基于应力形式的二维弹性问题的本征展开法

给出求解基于应力形式的二维弹性问题的本征函数展开方法．通过引入适当的状态函数，将该问题的基本偏微分方程等价地转化为上三角微分系统,导出相应的上三角算子矩阵．证明了该矩阵的两个对角块算子均具有规范的正交本征函数系,并得到它们在相应空间中的完备性．此外，基于本征函数系的完备性,应用本征函数展开法给出了二维弹性问题的一般解．

Eigenfunction Expansion Method and Its Application to Two-Dimensional Elasticity Problems Based on Stress Formulation

Eigen function expansion method of solving two-dmiensional elasticity problems was proposed based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above two-dmien sional problems was rewritten as an upper triangular differential system. For the associated operatorm atrix, the existence and comple teness of two normed or thogonal eigen function systems in some space are obtained, which belong to the two block operators arising in the operator. Moreover, the general solution of the proceeding two-dimensional problem is given by the eigenfunction expansion.