中文摘要：

针对在电磁场和机械场耦合作用下的载流矩形板的二维磁弹性问题进行了研究。在给出矩形薄板的磁弹性非线性运动方程、几何方程、物理方程、电动力学方程和Lorentz力表达式的基础上,建立了差分格式和线性化迭代方程,给出了这些方程的数值解系统,并以固定边矩形板为例,计算了该板在电磁场和机械载荷耦合作用下的应力及变形,研究了侧向电流和外磁场强度对该板的磁弹性效应。结果表明：通过改变电磁场和通电电流的相关参数,来达到控制薄板变形及应力-应变状态,提高薄板构件的承载能力,以达到工程结构优化设计的目的。

英文摘要：

The two-dimensional magnetic-elasticity problem of a current-carrying rectangular plate under the coupled actions of the electromagnetic field and the mechanical field is studied.Based on the nonlinear magneto-elastic kinetic equations,the geometric equations,the physical equations,the electrodynamics equations and the expressions of Lorentz force of thin rectangular plate,the corresponding difference form and linearized iteration equations are developed.And the numerical solutions for these equations are obtained.A rectangular plate with four edges fixed is used as an example to demonstrate the stresses and the deformations under the coupled actions of the electromagnetic field and mechanical load.The magneto-elastic effect on the plate by the side current and electromagnetic induction density is studied.The results show that the states of the deformation,the stress and the strain in thin plate can be controlled by changing relevant parameters of the magnetic field strength,and thus the current density and carrying capacity of thin plate components can be enhanced to accomplish an optimum design of engineering structures.