A GENERAL-SOLUTION OF AN INFINITE ELASTIC PLATE WITH AN ELLIPTIC HOLEUNDER BIAXIAL LOADING

A general analytical solution is obtained in this paper for an infinit e elastic plate with a traction-free elliptic hole subjected to arbitr ary biaxial loading. The boundary-value problem is solved by using the complex potential method, but the usual two-fold conformal transforma tions are avoided by employing the elliptic-hyperbolic coordinate syst em, which is physical and natural. All expressions for stress and disp lacement fields are derived in explicit form to provide a complete ana lysis and to make the solution ready for engineering use. With two adj ustable parameters-the biaxial loading factor lambda and the orientati on angle beta-contained in these expressions, the present solution fur nishes a most general account of the elliptic hole problem. It is show n that all existing solutions, including the solution of a cracked pla te under biaxial loading, can be obtained from this general solution. In addition, the solution for an important biaxial loading case charac terizing thin-walled cylindrical pressure vessels, which has not been reported before, is also derived in the paper as a specific case of th e general solution.