Stress concentration in finite metallic plates with regular holes

Abstract

This study involved the investigation of the stress distribution around regular holes in finite metallic plates, assuming a plane stress state and uniaxial loading condition. The analytical solution of Muskhelishvili’s complex variable method was utilized. The plate was considered to be finite, isotropic and linearly elastic. A finite plate implied that the proportion of hole side to the longest plate side in triangular and square holes and the proportion of the circle diameter surrounding the other polygonals to the longest plate side should be more than 0.2. The result from the present study necessitated the determination of the actual boundary between finite and infinite plate for the plates with various holes. The finite area with a regular hole in z-plane is mapped onto finite area with unit circle in ζ-plane using the conformal mapping function. To calculate the stress function of a finite plate with regular hole, the stress functions in ζ-plane were determined by superposition of the stress function in infinite plate containing regular hole with stress function in finite plate without hole. Using least square boundary collocation method and applying appropriate boundary conditions, unknown coefficients of stress function were obtained. The influence of parameters such as bluntness, rotation angle of hole, and hole size as effective parameters on stress distribution were investigated. The obtained results were in accordance with numerical results from ABAQUS software and other previous research on this issue. From the results, the study of stress distribution in finite plates, using the theory of infinite plates, could lead to significant errors.