ceramic. j. Am. Ceram. Soc.1995,78:1475-1480
[11]PARTON B Z. Fracture mechanics and piezoelectric material [J]. Acta Astronautica,1976(3):671-683.
[12]Shindo, Y., Tanaka, K., Narita, F.,Singular stress and electric fields of a piezoelectric ceramic cetamic strip with a finite crack under longitudinal shear. Acta Mech.1997,120:31-45
[13]Shindo, Y., Horiguchi, k., Murakami, H., Narita, F., Single-edge precracked beam test and electric fracture mechanics analysis for piezoelectric cetamics.In:Proc. SPIE-Int. Soc. Opt.Eng.Smart Structures and Devices, Melbourne,2001:311-320
[14]Wang, B., Three-dimensional analysis of a flat elliptical crack in a piezoelectric material.Int.J.Eng. Sci.1992:30,781-791
[15]Wang, Z. K., Huang, S. H., Fields near elliptical crack in a piezoelectric ceramics.Eng. Fract. Mech.1995,51:447-456
[16]Wang, Z. K., Zheng,B.L.,The general solution of three-dimensional piezoelectric media. Int.J. Solids Struct.1995,32:105-115
[17]Kogan, L., Hui, C.Y.,Stress and induction field of a spheroidal inclusion of a penny-shaped crack in a transversely isotropic piezoelectric material. Int. J. Solids Struct.1996,33:2719-2737
[18]Zhao,M.H., Shen, Y. P..LiuY.J., Liu, G. N., Isolated crack in three-dimensional piezoelectric solid:Part I-Solution by Hankel transform. Theor.Appl. Fract. Mech.1997a,26:129-139
[19]Zhao, M. H., Shen, Y. P., LiuY. J., Liu, G. N., Isolated crack in three-dimensional piezoelectric solid:Part Ⅱ-Stress intensity factors for circular crack. Theor. Appl. Fract. Mech.1997b,26:141-149
[20]SOSA H A. Plane problems in piezoelectric media with defects [J]. Int J Solids Structures,1991(28):491-505.
[21]王自强.压电材料裂纹顶端条状电饱和区模型的力学分析[J].力学学报,1999,31(3)：311-319.
[22]Zhang, T. Y., Qian, C. F., Tong, P., Linear electro-elastic analysis of
dynamic interaction between piezoelectric actuators. Intern-ational Journal of Solid and Structures.1998,35:2121-2149
[23]Wang, Xuyue; Yu, Shouwen. Scattering of SH waves by an arc-shaped crack between a cylindrical piezoelectric inclusion and matrix-Ⅱ: Far fields. International Journal of Fracture v 100 n 4,1999: L35-L40
[24]C.P.Jiang, Y.K.Cheung. An exact solution for the three-phase piezoelectric cylinder model under antiplane shear and its applications to piezoelectric compsites. Int J Solids Structures,2001 (38):4777-4796
[25]Liu, J.X., Liu, Y.L., Wang, B.,Du,S.Y., Mode-Ⅲ crack in the piezoelecreic layerof two dissimilar materials. Key Engineering Materials.1998:1167-1172
[26]Sosa, H. A., plne problems in piezoelectric media with defects. International Journal of Solids and Structures.1991,28: 491-505
[27]Zhao, M. H., Shen, Y. P., Liu, Y. j., Liu, G. N., Isolated cracks in three-dimensional piezoelectric solid. Part II:stress intensity factors for circular crack. theoretical and Applied Fracture Mechanics,1997,26,141-149
[28]Huang, Hai-Ming (Department of Engineering Mechanics, Tsinghua University); Shi, Hui-Ji; Yin, Ya-Jun, Multi-cracks problem for piezoelectric materials strip subjected to dynamic loading. Mechanics Research Communications, v 29, n 5, September/October, 2002, p 413-424
[29]Sun, Jian-Liang (Ctr. for Composite Mat., Harbin Inst. of Technol.); Zhou, Zhen-Gong; Wang, Biao; Dynamic behavior of two unequal parallel permeable interface cracks in a piezoelectric layer bonded to two half piezoelectric materials planes. Applied Mathematics and Mechanics (English Edition), v 26, n 2, February, 2005, p 160-170
[30]Zhou, Zhen-Gong (Ctr. Comp. Mat./Elect.-Optics, Harbin Institute of Technology); Wang, Biao; Sun, Yu-Guo;Investigation of the dynamic behavior of two parallel symmetric cracks in piezoelectric materials use of non-local theory. International Journal of Solids and Structures, v 40, n 3, February,2003, p 747-762
[31]Chen, Jian (Department of Engineering Mechanics, Shanghai Jiaotong University); Liu, Zhengxing; On the dynamic behavior of a functionally graded piezoelectric strip with periodic cracks vertical to the boundary. International Journal of Solids and Structures, v 42, n 11-12, June,2005, p 3133-3146
[32]Wang, B. L. (Harbin Inst of Technology); Han, J. C.; Du, S.Y. Dynamic response for non-homogeneous piezoelectric medium with multiple cracks. Source:Engineering Fracture Mechanics, v 61, n 5-6, Nov-Dec,1998, p 607-617
[33]Li, Xian-Fang (Coll. of Mathematics/Comp. Science, Hunan Normal University); Lee, Kang Yong, Dynamic behavior of a piezoelectric ceramic layer with two surface cracks. International Journal of Solids and Structures, v 41, n 11-12, June,2004, p 3193-3209
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