Fundamental Solutions for Two Dimensional Transversely Isotropic Elastic Solids

Select Volume / Issue:

• Volume 5,Issue 1, Jan. 2017

Year:

2017

Type of Publication:

Article

Keywords:

Hamiltonian, Separation of Variables, Local Effect, Semi-inverse Method, Transversely Isotropic

Authors:

Weixiang Zhang

Journal:

IJISM

Volume:

5

Number:

1

Pages:

7-10

Month:

January

ISSN:

2347-9051

Abstract:

The two dimensional problem of transversely isotropic elastic materials is discussed under the Hamiltonian system with the use of the method of separation of variables, and the original problem is transformed into finding eigenvalues and eigenvectors of the Hamiltonian operator matrix. The traditional semi-inverse method is no longer possible if local effects near the boundary are considered. The Hamiltonian approach is an alternative solution method. By solving the dual equations, all the fundamental solutions including zero and non-zero eigenvectors are derived analytically, and the adjoint relationships of the symplectic orthogonality between the eigenvectors are established. For any boundary condition problem, the solution can be obtained by expanding the fundamental solutions. Based on this method, boundary condition problems are discussed, in which the stress concentration phenomena caused by the restraint of displacement conditions exhibited.

Full text: IJISM_603_FINAL.pdf [Bibtex]