The stress and strain concentrations of an elliptical hole in an elastic plate of finite thickness subjected to tensile stress

Abstract

The elastic stress and strain fields in a plate of finite thickness containing an elliptical hole are systematically investigated using the 3D finite element method. It is found that the stress and strain concentrations are different in the plate of finite thickness even if the plate is in an elastic state. The relation between the stress and the strain concentration factors depends on Poisson's ratio, the hole's geometric configuration and the plate thickness. The stress concentration factor is equal to the strain concentration factor only at the notch root of the plate surface. The stress (or strain) concentration factor at the notch root of the plate surface decreases rapidly with increasing thickness and becomes lower than the stress and strain concentration factors corresponding to the plane stress state or at the notch root of the mid plane. It is too low to reflect the overall stress concentration as the thickness increases or as the b/a ratio decreases. The maximum stress concentration factor occurs on the mid plane only when the plate is thinner than the transition thickness of the stress concentration factor. When the plate is thicker than the transition thickness of the stress concentration factor, the distance between the location of the maximum stress concentration factor and plate surface tends to be constant with increasing thickness for the plate with a given b/a ratio. The differences between the maximum value and the surface value of the stress and strain concentration factors increase rapidly and tend to their respective constant values with increasing plate thickness. The smaller the b/a ratio, the larger these differences. The difference of the stress concentration factor is larger than that of the strain concentration factor in the same plate.

Determination of effect of elliptic notches and grooves on stress concentration factors on notched bar in tension and grooved shaft under torsion

“…The finite element models presented in this paper is justified by referring to the theoretical values of K t extracted from works of Pilkey (2008), Petersen (1974) and conclusion offered by Yang (2009). According to Yang (2009), stress concentration factors for 2-D designs are in good agreement with 3-D designs as long as the thickness of the geometry in kept small enough. Based on this comment, the thickness and diameter of the finite element models analyzed in this paper were kept considerably small.…”

“…Yang (2009) showed that the plane stress condition of 3D models is approximately achieved by the 2D ones when the plate thickness tends to zero. Zhao et al (2008) is a summarized the 3D effect of stress concentrations at notches.…”

“…Stress field and stress concentration factor in 3D models of elliptic holes in flat rectangular bars were also studied numerically by Yang (2009), Zhao et al (2008, Snowberger (2008), Pedersen et al (2007) etc. Yang (2009) showed that the plane stress condition of 3D models is approximately achieved by the 2D ones when the plate thickness tends to zero.…”

A numerical method of calculation of total stress in reinforced plates with pressurized hole

“…Also, the micro-stress concentrations in the orthotropic plates were calculated, considering the boundary conditions. [5,[8][9][10][11][12] The results were dependent on the internal shape of the plate and the volume ratio of the components. In this section, the finite element modelling and analysis of micro structure for a composite plate with a circular hole for unidirectional fibres using ANSYS is discussed.…”

“…Experimental results of the tensile strain field around circular hole in a composites plate by Toubal et al [8] were compared with the predictions of a theoretical model previously developed by Lekhnitskii and a finite element study. For a plate containing a hole that is subjected to uniaxial tension or out-of-plane bending, the sensitivity of the stress and strain concentration factors to plate thickness as well as the Poisson's ratio or moment ratio were done by Yang et al [9,10] and Yang [11]. Rhee et al Moreover, [12,13] examined extensive experimental and numerical studies for determining the stress concentration around circular, elliptical holes in composite infinite plate subjected to arbitrary uniaxial and biaxial loading at infinity using finite method obtained in works.…”