A general solution of an infinite elastic plate with an elliptic hole under biaxial loading

Abstract

A general analytical solution is obtained in this paper for an infinite elastic plate with a traction-free elliptic hole subjected to arbitrary biaxial loading. The boundary-value problem is solved by using the complex potential method, but the usual two-fold conformal transformations are avoided by employing the elliptic-hyperbolic coordinate system, which is physical and natural. All expressions for stress and displacement fields are derived in explicit form to provide a complete analysis and to make the solution ready for engineering use. With two adjustable parameters—the biaxial loading factor λ and the orientation angle β—contained in these expressions, the present solution furnishes a most general account of the elliptic hole problem. It is shown that all existing solutions, including the solution of a cracked plate under biaxial loading, can be obtained from this general solution. In addition, the solution for an important biaxial loading case characterizing thin-walled cylindrical pressure vessels, which has not been reported before, is also derived in the paper as a specific case of the general solution.