Stress and Displacement around an Elastic Artificial Rectangular Hole

Abstract

In engineering practice, rectangular holes (openings) are often encountered. The presence of rectangular holes increases the complexity of the analysis of engineering media (e.g., soils around a diaphragm wall panel) and structural members (e.g., floor slabs). However, there is currently no simple but sufficiently accurate solution readily available for engineers to obtain stress and displacement distributions around an artificial rectangular hole in an elastic plate. This paper presents a simple approximate solution to the problem for an infinite elastic and isotropic plate subjected to uniaxial stress at infinity. A linear elastic plane stress analysis is carried out using complex variables. By introducing a correction factor, simplified and explicitly expressed, a general conformal transformation function that transforms the area outside an arbitrary rectangular hole into the region inside a unit circle is created and used to obtain a solution. The solution is verified by comparing the calculated results using a finite-element method. Displacements caused by the formation of a rectangular hole are investigated. The ease of implementation of the solution is illustrated.