双相压电介质中非圆孔对瞬态SH波的散射
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摘要
压电材料在智能材料中使用非常广泛,例如力电传感器,传输器和执行器,因为它们有较好的力电耦合特性。本文采用有限元法研究双相压电介质中近场椭圆形孔洞对瞬态SH波的散射和动应力集中问题。有限元法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,用NEWMARK直接积分进行求解,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,其首要问题是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波入射到双相压电介质中界面上椭圆孔引起散射时,讨论的是在上部压电介质不同时和长、短轴比变化时对应力、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中界面附近含椭圆孔引起散射时,讨论的是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。
Piezoelectric materials have been more and more widely used in smart matrials such as electromechanical sensors, transducers and actuators due to their strong electromechanical coupling characteristics. The present thesis investigates the scattering problems and the dynamic stress concentration problems of SH-wave by ellips cavities in near field 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 an 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 vs. time.There are two problems in simulation 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 in space-time dispersing to reduce error.In additional,the problems of load's infliction an 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 edge of cavity,discussed the result.The present work is mainly as follows:
Scattering of transient SH-wave and dynamic stress conceatration problem are investigated by interface ellipse cavities in two dissimilar piezeoelectric media.The influence on stress and displacement and dynamic stress concentration of different piezeoelectric media and the cavities'radius are discussed. Then,Scattering of transient SH-wave and dynamic stress conceatration problem are investigated by an elliptic cavity in two dissimilar piezeoelectric media.The influence on stress and displacement and dynamic stress concentration of different piezeoelectric media is discussed.
研究了瞬态SH波入射到双相压电介质中界面上椭圆孔引起散射时,讨论的是在上部压电介质不同时和长、短轴比变化时对应力、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中界面附近含椭圆孔引起散射时,讨论的是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。
Piezoelectric materials have been more and more widely used in smart matrials such as electromechanical sensors, transducers and actuators due to their strong electromechanical coupling characteristics. The present thesis investigates the scattering problems and the dynamic stress concentration problems of SH-wave by ellips cavities in near field 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 an 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 vs. time.There are two problems in simulation 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 in space-time dispersing to reduce error.In additional,the problems of load's infliction an 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 edge of cavity,discussed the result.The present work is mainly as follows:
Scattering of transient SH-wave and dynamic stress conceatration problem are investigated by interface ellipse cavities in two dissimilar piezeoelectric media.The influence on stress and displacement and dynamic stress concentration of different piezeoelectric media and the cavities'radius are discussed. Then,Scattering of transient SH-wave and dynamic stress conceatration problem are investigated by an elliptic cavity in two dissimilar piezeoelectric media.The influence on stress and displacement and dynamic stress concentration of different piezeoelectric media is discussed.
引文
[1]Xu Yuhuan.Ferroelectric materials and their applications.New York: Elsevier
[2]张福学,王丽坤.现代压电学(中册).北京：科学出版社,2002：1-10页
[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页
[4]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页
[5]Bever MB,Duwez PE. Gradient in Composite Materials.Mater. Sci.Eng. 2004:1-8P
[6]杨大智.智能材料与智能系统.天津大学出版社,2000：183-242页
[7]Rogers C A. Intelligent materials system-the dawn of new materials age. J.Inter.Mater.Syst.Struct.1993:4-12P
[8]Pak Y.E.Crack extension force in a piezoelectric materials.ASME Trans. J.Appl.Mech.1990,57:647-653P
[9]Park S.B,Sun C.T.Effect of electric field on fracture of piezoelectric ceramic.Int.J.Fract.1995,70:203-216P
[10]Park S.B,Sun C.T.Fracture criteria for piezoelectric ceramic.J. Am. Ceram.Soc.1995,78:1475-1480P
[11]PARTON B Z. Fracture mechanics and piezoelectric material. Acta Astronautica.1976(3):671-683P
[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.1997,120:31-45P
[13]Shindo Y,Horiguchi k,Murakami H,Narita F.Single-edge precracked beam test and electric fracture mechanics analysis for piezoe- lectric cetamics. Structures and Devices.2001:311-320P
[14]Wang B,Three-dimensional analysis of a flat elliptical crack in a piezoelectric material.Int.J.Eng.Sci.1992,30:781-791P
[15]Wang Z.K,Huang S.H.Fields near elliptical crack in a piezo electric ceramics.Eng.Fract.Mech.1995,51:447-456P
[16]Wang Z.K,Zheng B.L.The general solution of three-dimensional piezoelectric media.Int.J.Solids Struct.1995,32:105-115P
[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.1996,33:2719-2737P
[18]Zhao M.H,Shen Y.P,Liu Y.J,Liu G.N.Isolated crack in three- dimensional piezoelectric solid. Theor.Appl. Fract. Mech.1997,26:129-139P
[19]Zhao M.H,Shen Y.P,Liu Y.J,Liu GN.Isolated crack in three- dimensional piezoelectric solid.Theor.Appl.Fract.Mech.1997,26:141-149P
[20]SOSA H A.Plane problems in piezoelectric media with defects.Int J Solids Structures,1991(28):491-505P
[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.力学学报.1999,31(3)：311-319页
[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.1998,35:2121-2149P
[23]Wang Xuyue,Yu Shouwen.Scattering of SH waves by an arc-shaped crack between a cylindrical piezoelectric inclusion. Intern- ational Journal of Fracture,1999:35-40P
[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):4777-4796P
[25]Liu J.X,Liu Y.L,Wang B,Du S.Y.Mode-Ⅲ crack in the piezo- elecreic layerof two dissimilar materials.Key Engineering Materials.1998:1167-1172P
[26]Sosa H.A.Plane problems in piezoelectric media with defects. International Journal of Solids and Structures.1991,28:491-505P
[27]Zhao M.H,Shen,Y.P,Liu Y.j,Liu GN.Isolated cracks in three-dimensional piezoelectric solid.Theoretical and Applied Fracture Mechanics.1997,26: 141-149P
[28]Huang Haiming,Shi Huiji,Yin Yajun.Multi-cracks problem for piezoelectric materials strip subjected to dynamic loading. Mechanics Research Communications.2002:413-424P
[29]Sun Jianliang, Zhou Zhengong,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.2005(2):160-170P
[30]Zhou Zhengong,Wang Biao,Sun Yuguo.Investigation of the dynamic behavior of two parallel symmetric cracks in piezoelectric materials use of non-local theory.International Journal of Solids and Structures.2003:747-762P
[31]Chen Jian,Liu Zhengxing.On the dynamic behavior of a func-tionally graded piezoelectric strip with periodic cracks vertical to the boundary. International Journal of Solids and Structures.2005:3133-3146P
[32]Wang B.L,HanJ.C,Du S.Y.Dynamic response for non-homogeneous piezoelectric medium with multiple cracks. Source.Engineering Fracture Mechanics.1998:607-617P
[33]Li Xianfang,Lee Kangyong.Dynamic behavior of a piezoelectric ceramic layer with two surface cracks.International Journal of Solids and Structures.2004:3193-3209P
[34]Ma Li,Wu,Lin Zhi,Zhou Zhengong,Guo Licheng.Scattering of harmonic antiplane shear waves by two collinear cracks in functionally graded piezoelectric materials. European Journal of Mechanics.2004:633-643P
[35]Chen Z.T,Worswick M.J.Dynamic fracture behavior of a cracked piezoelectric half space under anti-plane mechanical and in-plane electric impact.Archive of Applied Mechanics.2002:1-12P
[36]Kwon S.M.Department of Mechanical Design Changwon National University. Acta Mechanica.2004:73-89P
[37]Zhou Zhengong.Harbin Institute of Technology.Center for Composite Materials.2004:63-76P
[38]Li, X.F.Dynamic response of a piezoelectric material with a conducting rigid inclusion. Meccanica.2000:383-392P
[39]Narita F.Shindo Y,Moribayashi H.Circular inclusion problem in dynamic antiplane piezoelectricity Proceedings of SPIE.The International Society for Optical Engineering,2001:69-78P
[40]Xuyue Wang,Shouwen Yu.Scattering of SH waves by an arc-shaped crack between a cylindrical piezoelectric inclusion and the matrix.Key Engineering Materials.2003:215-220P
[41]Bardzokas D.I,Filshtinsky M.L.Anti-plane dynamic problem of an electroelastic cylinder with thin rigid inclusions excited by a system of surface electrodes.Archive of Applied Mechanics.2004:165-178P
[42]Gao Crunfa,Dong,Derngke Complex functions for plane problems of piezoelectric material with an elliptical hole.Engineering Mechanics.1998: 98-104P
[43]鲍亦兴,毛昭宙著.刘殿魁,苏先樾译.弹性波的衍射与动应力集中.北京：科学出版社,1993：72-202页
[44]赵寿根,程伟.1-3型压电复合材料及其研究进展.力学进展.2002,32(1)：57-68页
[45]杜善义,王彪.复合材料细观学.北京：科学出版社,1998
[46]张锦,张乃恭.新型压电复合材料力学机理及其应用.北京：北京航天航空大学出版社,1993
[47]刘晶波,廖振鹏.离散网格中的弹性波动(Ⅱ)——几种有限元离散模型的对比分析.地震工程与工程振动.1989,9(2)：1-14页
[48]刘晶波,廖振鹏.有限元离散模型中得出平面波动.力学学报.1992,242)：208-215页
[49]陈精一,蔡国忠编著.电脑辅助工程分析ANSYS使用指南.北京：中 国铁道出版社,2001
[50]姜勇,张波.ANSYS7.0实例精解.北京：清华大学出版社,2004.1
[51]张亚欧,谷志飞.ANSYS 7.0有限元分析实用教程.北京：清华出版社,2004.7
[52]刘晶波.波动的有限元模拟及复杂场地对地震动的影响.国家地震局工程力学研究所博士学位论文.1989
[53]钱七虎,黄小平等.冲击荷载作用下有限元方法求解波动过程的精度研究.爆炸与冲击.1995,15(1)：1-10页
[54]黎在良,刘殿魁.固体中的波.科学出版社,1995
[2]张福学,王丽坤.现代压电学(中册).北京：科学出版社,2002：1-10页
[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页
[4]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页
[5]Bever MB,Duwez PE. Gradient in Composite Materials.Mater. Sci.Eng. 2004:1-8P
[6]杨大智.智能材料与智能系统.天津大学出版社,2000：183-242页
[7]Rogers C A. Intelligent materials system-the dawn of new materials age. J.Inter.Mater.Syst.Struct.1993:4-12P
[8]Pak Y.E.Crack extension force in a piezoelectric materials.ASME Trans. J.Appl.Mech.1990,57:647-653P
[9]Park S.B,Sun C.T.Effect of electric field on fracture of piezoelectric ceramic.Int.J.Fract.1995,70:203-216P
[10]Park S.B,Sun C.T.Fracture criteria for piezoelectric ceramic.J. Am. Ceram.Soc.1995,78:1475-1480P
[11]PARTON B Z. Fracture mechanics and piezoelectric material. Acta Astronautica.1976(3):671-683P
[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.1997,120:31-45P
[13]Shindo Y,Horiguchi k,Murakami H,Narita F.Single-edge precracked beam test and electric fracture mechanics analysis for piezoe- lectric cetamics. Structures and Devices.2001:311-320P
[14]Wang B,Three-dimensional analysis of a flat elliptical crack in a piezoelectric material.Int.J.Eng.Sci.1992,30:781-791P
[15]Wang Z.K,Huang S.H.Fields near elliptical crack in a piezo electric ceramics.Eng.Fract.Mech.1995,51:447-456P
[16]Wang Z.K,Zheng B.L.The general solution of three-dimensional piezoelectric media.Int.J.Solids Struct.1995,32:105-115P
[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.1996,33:2719-2737P
[18]Zhao M.H,Shen Y.P,Liu Y.J,Liu G.N.Isolated crack in three- dimensional piezoelectric solid. Theor.Appl. Fract. Mech.1997,26:129-139P
[19]Zhao M.H,Shen Y.P,Liu Y.J,Liu GN.Isolated crack in three- dimensional piezoelectric solid.Theor.Appl.Fract.Mech.1997,26:141-149P
[20]SOSA H A.Plane problems in piezoelectric media with defects.Int J Solids Structures,1991(28):491-505P
[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.力学学报.1999,31(3)：311-319页
[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.1998,35:2121-2149P
[23]Wang Xuyue,Yu Shouwen.Scattering of SH waves by an arc-shaped crack between a cylindrical piezoelectric inclusion. Intern- ational Journal of Fracture,1999:35-40P
[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):4777-4796P
[25]Liu J.X,Liu Y.L,Wang B,Du S.Y.Mode-Ⅲ crack in the piezo- elecreic layerof two dissimilar materials.Key Engineering Materials.1998:1167-1172P
[26]Sosa H.A.Plane problems in piezoelectric media with defects. International Journal of Solids and Structures.1991,28:491-505P
[27]Zhao M.H,Shen,Y.P,Liu Y.j,Liu GN.Isolated cracks in three-dimensional piezoelectric solid.Theoretical and Applied Fracture Mechanics.1997,26: 141-149P
[28]Huang Haiming,Shi Huiji,Yin Yajun.Multi-cracks problem for piezoelectric materials strip subjected to dynamic loading. Mechanics Research Communications.2002:413-424P
[29]Sun Jianliang, Zhou Zhengong,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.2005(2):160-170P
[30]Zhou Zhengong,Wang Biao,Sun Yuguo.Investigation of the dynamic behavior of two parallel symmetric cracks in piezoelectric materials use of non-local theory.International Journal of Solids and Structures.2003:747-762P
[31]Chen Jian,Liu Zhengxing.On the dynamic behavior of a func-tionally graded piezoelectric strip with periodic cracks vertical to the boundary. International Journal of Solids and Structures.2005:3133-3146P
[32]Wang B.L,HanJ.C,Du S.Y.Dynamic response for non-homogeneous piezoelectric medium with multiple cracks. Source.Engineering Fracture Mechanics.1998:607-617P
[33]Li Xianfang,Lee Kangyong.Dynamic behavior of a piezoelectric ceramic layer with two surface cracks.International Journal of Solids and Structures.2004:3193-3209P
[34]Ma Li,Wu,Lin Zhi,Zhou Zhengong,Guo Licheng.Scattering of harmonic antiplane shear waves by two collinear cracks in functionally graded piezoelectric materials. European Journal of Mechanics.2004:633-643P
[35]Chen Z.T,Worswick M.J.Dynamic fracture behavior of a cracked piezoelectric half space under anti-plane mechanical and in-plane electric impact.Archive of Applied Mechanics.2002:1-12P
[36]Kwon S.M.Department of Mechanical Design Changwon National University. Acta Mechanica.2004:73-89P
[37]Zhou Zhengong.Harbin Institute of Technology.Center for Composite Materials.2004:63-76P
[38]Li, X.F.Dynamic response of a piezoelectric material with a conducting rigid inclusion. Meccanica.2000:383-392P
[39]Narita F.Shindo Y,Moribayashi H.Circular inclusion problem in dynamic antiplane piezoelectricity Proceedings of SPIE.The International Society for Optical Engineering,2001:69-78P
[40]Xuyue Wang,Shouwen Yu.Scattering of SH waves by an arc-shaped crack between a cylindrical piezoelectric inclusion and the matrix.Key Engineering Materials.2003:215-220P
[41]Bardzokas D.I,Filshtinsky M.L.Anti-plane dynamic problem of an electroelastic cylinder with thin rigid inclusions excited by a system of surface electrodes.Archive of Applied Mechanics.2004:165-178P
[42]Gao Crunfa,Dong,Derngke Complex functions for plane problems of piezoelectric material with an elliptical hole.Engineering Mechanics.1998: 98-104P
[43]鲍亦兴,毛昭宙著.刘殿魁,苏先樾译.弹性波的衍射与动应力集中.北京：科学出版社,1993：72-202页
[44]赵寿根,程伟.1-3型压电复合材料及其研究进展.力学进展.2002,32(1)：57-68页
[45]杜善义,王彪.复合材料细观学.北京：科学出版社,1998
[46]张锦,张乃恭.新型压电复合材料力学机理及其应用.北京：北京航天航空大学出版社,1993
[47]刘晶波,廖振鹏.离散网格中的弹性波动(Ⅱ)——几种有限元离散模型的对比分析.地震工程与工程振动.1989,9(2)：1-14页
[48]刘晶波,廖振鹏.有限元离散模型中得出平面波动.力学学报.1992,242)：208-215页
[49]陈精一,蔡国忠编著.电脑辅助工程分析ANSYS使用指南.北京：中 国铁道出版社,2001
[50]姜勇,张波.ANSYS7.0实例精解.北京：清华大学出版社,2004.1
[51]张亚欧,谷志飞.ANSYS 7.0有限元分析实用教程.北京：清华出版社,2004.7
[52]刘晶波.波动的有限元模拟及复杂场地对地震动的影响.国家地震局工程力学研究所博士学位论文.1989
[53]钱七虎,黄小平等.冲击荷载作用下有限元方法求解波动过程的精度研究.爆炸与冲击.1995,15(1)：1-10页
[54]黎在良,刘殿魁.固体中的波.科学出版社,1995