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.