Generalized Variational Principles for Boundary Value Problem of Electromagnetic Field in Electrodynamics
-
摘要: 给出了线性各项异性电磁场边值问题的广义虚功原理表达式，运用钱伟长教授提出的方法建立了该问题的广义变分原理，可直接反映该问题的全部特征，即4个Maxwell方程、2个场强-位势方程、2个本构方程和8个边界条件．继而导出了一族有先决条件的广义变分原理．作为例证，导出了两个退化形式的广义变分原理，和已知的广义变分原理等价．此外还导出了两个修正的广义变分原理，可为该问题提供杂交有限元模型．建立的各广义变分原理可为电磁场边值问题的有限元应用提供更为完善的理论基础．Abstract: The expression of the generalized principle of virtual work for the boundary value problem of linear and aniso tropic electromagnetic field was given.Using Pro.fW.Z.Chien's method,a pair of generalized variational principles(GVP s)were established,which could directly lead to all four Maxwell equations,two intensity-potential equations,two constitutive equations and eight boundary conditions.A family of constrained variational principles was deduced sequentially.As the additional verifications,two degenerated forms were obtained,which were equivalent to two known variational principles.Two modified GVPs were given to provide the hybrid finite element models for the present problem.A more complete theoretical foundation for the finite element applications was provided for the discussed problem.
-
[1] 钱伟长.变分法及有限元(上册)[M].北京:科学出版社，1980． [2] 钱伟长.广义变分原理[M].上海:知识出版社，1985． [3] 钱伟长. 格林函数和变分法在电磁场和电磁波计算中的应用[M]. 上海: 上海大学出版社，2000． [4] 梁立孚.变分原理及其应用[M].哈尔滨:哈尔滨工程大学出版社，2005:116-135． [5] 刘艳红，张惠明. 压电热弹性体的变分原理及正则方程和齐次方程[J].应用数学和力学，2007，28(2):176-182. [6] Wang X Z，Zhou Y H，Zheng X J. Generalized variational model of magneto-thermoelasticity for nonlinearly magnetized ferroelastic bodies[J]. International Journal of Engineering Science，2002，40(17): 1957-1973． doi: 10.1016/S0020-7225(02)00064-2 [7] Lee P C Y. A variational principle for the equations of piezoelectromagnetism in elastic dielectric crystals[J]. Journal of Applied Physics，1991，69(11): 4770-4773． doi: 10.1063/1.348274 [8] Yang J S. A generalized variational principle for piezoelectromagnetism in an elastic medium[J]. Archives of Mechanics，1991，43(6): 795-798． [9] 卿光辉，邱家俊，刘艳红. 磁电弹性体修正后的H-R混合变分原理和状态向量方程[J].应用数学和力学，2005，26(6):665-671. [10] Luo E，Zhu H J，Yuan L. Unconventional Hamilton-type variational principles for electromagnetic elastodynamics[J]. Science in China，Series G(Physics，Mechanics & Astronomy)，2006，49(1): 119-128． [11] Rothwell E J，Cloud M J. Electromagnetics[M]. Boca Raton:CRC Press，2001． [12] 洪伟，孙连友，尹雷，等.电磁场边值问题的区域分解算法[M].北京:科学出版社，2005:1-8． [13] 黄伟江，罗恩，佘慧. Reissner夹层板动力学的非传统Hamilton型变分原理[J].应用数学和力学，2006，27(1):67-74. [14] 李纬华，罗恩，黄伟江. 弹性正交索网结构动力学的各类非传统Hamilton型变分原理[J].应用数学和力学，2007，28(7):833-843. -
计量
- 文章访问数: 1934
- HTML全文浏览量: 122
- PDF下载量: 959
- 被引次数: 0
下载:
渝公网安备50010802005915号