Stress analysis of a finite plate with a rectangular hole subjected to uniaxial tension using modified stress functions

•Modified stress functions for a finite plate with a rectangular hole are proposed.•The proposed stress functions can be used for both infinite and finite plates.•The effects of hole size and orientation and plate's aspect ratio are studied.

Stress distribution around a rectangular hole in a finite plate under uniaxial tension is studied using the Muskhelishvili's complex variable method together with the proposed stress functions. The finite area with a rectangular hole in z-plane is mapped onto finite area outside a unit circle in ζ-plane using the mapping function. The proposed stress functions in ζ-plane are presented by superposition of the stress functions for an infinite plate with a rectangular hole and the ones for a finite plate without a hole. The stress results are compared with those of FE simulation and effects of parameters on the stress distribution are studied.