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

Abstract

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.

Effect of various discontinuities present in a plate on stress concentration: a review

“…He had added a new variable in the rational mapping theory, it was projected, and therefore every parameter variation and range within the formula were given as stated in the structural characteristics of the waist hole. Figure 5 shows the thin plate with a hole [68]. Zuxing Pan et al have analyzed the stress distribution around a rectangular hole in a finite plate subjected to uniaxial tension with help of the Muskhelishvili's complex variable method.…”

“…They had concluded when the perforated plate was under a tensile load along the X-axis direction, the stress around the tripling waist hole was smaller than that around the two times waist hole. In that case, a tripling waist hole should be chosen whenever in the case of Y-axis loading the highest stress concentration factor of the tripling waist hole was high, so it was advised to use two times waist hole [68]. E. Madenci et al have analyzed the results of finite composite laminates with multiple circular holes subjected to uniform loading [69].…”

Analysis of stress concentration at the edge of hole in plates with different widths by using FEM

“…Cabrera-Gonzalez et al [12] simulated originated perforation from riveted join failure behaviour in composite plates, and the stress concentration around the hole of the riveted joint which is caused by orthotropic behaviour of join and nonlinear connection of rivet, in order to forecast the amount of failure. It is worth mentioning that a pioneering work on this topic was conducted by Ding et al [13][14][15] who applied linear elastic FEM method to demonstrate the influences of notch depth, width, and thickness of ground blade on stress distribution.…”