对边简支的矩形平面弹性问题的辛本征展开定理  

Symplectic Eigenfunction Expansion Theorem for the Rectangular Plane Elasticity Problems With Two Opposite Simply Supported

作　　者：侯国林[1] 阿拉坦仓[1] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《应用数学和力学》2010年第10期1181-1190,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10962004);高等学校博士学科点专项科研基金资助项目(20070126002);内蒙古自治区自然科学基金资助项目(20080404MS0104)

摘　　要：对来源于平面弹性问题的Hamilton算子的本征值问题进行了研究.在矩形域内含位移和应力的混合边界条件下,首先求解了相应算子的本征函数.接着,证明了本征函数系的完备性,这为施行分离变量法求解相应问题提供了可行性.最后,利用文中的辛本征展开定理获得了问题的一般解.The eigenvalue problem of the Hamiltonian operator associated with the plane elasticity problems was investigated. First, the eigenfunctions of the operator with the mixed boundary conditions for the displacement and stress in the rectangular region was solved direct- ly. Then, the completeness of the eigenfunctions was proved, thereby demonstrating the feasi- bility of using separation of variables to solve the problems. Finally, the general solution was obtained by using the symplectic eigenftmction expansion theorem.

关 键 词：平面弹性问题 HAMILTON系统 辛正交性 本征展开 HAMILTON算子 

分 类 号：O175.3[理学—数学] O343.1[理学—基础数学]