求解载流薄壳二维磁弹性的差分法  

Difference Method for Solving Two-dimensional Magneto-elasticity of Thin Current-carrying Shells

作　　者：边宇虹[1,2] 田振国[1,2] 白象忠[1,2] 

机构地区：[1]燕山大学建筑工程与力学学院,秦皇岛066004 [2]中国科学院力学研究所,国家非线性连续介质力学重点实验室(LNM),北京100080

出　　处：《工程数学学报》2008年第2期267-272,共6页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(50275128);河北省自然科学基金(A2006000190)．

摘　　要：本文针对在电磁场和机械场耦合作用下的载流薄壳的非线性变形问题进行了研究。给出了载流薄壳在耦合场作用下的二维电动力学方程、磁弹性非线性运动方程和Lorentz力表达式,通过变量代换将描述载流薄壳的磁弹性状态方程整理成含有10个基本未知函数的标准Cauchy型。并通过差分法及准线性化方法,将标准Cauchy型非线性偏微分方程组,变换成为能够用正交离散法编程求解的准线性微分方程组,实现了载流薄壳的磁弹性应力与变形的数值解。In this paper, the problems of nonlinear deformation of thin current-carrying shell under the coupled action of the electromagnetic field and mechanical field are studied. Derived are the two-dimensional electrodynamics equations, the nonlinear magneto-elastic kinetic equations and the expressions of Lorentz force of thin current-carrying shell under the action of the coupled field, the normal Cauchy form nonlinear differential equations, which includes ten basic unknown functions in all, are obtained by means of the variable replacement method. Using the difference method and quasilinearization method, the nonlinear magneto-elastic equations are reduced to a sequence of quasi-linear differential equations, which can be solved by the orthogonal discrete method. The numerical solution of the stresses and deformations in thin current-carrying shell is realized.

关 键 词：载流 薄壳 磁弹性 非线性 差分法 

分 类 号：O441[理学—电磁学] O482.6[理学—物理]