Revisit of an elliptic hole problem by using complex variable method

摘要

In this paper, the problem of an elliptic hole embedded in an infinite plate interacting with an arbitrary point load is revisited by using the complex variable method. Based on analytical continuation theorem, the continuity conditions across the interface are automatically satisfied in a straightforward manner. It is shown that the solution for an infinite domain with an elliptic hole can be obtained from the solution of the corresponding homogeneous problem merely by a simple algebraic expression. This relation is universal in the sense of being independent of the loading considered. The solution of the corresponding homogeneous problem is considered as the principal part of the complex potentials while the complementary part of the complex potentials can be obtained by using analytical continuation theorem. Different expressions of the complementary part of the complex potentials are presented in this paper which are all proved to be the same result.