Effect of Thickness on the Stresses in a Plate With an Elliptic Hole

1977 ◽  
Vol 99 (2) ◽  
pp. 401-403 ◽  
Author(s):  
M. N. Bapu Rao
Keyword(s):  
Circular Hole ◽  
Thick Plate ◽  
Maximum Stress ◽  
Semimajor Axis ◽  
Plate Thickness ◽  
Elliptic Hole ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Uniform Tension

A three-dimensional analysis is presented for the stresses around an elliptic hole in an infinitely long thick plate subjected to uniform tension and shear. The maximum stress is found to depend on the ratio of plate thickness to the length of the semimajor axis of the hole, as well as on Poisson’s ratio. In the limiting cases the solution reduces to that of the circular-hole problem and the two-dimensional solution of the elliptic-hole problem.

Three-dimensional photoelastic analysis in axially loaded thick plate with hole

1973 ◽  
Vol 8 (3) ◽  
pp. 220-227 ◽  
Author(s):  
N A Rubayi ◽  
V Yadava
Keyword(s):  
Circular Hole ◽  
Thick Plate ◽  
Maximum Stress ◽  
Three Dimensional ◽  
Tensile Loading ◽  
Stress Concentrations ◽  
Precise Location ◽  
Stress Variation ◽  
Photoelastic Analysis ◽  
Different Thickness

In this study three-dimensional photoelasticity is used to analyse the stress variation through different layers of a thick plate containing a circular hole and subjected to uniform tensile loading. The effect of the thickness/diameter ratios on the stress concentrations with thickness is investigated. The experimental results are correlated with the existing three-dimensional theoretical solutions. The data establish, both experimentally and theoretically, the precise location of the maximum-stress layers in plates having different thickness/diameter ratios and thus resolves the discrepancies which existed in previous studies.

Determination of Stress Concentration Around an Oblique Hole by a Finite-Element Technique

1983 ◽  
Vol 105 (2) ◽  
pp. 206-212 ◽  
Author(s):  
Hua-Ping Li ◽  
F. Ellyin
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Maximum Stress ◽  
Plate Thickness ◽  
Two Dimensional ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Parametric Studies ◽  
Element Technique

A plate weakened by an oblique penetration of a circular cylindrical hole has been investigated. The stress concentration around the hole is determined by a finite-element method. The results are compared with experimental data and other analytical works. Parametric studies of effects of angle of inclination, plate thickness, and width are performed. The maximum stress concentration factor (SCF) obtained from the finite-element analysis is higher than experimental results, and this deviation increases with the increase of angle of skewness. The major reason for this difference is attributed to the shear-action between layers parallel to the plate surface which cannot be directly included in the two-dimensional elements. An empirical formula is derived which accounts for the shear-action and renders the finite-element predictions in line with experimentally observed data.

scholarly journals Visualization of CD2 interaction with LFA-3 and determination of the two-dimensional dissociation constant for adhesion receptors in a contact area.

1996 ◽  
Vol 132 (3) ◽  
pp. 465-474 ◽  
Author(s):  
M L Dustin ◽  
L M Ferguson ◽  
P Y Chan ◽  
T A Springer ◽  
D E Golan
Keyword(s):  
Contact Area ◽  
Dissociation Constants ◽  
Three Dimensional ◽  
Lateral Diffusion ◽  
Solution Phase ◽  
Phospholipid Bilayer ◽  
Cell Contact ◽  
Two Dimensional ◽  
Adhesion Receptors ◽  
Dimensional Solution

Many adhesion receptors have high three-dimensional dissociation constants (Kd) for counter-receptors compared to the KdS of receptors for soluble extracellular ligands such as cytokines and hormones. Interaction of the T lymphocyte adhesion receptor CD2 with its counter-receptor, LFA-3, has a high solution-phase Kd (16 microM at 37 degrees C), yet the CD2/LFA-3 interaction serves as an effective adhesion mechanism. We have studied the interaction of CD2 with LFA-3 in the contact area between Jurkat T lymphoblasts and planar phospholipid bilayers containing purified, fluorescently labeled LFA-3. Redistribution and lateral mobility of LFA-3 were measured in contact areas as functions of the initial LFA-3 surface density and of time after contact of the cells with the bilayers. LFA-3 accumulated at sites of contact with a half-time of approximately 15 min, consistent with the previously determined kinetics of adhesion strengthening. The two-dimensional Kd for the CD2/LFA-3 interaction was 21 molecules/microns 2, which is lower than the surface densities of CD2 on T cells and LFA-3 on most target or stimulator cells. Thus, formation of CD2/LFA-3 complexes should be highly favored in physiological interactions. Comparison of the two-dimensional (membrane-bound) and three-dimensional (solution-phase) KdS suggest that cell-cell contact favors CD2/LFA-3 interaction to a greater extent than that predicted by the three-dimensional Kd and the intermembrane distance at the site of contact. LFA-3 molecules in the contact site were capable of lateral diffusion in the plane of the phospholipid bilayer and did not appear to be irreversibly trapped in the contact area, consistent with a rapid off-rate. These data provide insights into the function of low affinity interactions in adhesion.

Three-Dimensional Elastic Stress Fields of Finite Thickness Plates with Elliptical Hole

2007 ◽  
Vol 353-358 ◽  
pp. 74-77
Author(s):  
Zheng Yang ◽  
Chong Du Cho ◽  
Ting Ya Su ◽  
Chang Boo Kim ◽  
Hyeon Gyu Beom
Keyword(s):  
Stress Concentration ◽  
Plane Strain ◽  
Plane Stress ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Maximum Stress ◽  
Elastic Stress ◽  
Finite Thickness ◽  
Plate Thickness ◽  
Three Dimensional

Based on detailed three-dimensional finite element analyses, elastic stress and strain field of ellipse major axis end in plates with different thickness and ellipse configurations subjected to uniaxial tension have been investigated. The plate thickness and ellipse configuration have obvious effects on the stress concentration factor, which is higher in finite thickness plates than in plane stress and plane strain cases. The out-of-plane stress constraint factor tends the maximum on the mid-plane and approaches to zero on the free plane. Stress concentration factors distribute ununiformly through the plate thickness, the value and location of maximum stress concentration factor depend on the plate thickness and the ellipse configurations. Both stress concentration factor in the middle plane and the maximum stress concentration factor are greater than that under plane stress or plane strain states, so it is unsafe to suppose a tensioned plate with finite thickness as one undergone plane stress or plane strain. For the sharper notch, the influence of three-dimensional stress state on the SCF must be considered.

scholarly journals Three-Dimensional Stress Concentration Around a Cylindrical Hole in a Semi-Infinite Elastic Body

1966 ◽  
Vol 33 (4) ◽  
pp. 855-865 ◽  
Author(s):  
C. K. Youngdahl ◽  
E. Sternberg
Keyword(s):  
Integral Transform ◽  
Finite Thickness ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Integral Form ◽  
The Body ◽  
Cylindrical Hole ◽  
Normal Displacement ◽  
Plane Boundary ◽  
Dimensional Solution

This paper contains a three-dimensional solution, exact within classical elastostatics, for the stresses and deformations arising in a half-space with a semi-infinite transverse cylindrical hole, if the body—at infinite distances from its cylindrical boundary—is subjected to an arbitrary uniform plane field of stress that is parallel to the bounding plane. The solution presented is in integral form and is deduced with the aid of the Papkovich stress functions by means of an especially adapted, unconventional, integral-transform technique. Numerical results for the nonvanishing stresses along the boundary of the hole and for the normal displacement at the plane boundary, corresponding to several values of Poisson’s ratio, are also included. These results exhibit in detail the three-dimensional stress boundary layer that emerges near the edges of the hole in the analogous problem for a plate of finite thickness, as the ratio of the plate thickness to the diameter of the hole grows beyond bounds. The results obtained thus illustrate the limitations inherent in the two-dimensional plane-strain treatment of the spatial plane problem; in addition, they are relevant to failure considerations and of interest in connection with experimental stress analysis.

A Model for Heat Transfer From Embedded Blood Vessels in Two-Dimensional Tissue Preparations

1995 ◽  
Vol 117 (1) ◽  
pp. 64-73 ◽  
Author(s):  
Liang Zhu ◽  
Sheldon Weinbaum
Keyword(s):  
Heat Transfer ◽  
Blood Vessels ◽  
Three Dimensional ◽  
Tissue Preparation ◽  
Basic Solution ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Tissue Conductivity ◽  
Thermal Equilibration ◽  
Insight Into

Two-dimensional microvascular tissue preparations have been extensively used to study blood flow in the microcirculation, and, most recently, the mechanism of thermal equilibration between thermally significant countercurrent artery-vein pairs. In this paper, an approximate three-dimensional solution for the heat transfer from a periodic array of blood vessels in a tissue preparation of uniform thickness with surface convection is constructed using a newly derived fundamental solution for a Green’s function for this flow geometry. This approximate solution is exact when the ratio K′ of the blood to tissue conductivity is unity and a highly accurate approximation when K′ ≠ 1. This basic solution is applied to develop a model for the heat transfer from a countercurrent artery-vein pair in an exteriorized rat cremaster muscle preparation. The numerical results provide important new insight into the design of microvascular experiments in which the axial variation of the thermal equilibration in microvessels can be measured for the first time. The solutions also provide new insight into the design of fluted fins and microchips that are convectively cooled by internal pores.

Thickness Effects Are Minor in the Energy-Release Rate Integral for Bent Plates Containing Elliptic Holes or Cracks

1981 ◽  
Vol 48 (2) ◽  
pp. 320-326 ◽  
Author(s):  
J. G. Simmonds ◽  
J. Duva
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Relative Error ◽  
Release Rate ◽  
Plate Theory ◽  
Semimajor Axis ◽  
Elliptic Hole ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Classical Plate Theory

The exact value of Sanders’ path-independent, energy-release rate integral I for an infinite, bent elastic slab containing an elliptic hole is shown to be approximated by its value from classical plate theory to within a relative error of O(h/c)F(e), where h is the thickness, c is the semimajor axis of the ellipse, and F is a function of the eccentricity e. This result is based on Golden’veiser’s analysis of three-dimensional edge effects in plates, as developed by van der Heijden. As the elliptic hole approaches a crack, F(e)~In (1−e). However, this limit is physically meaningless, because Golden’veiser’s analysis assumes that h is small compared to the minimum radius of curvature of the ellipse. Using Knowles and Wang’s analysis of the stresses in a cracked plate predicted by Reissner’s theory, we show that the relative error in computing I from classical plate theory is only O(h/c)In(h/c), where c is the semicrack length. Our results suggest that classical plate and shell theories are entirely adequate for predicting crack growth, within the limitations of applying any elastic theory to an inherently inelastic phenomenon.

scholarly journals Comparison of Two- and Three-Dimensional Flow Computations With Laser Anemometer Measurements in a Transonic Compressor Rotor

1983 ◽  
Vol 105 (3) ◽  
pp. 596-605 ◽  
Author(s):  
R. V. Chima ◽  
A. J. Strazisar
Keyword(s):  
Three Dimensional ◽  
Axial Compressor ◽  
Maximum Flow ◽  
Wave System ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Transonic Compressor ◽  
Function Solution ◽  
Compressor Rotor ◽  
Laser Anemometer

Two-and three-dimensional inviscid solutions for the flow within a transonic axial compressor rotor at design speed are compared to laser anemometer measurements at maximum flow and near stall operating points. Computational details of the two-dimensional axisymmetric stream function solution and the three-dimensional full Euler solution are described. Upstream of the rotor, the two and three-dimensional solutions for radial distribution of relative Mach number and total pressure agree well with the data. Within the bow wave system and the blade row, the axisymmetric two-dimensional solution shows only qualitative agreement with the data.

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