磁-电-弹性半空间在轴对称热载荷作用下的三维问题研究  

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

作　　者：胡克强 高存法 仲政 Chen Zengtao Hu Keqiang;Gao Cunfa;Zhong Zheng;Chen Zengtao(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)

机构地区：[1]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 [2]哈尔滨工业大学(深圳)理学院,深圳518055 [3]Department of Mechanical Engineering,University of Alberta,Edmonton,AB,T6G 2G8,Canada

出　　处：《力学学报》2020年第5期1235-1244,I0001,共11页Chinese Journal of Theoretical and Applied Mechanics

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

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.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 boundar

关 键 词：磁-电-弹性材料 轴对称温度载荷 HANKEL变换 热传导 磁-电-弹性场 

分 类 号：O343.6[理学—固体力学]