Three-Dimensional Solution for the Stress Concentration Around a Circular Hole in a Plate of Arbitrary Thickness

1949 ◽  
Vol 16 (1) ◽  
pp. 27-38
Author(s):  
E. Sternberg ◽  
M. A. Sadowsky
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Ritz Method ◽  
Three Dimensional ◽  
Infinite Plate ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Uniform State ◽  
Arbitrary Thickness

Abstract This paper contains an approximate three-dimensional solution for the stress distribution around a circular cylindrical hole in an infinite plate of arbitrary thickness, which is otherwise in a uniform state of plane stress parallel to the bounding planes. The approach used rests on a modification of the Ritz method in the theory of elasticity. A knowledge of the triaxial characteristics of the ensuing stress concentration is held important in connection with modern views on failure. The results furthermore illuminate critically the significance of two-dimensional analysis in problems of the type under consideration.

Equivalent Circuits of the Elastic Field

1944 ◽  
Vol 11 (3) ◽  
pp. A149-A161
Author(s):  
Gabriel Kron
Keyword(s):  
Steady State ◽  
Reference Frames ◽  
Three Dimensional ◽  
Elastic Field ◽  
Companion Paper ◽  
Theory Of Elasticity ◽  
Equivalent Circuits ◽  
Two Dimensional ◽  
Arbitrary Boundary ◽  
Nonlinear Stress

Abstract This paper presents equivalent circuits representing the partial differential equations of the theory of elasticity for bodies of arbitrary shapes. Transient, steady-state, or sinusoidally oscillating elastic-field phenomena may now be studied, within any desired degree of accuracy, either by a “network analyzer,” or by numerical- and analytical-circuit methods. Such problems are the propagation of elastic waves, determination of the natural frequencies of vibration of elastic bodies, or of stresses and strains in steady-stressed states. The elastic body may be non-homogeneous, may have arbitrary shape and arbitrary boundary conditions, it may rotate at a uniform angular velocity and may, for representation, be divided into blocks of uneven length in different directions. The circuits are developed to handle both two- and three-dimensional phenomena. They are expressed in all types of orthogonal curvilinear reference frames in order to simplify the boundary relations and to allow the solution of three-dimensional problems with axial and other symmetry by the use of only a two-dimensional network. Detailed circuits are given for the important cases of axial symmetry, cylindrical co-ordinates (two-dimensional) and rectangular co-ordinates (two- and three-dimensional). Nonlinear stress-strain relations in the plastic range may be handled by a step-by-step variation of the circuit constants. Nonisotropic bodies and nonorthogonal reference frames, however, require an extension of the circuits given. The circuits for steady-state stress and small oscillation phenomena require only inductances and capacitors, while the circuits for transients require also standard (not ideal) transformers. A companion paper deals in detail with numerical and experimental methods to solve the equivalent circuits.

Separation of the 3D stress state of a loaded plate into two-dimensional tasks: bending and symmetric compression of the plate

2021 ◽  
Vol 103 (3) ◽  
pp. 53-62
Author(s):  
Victor Revenko ◽  
Andrian Revenko
Keyword(s):  
Boundary Conditions ◽  
Harmonic Functions ◽  
Three Dimensional ◽  
Partial Solution ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Normal Stresses ◽  
Equilibrium Equations ◽  
Dimensional Boundary ◽  
The Right

The three-dimensional stress-strain state of an isotropic plate loaded on all its surfaces is considered in the article. The initial problem is divided into two ones: symmetrical bending of the plate and a symmetrical compression of the plate, by specified loads. It is shown that the plane problem of the theory of elasticity is a special case of the second task. To solve the second task, the symmetry of normal stresses is used. Boundary conditions on plane surfaces are satisfied and harmonic conditions are obtained for some functions. Expressions of effort were found after integrating three-dimensional stresses that satisfy three equilibrium equations. For a thin plate, a closed system of equations was obtained to determine the harmonic functions. Displacements and stresses in the plate were expressed in two two-dimensional harmonic functions and a partial solution of the Laplace equation with the right-hand side, which is determined by the end loads. Three-dimensional boundary conditions were reduced to two-dimensional ones. The formula was found for experimental determination of the sum of normal stresses via the displacements of the surface of the plate.

Shear Stress Discontinuities in Adhesive Joints

2015 ◽  
Vol 1088 ◽  
pp. 758-762
Author(s):  
Xiao Cong He
Keyword(s):  
Shear Stress ◽  
Stress Concentration ◽  
Stress Distribution ◽  
Three Dimensional ◽  
Adhesive Layer ◽  
Adhesive Joints ◽  
Shear Stress Distribution ◽  
Element Analysis ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

This paper deals with the stress discontinuities in shear stress distribution of adhesive joints. The three-dimensional finite element analysis (FEA) software was used to model the joints and predict the shear stress distribution along the whole beam. The FEA results indicated that there are stress discontinuities existing in the shear stress distribution within adhesive layer and adherends at the lower interface and the upper interface of the boded section. The numerical values of the shear stress concentration at key locations of the joints and the stress concentration ratio are discussed.

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.

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.

The Prediction of Three-Dimensional Stress Concentration Factors

1959 ◽  
Vol 63 (585) ◽  
pp. 549-551 ◽  
Author(s):  
I. M. Allison
Keyword(s):  
Stress Concentration ◽  
Mathematical Analysis ◽  
Three Dimensional ◽  
Stress Raiser ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Torsional Loading ◽  
Loading System ◽  
Concentration Factors ◽  
Stress Concentration Factors

Two-Dimensional Stress concentration factors may be obtained more quickly and simply than the corresponding three-dimensional factors, either by experiment or mathematical analysis. It would be convenient to obtain information, for varying geometry in the two-dimensional case of a particular type of stress raiser, e.g. a shoulder, groove or hole, and use this either to predict the three-dimensional stress concentration factors or to extend the range of existing three-dimensional results. Clearly a comparison is only possible if the three-dimensional stress raiser embodies a plane of symmetry (which gives the geometry of the similar two-dimensional stress raiser), and if the loading conditions can be reproduced in both the two- and three-dimensional cases. The latter requirement restricts the correlation to the stress concentration factors obtained in tension and in bending. The three-dimensional torsional loading system has no plane of symmetry which can be simulated in two dimensions.

Sign in / Sign up

Export Citation Format

Share Document