层状地基问题的辛几何本征解法

A New Systematic Computational Method for Layered Halfspace Solid

通过引入哈密顿体系,导出了横观各向同性层状半空间体的对偶方程组,将地基问题归结为哈密顿体系下的本征值和本征解问题.利用辛本征解空间的完备性,建立一套封闭的求解问题的方法.实现了欧几里德空间向辛几何空间的转换,从而使得分离变量及本征函数向量展开的解法得以实施,为地基的研究提供了一条新的途径.

Based on the dual variables, the Hamiltonian system theory was introduced into space foundation, and the transformation from Euclidian space to symplectic space was realized. Therefore, the method of separation of variable and eigenfunction expansion method were derived to solve this problem,i, e. a new systematic methodology for foundation was presented.