磁弹性广义平面问题的分解形式  

The decomposed form of magnetoelastic generalized plane problems

作　　者：杨连枝[1] 高阳[1] 

机构地区：[1]中国农业大学,北京100083

出　　处：《应用力学学报》2012年第6期666-669,772,共4页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11172319);中央高校基本科研业务费专项资金(2011JS046)

摘　　要：通过将分解形式从弹性梁板推广到磁弹性广义平面问题,得到了磁弹性板的分解定理,表明表面不受外力的板内的应力状态可以分解为四部分:平面应力状态、剪切状态、Papkovich-Fadle(P-F)状态、磁应力状态。通过引入并证明了四个引理,简明直接地给出了分解定理的一个严格数学证明。此证明不依赖于双调和函数的P-F本征函数展开,且在证明过程中只应用了一些基本的数学方法,更易于理解。The decomposed form of an elastic beam or plate is extended for magnetoelastic generalized plane problems,and the decomposed theorem of magnetoelastic plate is presented.It is shown that the stress states of the plate with free faces can be decomposed into four parts: the plane-stress state,the shear state,the Papkovich-Fadle(P-F) state and the magnetoelastic state.With the introduction and proof of four lemmas,a rigorous mathematical proof of the decomposed theorem is given concisely and directly,and it is independent of the P-F eigenfunction expansion of bi-harmonic functions.In the proof course,some basic mathematical methods are used only,and the proof is more convenient to be understood.

关 键 词：磁弹性 广义平面问题 分解形式 平面应力状态 剪切状态 P-F状态 磁应力状态 

分 类 号：O343.6[理学—固体力学]