A Study of the Stresses Around Elliptical Holes in Flat Plates

1971 ◽  
Vol 93 (2) ◽  
pp. 688-694 ◽  
Author(s):  
Norman Jones ◽  
Demosthenes Hozos
Keyword(s):  
Stress Distribution ◽  
Flat Plate ◽  
Experimental Work ◽  
Elastic Stress ◽  
Elliptical Hole ◽  
Finite Width ◽  
Flat Plates ◽  
Elliptical Holes

The theoretical elastic stress distribution is presented for a thin flat plate of finite width which contains an elliptical hole. Various uniaxial and biaxial in-plane loads are applied to the plate and the results are compared with some existing experimental work. The results of a series of photoelastic tests which were arranged to examine the interaction between the stresses around two neighboring elliptical holes in flat plates are also presented.

Stress Distribution Around Edge Slits in a Plate Loaded in Tension —the Effect of Finite Width of Plate

1962 ◽  
Vol 66 (617) ◽  
pp. 320-322 ◽  
Author(s):  
J. R. Dixon
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Flat Plate ◽  
Elastic Stress ◽  
Width Ratio ◽  
Finite Width ◽  
Two Dimensional ◽  
Finite Plate ◽  
Edge Slit ◽  
Plate Width

SummaryTwo-dimensional photoelastic tests have been carried out on uni-axially loaded flat-plate specimens with two collinear edge slits, to investigate the effect of finite plate width on the elastic stress distribution. It was found that the effect of slitlength/ plate-width ratio on the elastic stress concentration at the end of the edge slit of length l was virtually the same as that for a central slit of length 2l in a plate of the same width, and could be adequately expressed by existing theories.

Stress Distribution Around a Central Crack in a Plate Loaded in Tension ; Effect of Finite Width of Plate

1960 ◽  
Vol 64 (591) ◽  
pp. 141-145 ◽  
Author(s):  
J. R. Dixon
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Flat Plate ◽  
Elastic Stress ◽  
Width Ratio ◽  
Finite Width ◽  
Two Dimensional ◽  
Central Crack ◽  
Image Position ◽  
Plate Width

Summary:The purpose of the work was to investigate the effect of the finite width of plate on the elastic-stress distribution due to a central crack in a flat plate loaded in tension.The range of investigation: (i) Two-dimensional photoelastic tests were carried out on flat-plate specimens. The photoelastic specimens were geometrically similar to the 10 in. wide fatigue specimens used by Frost and Dugdale, with the central crack simulated by a slot bounded by holes of small radii, (ii) A theoretical solution of the problem was derived and compared with the present and other photoelastic results.It is shown that the effect of the crack-length/plate-width ratio on the elastic-stress concentration at the head of the crack can be expressed by the following formulae:

The Behavior of Rectangular Plates Under Concentrated Load

1937 ◽  
Vol 4 (2) ◽  
pp. A75-A85
Author(s):  
R. G. Sturm ◽  
R. L. Moore
Keyword(s):  
Flat Plate ◽  
Experimental Work ◽  
General Analysis ◽  
Rectangular Plates ◽  
Flat Plates ◽  
Concentrated Load ◽  
Analytical Work ◽  
Analytical Research

Abstract This paper presents a summary of the experimental and analytical research on flat plates under concentrated normal loads conducted at the Aluminum Research Laboratories. The experimental work includes tests on a number of different sizes of plates, ranging from 1/8 in. to 1 in. thickness, loaded on spans of from 48 to 384 times the thickness. The effect of the degree of load concentration, types of edge support, and position of the load upon the stresses and deflections have been the principal variables studied. Cases of bending alone, and combined bending and direct stress have been considered. The analytical work refers to the existing general analysis of the flat-plate problem, from which formulas suitable for design purposes have been derived.

Reinforced Elliptical Holes in Stressed Plates

1957 ◽  
Vol 61 (562) ◽  
pp. 688-693 ◽  
Author(s):  
Raymond Hicks
Keyword(s):  
Stress Distribution ◽  
Cross Section ◽  
Maximum Stress ◽  
Elliptical Hole ◽  
Pressure Vessels ◽  
Stress System ◽  
Sectional Area ◽  
Principal Stresses ◽  
Cross Sectional ◽  
Elliptical Holes

SummaryThis paper considers the problem of a reinforced elliptical hole in a plate under the action of a principal stress system of the type found in cylindrical and ellipsoidal pressure vessels. That is, stress systems in which the ratio of the principal stresses is not greater than two to one. It is shown that when the ratio of the major and minor axes of the ellipse can be chosen arbitrarily, practical reinforcements can be designed to give a maximum stress around the hole which is only slightly greater than the maximum stress in a similarly loaded plate with no hole. General expressions are obtained for the stress distribution in the plate around the hole, for the stress acting on a normal cross section of the reinforcement, and for the cross-sectional area of a reinforcement which gives a small stress concentration. These are used to find the variation in the stress distribution around the hole due to reinforcements having different cross-sectional areas when the applied principal stresses are in the ratio of two to one and Poisson's ratio for the material of the plate and reinforcement has practical values.

Stresses Around Reinforced Elliptical Holes, with Applications to Pressure Cabin Windows

1959 ◽  
Vol 10 (4) ◽  
pp. 373-400 ◽  
Author(s):  
W. H. Wittrick
Keyword(s):  
Stress Distribution ◽  
Analytical Solution ◽  
Arbitrary Constant ◽  
Elliptical Hole ◽  
Stress System ◽  
Complex Variable Methods ◽  
Wide Range ◽  
Plane Sheet ◽  
Elliptical Holes ◽  
Different Shapes

An analytical solution, using complex variable methods, is given for the problem of the stress distribution due to an elliptical hole, reinforced around its boundary, in a plane sheet subjected at infinity either to an arbitrary constant stress system or to a bending type stress system. Numerical results were obtained for a wide range of parameters, including three different shapes of ellipse, and ten different amounts of reinforcement. Poisson's ratio was assumed to be 1/3.

Elastic Stress Singularities: Implications for the Attachment of Tendon to Bone

2011 ◽  
Author(s):  
Yanxin Liu ◽  
Victor Birman ◽  
Chanqing Chen ◽  
Stavros Thomopoulos ◽  
Guy M. Genin
Keyword(s):  
Stress Distribution ◽  
Abrupt Change ◽  
Elastic Stress ◽  
Insertion Site ◽  
Stress Singularities ◽  
Local Stresses ◽  
Material Mismatch ◽  
Moduli Of Elasticity

The material mismatch at the attachment of tendon to bone is amongst the most severe for any tensile connection in nature. This is related to the large difference between the stiffness of tendon and bone, whose moduli of elasticity vary by two orders of magnitude. Predictably, such an abrupt change in the stiffness realized over a very narrow insertion site results in high local stresses. One of the implications of the stress distribution is a potential for stress singularities at the junction of the insertion to the bone.

scholarly journals Stress analysis of infinite laminated composite plate with elliptical cutout under different in plane loadings in hygrothermal environment

2021 ◽  
Vol 8 (1) ◽  
pp. 1-12
Author(s):  
Ashok Magar ◽  
Achchhe Lal
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Composite Plate ◽  
Volume Fraction ◽  
Elliptical Hole ◽  
Laminated Composite ◽  
Laminated Composite Plate ◽  
Concentration Changes ◽  
Hygrothermal Environment ◽  
Plate Analysis

Abstract This paper presents the solution of stress distribution around elliptical cutout in an infinite laminated composite plate. Analysis is done for in plane loading under hygrothermal environment. The formulation to obtain stresses around elliptical hole is based on Muskhelishvili’s complex variable method. The effect of fibre angle, type of in plane loading, volume fraction of fibre, change in temperature, fibre materials, stacking sequence and environmental conditions on stress distribution around elliptical hole is presented. The study revealed, these factors have significant effect on stress concentration in hygrothermal environment and stress concentration changes are significant with change in temperature.

scholarly journals A Generalized Method for Flat Plates Impact Detection and Location

2013 ◽  
Vol 543 ◽  
pp. 171-175
Author(s):  
Jose Andrés Somolinos ◽  
Rafael Morales ◽  
Carlos Morón ◽  
Alfonso Garcia
Keyword(s):  
Signal Processing ◽  
Flat Plate ◽  
Acoustic Signal ◽  
Experimental Results ◽  
Piezoelectric Sensors ◽  
Experimental Setup ◽  
Flat Plates ◽  
Impact Detection ◽  
Timing Difference

In the last years, many analyses from acoustic signal processing have been used for different applications. In most cases, these sensor systems are based on the determination of times of flight for signals from every transducer. This paper presents a flat plate generalization method for impact detection and location over linear links or bars-based structures. The use of three piezoelectric sensors allow to achieve the position and impact time while the use of additional sensors lets cover a larger area of detection and avoid wrong timing difference measurements. An experimental setup and some experimental results are briefly presented.

Experimental Study of Multiple Air Jets Impinging a Moving Flat Plate

2020 ◽  
Author(s):  
Flavia Barbosa ◽  
Senhorinha Teixeira ◽  
Carlos Costa ◽  
Filipe Marques ◽  
José Carlos Teixeira
Keyword(s):  
Heat Transfer ◽  
Flat Plate ◽  
Jet Impingement ◽  
Plate Motion ◽  
Test Facility ◽  
Flat Plates ◽  
Target Plate ◽  
Wall Jets ◽  
Air Jets ◽  
Flow Interactions

Abstract The motion of the target plate is important in some industrial applications which apply multiple jet impingement, such as reflow soldering, drying and food processing. Multiple jet impingement is widely used due to its ability to generate high heat transfer rates over large and complex areas. This convective process is characterized by several flow interactions essentially due to adjacent jets mixing prior the impingement, wall jets collision after the impingement, as well as crossflow interactions induced by the motion of the wall jets that flow through the exits of the domain. These interactions lead to strong flow recirculation, pressure gradients and boundary layer development. However, the complexity of the flow interactions is increased with the surface motion in confined space, due to the generation of strong shear regions. These interactions can induce problems and product defects due to complicated thermal behavior and non-uniform heating or cooling, being important to fully understand the process in order to reduce time and costs. This work addresses the experimental analysis of multiple air jets impinging on a moving flat plate. The experiments are conducted on a purpose-built test facility which has been commissioned, using a 2D-PIV system. Through this technique, the flow structure and velocity profiles will be analyzed in detail. The effects of the impinging plate motion on the resulting global and local velocity profile is compared with a static flat plate. The multiple jet configuration consists on air flowing through 14 circular nozzles, at a Reynolds number of 690 and 1,380. The experiments are conducted for a nozzle-to-plate distance of 8 and a jet-to-jet spacing of 2. The target plate motion remains constant throughout the experiments and equal to 0.03 m/s. The results are compared for both stationary and moving flat plates cases and express the increased complexity of the flow due to strong interaction between jets and the target surface, which affects the heat transfer performance. The results obtained experimentally are important to clearly define this complex flow and these data can be used in future works for numerical model validation.

Interaction between two nanoscale elliptical holes with surface tension

2018 ◽  
Vol 24 (5) ◽  
pp. 1556-1566 ◽  
Author(s):  
Shuang Wang ◽  
Cun-Fa Gao ◽  
Zeng-Tao Chen
Keyword(s):  
Surface Tension ◽  
Stress Field ◽  
Hoop Stress ◽  
Elliptical Hole ◽  
Integral Form ◽  
Maximum Hoop Stress ◽  
Stress Boundary Condition ◽  
Elliptical Holes ◽  
Basic Equations ◽  
Stress Boundary

In this paper, the plane problem of two elliptical nanoscale holes with surface tension is investigated. Firstly, the basic equations are given via the complex variable methods. Then, the stress boundary condition caused by surface tension is derived through the integral-form Gurtin–Murdoch model. The problem is finally solved by the conformal mapping along with the series expansion methods. The results show that the stress field decreases as the two holes become further away from each other. When the distance between the two holes is more than three times the sum of their sizes, the interaction between the two holes can be neglected. In addition, the stress field is greatly influenced by the orientation, aspect ratio and size of the holes. The positions of the maximum hoop stress are also discussed. When the two elliptical holes are put close horizontally, the hoop stress around one hole usually obtain its maximum at the endpoint close to the other hole. However, if one elliptical hole is not horizontal, the hoop stress around it will no longer attain its maximum at the endpoints. Another exception is that when one elliptical hole becomes larger, the hoop stress around the smaller hole would tend to achieve a local minimum at the endpoint close to the larger hole.

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