Plane Strain Problem of Piezoelectric Solid With an Elliptic Inclusion

DAI Long-chao; GUO Wan-lin; SHE Chong-min

Volume 26 Issue 12

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(12): 1463-1469

DAI Long-chao, GUO Wan-lin, SHE Chong-min. Plane Strain Problem of Piezoelectric Solid With an Elliptic Inclusion[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1463-1469.

Citation:

DAI Long-chao, GUO Wan-lin, SHE Chong-min. Plane Strain Problem of Piezoelectric Solid With an Elliptic Inclusion[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1463-1469.

Citation:

DAI Long-chao, GUO Wan-lin, SHE Chong-min. Plane Strain Problem of Piezoelectric Solid With an Elliptic Inclusion[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1463-1469.

PDF( 2228 KB)

Plane Strain Problem of Piezoelectric Solid With an Elliptic Inclusion

College of Aerospace Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, P. R. China

Received Date: 2003-11-18
Rev Recd Date: 2005-08-17
Publish Date: 2005-12-15

Abstract

Abstract

By using the complex variables function theory,a plane strain electro-elastic analysis was perfor medona transversely isotropic piezoelectric material containing an elliptic elastic inclusion,which is subje cted to a unifor mstress field and a uniform electric displacement loads at infinity.Based on the present finite elementresults and somerelated the oretical solutions,an acceptable conjecture was found that the stress field is constant inside the elastic inclusion.The stress field solutions in the piezoele ctric matrix and the elastic inclusion were obtained in the form of complex potentials based on the impermeable electric bo undary conditions.
- elliptical inclusion,
- transversely isotropic,
- piezo electric,
- complex potential

FullText(HTML)

References(12)

References

[1]	Hwu Chyanbin,Ting T C T.Two-dimensional problems of the anisotropic elastic solid with an elliptic inclusion[J].Q J I Mech Appl Math,1989,42(4):553—572. doi: 10.1093/qjmam/42.4.553
[2]	Ting T C T,YAN Gong-pu.The anisotropic elastic hole or rigid inclusion[J].Internat J Solids Structures,1991,27(15):1879—1894. doi: 10.1016/0020-7683(91)90183-G
[3]	Sosa Horacio.Plane problems in piezoelectric media with defects[J].Internat J Solids Structures,1991,28(4):491—505. doi: 10.1016/0020-7683(91)90061-J
[4]	戴隆超,郭万林.压电体椭圆孔边的力学分析[J].力学学报,2004,36(2):224—228.
[5]	邓其林,王自强.压电材料椭圆切口的力学分析[J].力学学报,2002，34(1):109—115.
[6]	WANG Xin-wei,ZHOU Yong,ZHOU Wan-lin.A novel hybrid finite element with a hole analysis of plane piezoelectric medium with defects[J].Internat J Solids Structures,2004,41(24/25):7111—7128. doi: 10.1016/j.ijsolstr.2004.06.012
[7]	周勇,王鑫伟.压电材料平面裂纹尖端场的杂交应力有限元分析[J].力学学报,2004,36(3):354—358.
[8]	Chung M Y,Ting T C T.Piezoelectric solid with an elliptic inclusion or hole[J].Internat J Solids Structures,1996,33(23):3343—3361. doi: 10.1016/0020-7683(95)00189-1
[9]	Sosa Horacio,Khutoryansky Naum.New developments concerning piezoelectric materials with defects[J].Internat J Solids Structures,1996,33(23):3399—3414. doi: 10.1016/0020-7683(95)00187-5
[10]	GAO Cun-fa,FAN Wei-xun.Exact solutions for the plane problem in piezoelectric materials with an elliptic or a crack[J].Internat J Solids Structures,1999,36(17):2527—2540. doi: 10.1016/S0020-7683(98)00120-6
[11]	ZHANG Tong-yi,QIAN Cai-fu,TONG Pin.Linear electro-elastic analysis of a cavity or a crack in a piezoelectric material[J].Internat J Solids Structures,1998,35(17):2121—2149. doi: 10.1016/S0020-7683(97)00168-6
[12]	列赫尼茨基 S G.各向异性板[M].胡海昌译.北京:科学出版社,1963,168—174.

Relative Articles

[1]	WANG Shaojie, ZENG Xiangtai, Lü Aizhong. Analytical Analysis of Non-Circular Hydraulic Lined Tunnels Under Smooth Contact With Transversely Isotropic Rock Mass[J]. Applied Mathematics and Mechanics, 2021, 42(4): 342-353. doi: 10.21656/1000-0887.410182
[2]	ZHANG Ming-ming, LIANG Li-xi, LIU Xiang-jun. Impacts of Rock Anisotropy on Horizontal Wellbore Stability in Shale Reservoir[J]. Applied Mathematics and Mechanics, 2017, 38(3): 295-309. doi: 10.21656/1000-0887.370155
[3]	Rajneesh Kumar, Tarun Kansal. Effect of Relaxation Times on Circular Crested Waves in Thermoelastic Diffusive Plate[J]. Applied Mathematics and Mechanics, 2010, 31(4): 463-471. doi: 10.3879/j.issn.1000-0887.2010.04.008
[4]	Rajneesh Kumar, Rajeev Kumar. Propagation of Wave at the Boundary Surface of Transversely Isotropic Thermoelastic Material With Voids and Isotropic Elastic Half-Space[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1101-1117. doi: 10.3879/j.issn.1000-0887.2010.09.010
[5]	Rajneesh Kumar, Tarun Kansal. Propagation of Rayleigh Waves at the Free Surface of Transversely Isotropic Generalized Thermoelastic Diffusion[J]. Applied Mathematics and Mechanics, 2008, 29(11): 1314-1324.
[6]	A. Y. T. Leung, ZHENG Jian-jun. Closed Form Stress Distribution in 2D Elasticity for all Boundary Conditions[J]. Applied Mathematics and Mechanics, 2007, 28(12): 1455-1467.
[7]	WANG Xiao-gang. Non-Axisymmetrical Vibration of Elastic Circular Plate on Layered Transversely Isotropic Saturated Ground[J]. Applied Mathematics and Mechanics, 2007, 28(10): 1232-1244.
[8]	YANG Xin-hua, DONG Liang, WANG Cheng, CHEN Chuan-yao, HU Yuan-tai. Transversely Isotropic Damage Around Conducting Crack-Tip in Four-Point Bending Piezoelectric Beam[J]. Applied Mathematics and Mechanics, 2005, 26(4): 394-402.
[9]	ZHAO Ming-hao, LI Dong-xia, SHEN Ya-peng. Interfacial Crack Analysis in Three-Dimensional Transversely Isotropic Bi-Materials by Boundary Integral Equation Method[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1394-1400.
[10]	LIU Ying, LIU Kai-xin. Characteristic Analysis for Stress Wave Propagation in Transversely Isotropic Fluid-Saturated Porous Media[J]. Applied Mathematics and Mechanics, 2004, 25(6): 599-606.
[11]	CHENG Chang-jun, REN Jiu-sheng. Transversely Isotropic Hyper-Elastic Material Rectangular Plate With Voids Under a Uniaxial Extension[J]. Applied Mathematics and Mechanics, 2003, 24(7): 675-683.
[12]	DING Hao-jiang, CHEN Wei-qiu, XU Rong-qiao. On the Bending, Vibration and Stability of Laminated Rectangular Plates With Transversely Isotropic Layers[J]. Applied Mathematics and Mechanics, 2001, 22(1): 16-22.
[13]	GAO Cun-fa, FAN Wei-xun. An Interface Inclusion Between Two Dissimilar Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2001, 22(1): 85-92.
[14]	WU Shi-ming, LIANG Jian, HU Ya-yuan. Stress in Transversely Isotropic Half-Space With Typical Loads Acting on Its Surface[J]. Applied Mathematics and Mechanics, 2000, 21(8): 809-816.
[15]	Chen Rong, Xue Songtao, Chen Zhuchang, Chen Jun. The Numerical Solution of Green’s Functions for Transversely Isotropic Elastic Strata[J]. Applied Mathematics and Mechanics, 2000, (1): 45-52.
[16]	Jiang Bing, Fang Daining. The Effective Properties of Piezoelectric Composite Materials with Transversely Isotropic Spherical Inclusions[J]. Applied Mathematics and Mechanics, 1999, 20(4): 371-380.
[17]	Hou Mishall, Yang Qijun. Plane Problems in Piezoelectric Media with Elliptic Inclusion[J]. Applied Mathematics and Mechanics, 1998, 19(2): 136-144.
[18]	Ding Haojiang, Liang Jian, Wang Yun. Point Force Solution for a Transversely Isotropic Elastic Layer[J]. Applied Mathematics and Mechanics, 1996, 17(4): 297-305.
[19]	Ruan Huai-ning, Wang Wei-xiang. Slip-Line Field Theory of Transversely Isotrropic Body[J]. Applied Mathematics and Mechanics, 1994, 15(4): 313-322.
[20]	Yang Zheng-wen, Loo Wen-da. Finite Layer Analysis for Semi-Infinite Soils (Ⅰ)——General Theory[J]. Applied Mathematics and Mechanics, 1992, 13(10): 881-890.