Stress distribution around waist hole on finite plate based on mapping function

Holes exist on parts of ships and offshore structures to satisfy functional requirements, reduce weight, and achieve economic benefits. However, stress concentration often occurs around holes and affects the safety of structures. Analytical methods have been proposed for calculating the stress distribution for regular shapes of holes, such as circular, square, and triangular, particularly for the waist hole on the infinite plate. However, the stress distribution of other types of holes on the finite plate is difficult to calculate, although it is more important in practice. In this study, the stress distribution around the waist hole on the finite plate is explored. An improved mapping function for the waist hole, which introduces a new variable based on the rational mapping theory, is proposed, and the range and variation of each parameter in the formula are given according to the structural characteristics of the waist hole. The typical waist hole on the finite plate is calculated using the proposed method, and related numerical simulations are also performed. The results verify the accuracy and reliability of the proposed method. Moreover, the stress distribution of the waist hole under different loads is calculated and discussed. The findings of this study provide a theoretical reference for practical engineering applications.