Abstract:

It is a basic problem to solve the space foundation in geotechnical engineering. The problem is always solved with one kind of variables in traditional methodology, which is under Lagrange system. Dual variables were employed into the governing equations of mechanics via variable substitutions. Through this way, the governing equations were transmitted into Hamiltonian system. Therefore, the methods of separation of variables can be applied to solving the problem. In the completed solution space, the eigenfunction expansion of the solutions of the equations was obtained by the use of the properties of symplectic geometry. Discussed the zero and nonzero eigenvalues of the equations and their physical meanings. Different from the traditional methods, the paper gives a direct method to solve the problem of the half space foundation

Key words: Hamilton system, symplectic method, eigenfunction, transversely isotropy, Laplace transform