磁-电-弹性半空间在轴对称热载荷作用下的三维问题研究

胡克强; 高存法; 仲政; Chen Zengtao

doi:10.6052/0459-1879-20-127

磁-电-弹性半空间在轴对称热载荷作用下的三维问题研究

胡克强^*2), ,,
高存法^*,
仲政^†,
Chen Zengtao^**

^*南京航空航天大学机械结构强度与振动国家重点实验室, 南京 210016
^†哈尔滨工业大学(深圳)理学院, 深圳 518055
^**Department of Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 2G8, Canada

基金项目: 1)国家自然科学基金项目(11872203);创新研究群体项目(51921003)

详细信息

通讯作者:
胡克强

中图分类号: O343.6
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出版历程
- 收稿日期: 2020-04-19
- 刊出日期: 2020-10-09

THREE-DIMENSIONAL ANALYSIS OF A MAGNETOELECTROELASTIC HALF-SPACE UNDER AXISYMMETRIC TEMPERATURE LOADING

^*State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
^†School of Science, Harbin Institute of Technology, Shenzhen 518055, China
^**Department of Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 2G8, Canada

摘要

摘要: 考虑力-电-磁-热等多场耦合作用, 基于线性理论给出了磁-电-弹性半空间在表面轴对称温度载荷作用下的热-磁-电-弹性分析, 并得到了问题的解析解. 利用Hankel 积分变换法求解了磁-电-弹性材料中的热传导及控制方程, 讨论了在磁-电-弹性半空间在边界表面上作用局部热载荷时的混合边值问题, 利用积分变换和积分方程技术, 通过在边界表面上施加应力自由及磁-电开路条件, 推导得到了磁-电-弹性半空间中位移、电势及磁势的积分形式的表达式. 获得了磁-电-弹性半空间中温度场的解析表达式并且给出了应力, 电位移和磁通量的解析解. 数值计算结果表明温度载荷对磁-电-弹性场的分布有显著影响. 当温度载荷作用的圆域半径增大时, 最大正应力发生的位置会远离半无限大体的边界; 反之当温度载荷作用的圆域半径减小时, 最大应力发生的位置会靠近半无限大体的边界. 电场和磁场在温度载荷作用的圆域内在边界表面附近有明显的强化, 而磁-电-弹性场强化区域的强化程度跟温度载荷的大小和作用区域大小相关. 本研究的相关结果对智能材料和结构在热载荷作用下的设计和制造具有指导意义.
- 磁-电-弹性材料 /
- 轴对称温度载荷 /
- Hankel变换 /
- 热传导 /
- 磁-电-弹性场
Abstract: Considering the coupling effects between mechanical, electrical, magnetic and thermal fields, we have presented an analytical solution for the thermo-magneto-electro-elastic problem of a magnetoelectroelastic half-space under axisymmetric thermal loading based on the linear theory. Integral transform method and integral equation technique are applied to analytically solve the heat conduction equation, the governing equations of the magnetoelectroelastic material, and the mixed boundary value problem on the boundary of the magnetoelectroelastic half-space. A general closed-form solution is presented for the complementary and particular parts of the components of the displacement, electric potential and magnetic potential. Traction-free and open circuit electro-magnetic conditions are applied on the boundary surface and an integral form solution for the displacement, electric and magnetic potentials in the magnetoelectroelastic half-space has been successfully obtained. Temperature field in the half-space has been obtained analytically and the expression of the stresses, electric displacements and magnetic induction due to the temperature change applied on the surface are derived and given in an explicit closed form. Numerical results show that the temperature loading has much effect on the field distribution of the mechanical, electric and magnetic fields in the magnetoelectroelastic half-space. As the radius of the constant temperature loading increases, the distance from the region of the maximum normal stress to the free boundary will become larger, and the normal stress becomes much smaller in the regions outside of the circular region. The maximum shear stress appears just below the boundary surface at the edge of the circular region. The electric field is found to be intensified near to the boundary surface within the circular region, and similarly, intensities of the positive and negative magnetic fields are observed at different locations in the half-space under the temperature loading applied on the boundary. The results of this study are helpful for the design and manufacturing of smart materials/structures under thermal loading.
- magnetoelectroelastic material /
- axisymmetric temperature loading /
- Hankel transform /
- heat conduction /
- electric and magnetic field

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参考文献(1)

[1]	Huang JH, Kuo WS. The analysis of piezoelectric/piezomagnetic composite materials containing an ellipsoidal inclusion. Journal of Applied Physics, 1997,81:1378-1386
[2]	Benveniste Y. Magnetoelectric effect in fibrous composites with piezoelectric and piezomagnetic phases. Physics Review B, 1995,B51:16424-16427
[3]	Liu SL, Li YD. Fracture of a multiferroic semicylinder with a magnetoelectroelastic interlayer: Piezoelectric stiffening/softening effects and peak removal of stress intensity factor. International Journal of Solids and Structures, 2016, 88-89:110-118
[4]	詹世革, 方岱宁, 李法新等. 层状电磁复合材料的界面结构与力学行为 -- 国家自然科学基金重大项目成果综述. 中国科学基金, 2015,5:332-336
[4]	( Zhan Shige, Fang Daining, Li Faxin, et al. Final report of key project of NSFC "The interfacial structure and mechanics of laminated magnetoelectric composites". National Science Foundation of China, 2015,5:332-336 (in Chinese))
[5]	Arefi M, Amir HAS. Higher order shear deformation bending results of a magnetoelectrothermoelastic functionally graded nanobeam in thermal, mechanical, electrical, and magnetic environments. Mechanics Based Design of Structures and Machines, 2018,46(6):669-692
[6]	胡骏, 亢战. 考虑可控性的压电作动器拓扑优化设计. 力学学报, 2019,51(4):1073-1081
[6]	( Hu Jun, Kang Zhan. Topology optimization of piezoelectric actuator considering controllability. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(4):324-332 (in Chinese))
[7]	牛牧青, 杨斌堂, 杨诣坤等. 磁致伸缩主被动隔振装置中的磁机耦合效应研究. 力学学报, 2019,51(2):324-332
[7]	( Niu Muqing, Yang Bintang, Yang Yikun, et al. Research on the magneto-mechanical effect in active and passive magnetostrictive vibration isolator. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(2):324-332 (in Chinese))
[8]	张乐乐, 刘响林, 刘金喜. 压电纳米板中SH型导波的传播特性. 力学学报, 2019,51(2):503-511
[8]	( Zhang Lele, Liu Xianglin, Liu Jinxi. Propagation characteristics of SH guided waves in a piezoelectric nanoplate. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(2):324-332 (in Chinese))
[9]	Wang HM, Pan E, Sangghaleh A, et al. Circular loadings on the surface of an anisotropic and magentoelectroelastic half-space. Smart Materials and Structures, 2012,21:075003
[10]	Qin QH. Green's functions of magnetoelastic solids with a half-plane boundary or biomaterial interface. Philosophical Magazine Letters, 2004,84:771-779
[11]	Hu KQ, Chen ZT, Zhong Z. Interface crack between magnetoelectroelastic and orthotropic half-spaces under in-plane loading. Theoretical and Applied Fracture Mechanics, 2018,96:285-295
[12]	段淑敏, 周敏娟, 薛雁等. 加层电磁弹性材料界面裂纹瞬态响应. 工程力学, 2007,24(8):101-107
[12]	( Duan Shumin, Zhou Minjuan, Xue Yan, et al. Transient response of an interface crack between magneto-electro-elastic layer and dissimilar half-infinite medium. Engineering Mechanics, 2007,24(8):101-107 (in Chinese))
[13]	Ma P, Su RKL, Feng WJ. Crack tip enrichment functions for extended finite element analysis of two-dimensional interface cracks in anisotropic magnetoelectroelastic bimaterials. Engineering Fracture Mechanics, 2016,161:21-39
[14]	Yang Y, Li XF. Bending and free vibration of a circular magnetoelectroelastic plate with surface effects. International Journal of Mechanical Sciences, 2019, 157-158:858-871
[15]	Chen WQ, Zhu J, Li XY. General solutions for elasticity of transversely isotropic materials with thermal and other effects: A review. Journal of Thermal Stresses, 2019,42(1):90-106
[16]	Hou PF, Yi T, Wang L. 2D general solution and fundamental solution for orthotropic electro-magneto-thermo-elastic materials. Journal of Thermal Stresses, 2008,31:807-822
[17]	Chen WQ, Lee KY, Ding HJ. General solution for transversely isotropic magneto-electro-thermo-elasticity and the potential theory method. International Journal of Engineering Science, 2004,42:1361-1379
[18]	Carman GP, Cheung KS, Wang D. Micro-mechanical model of a composite containing a conservative nonlinear electro-magneto-thermo- mechanical material. Journal of Intelligent Material Systems and Structures, 1995,6:691-698
[19]	Li JY, Dunn ML. Micromechanics of magnetoelectroelastic composite materials: Average field and effective behavior. Journal of Intelligent Material Systems and Structures, 1998,9:404-416
[20]	Aboudi J. Micromechanical analysis of fully coupled electro-magneto-thermo-elastic multiphase composites. Smart Materials and Structures, 2001,10:867-877
[21]	Ke LL, Wang YS. Free vibration of size-dependent magneto-electro- elastic nanobeams based on the nonlocal theory. Acta Mechanica Sinica, 2014,30(4):516-525
[22]	田晓耕, 沈亚鹏. 广义热弹性问题研究进展. 力学进展, 2012,42(1):18-28
[22]	( Tian Xiaogeng, Shen Yapeng. Research progress in generalized thermoelastic problems. Advances in Mechanics, 2012,42(1):18-28 (in Chinese))
[23]	He TH, Ma JT, Li Y. The generalized electromagnetic-thermoelastic coupling problem of hollow cylindrical conductor based on the memory-dependent derivative. International Journal of Applied Electromagnetics and Mechanics, 2019,61:357-375
[24]	Ootao Y, Tanigawa Y. Transient analysis of multilayered magneto electrothermoelastic strip due to nonuniform heat supply. Composite Structures, 2005,68:471-480
[25]	Karimi M, Shahidi AR. Nonlocal, refined plate, and surface effects used to analyze vibration of magnetoelectroelastic nanoplates under thermo-mechanical and shear loading. Applied Physics A, 2017,123(5):304
[26]	Gao CF, Kessler H, Balke H. Fracture analysis of electromagnetic thermoelastic solids. European Journal of Mechanics A/Solids, 2003,22:433-442
[27]	Niraula OP, Wang BL. Thermal stress analysis in magneto-electro-thermoelasticity with a penny-shaped crack under uniform heat flow. Journal of Thermal Stresses, 2006,29:423-437
[28]	Li PD, Li XY, Kang GZ, et al. Three-dimensional fundamental solution of a penny-shaped crack in an infinite thermo-magneto-electro- elastic medium with transverse isotropy. International Journal of Mechanical Sciences, 2017,130:203-220
[29]	Zhao MH, Dang HY, Fan CY, et al. Analysis of an interface crack of arbitrary shape in a three-dimensional transversely isotropic magnetoelectrothermoelastic biomaterial -- part 1: Theoretical solution. Journal of Thermal Stresses, 2017,40(8):929-952
[30]	Zhao MH, Dang HY, Fan CY, et al. Analysis of an interface crack of arbitrary shape in a three-dimensional transversely isotropic magnetoelectrothermoelastic biomaterial -- part 2: Numerical method. Journal of Thermal Stresses, 2017,40(8):953-972
[31]	Hu KQ, Chen ZT. Pre-kinking of a moving crack in a magnetoelectroelastic material under in-plane loading. International Journal of Solids and Structures, 2013,50:2667-2677
[32]	Hu KQ, Chen ZT, Zhong Z. Pre-kinking analysis of a constant moving crack in a magnetoelectroelastic strip under in-plane loading. European Journal of Mechanics-A/Solids, 2014,43:25-43