Complete Two-Dimensional Principal Stress Separation by the Photoelastic Oblique Incidence Method

2006 ◽  
Vol 3-4 ◽  
pp. 229-234 ◽  
Author(s):  
Mark N. Pacey ◽  
Rachel A Tomlinson
Keyword(s):  
Principal Stress ◽  
Oblique Incidence ◽  
Normal Incidence ◽  
New Method ◽  
Two Dimensional ◽  
Principal Stresses ◽  
Isochromatic Fringe ◽  
Stress Separation

The oblique incidence method of photoelastic principal stress separation is reconsidered and presented in a form that allows the existence of negative fringe orders to be identified. The normal incidence isoclinic angle, two oblique incidence isoclinic angles and two oblique incidence isochromatic fringe orders are required for the new method. However, by allowing negative fringe orders to be identified, significant uncertainty relating to the separated principal stresses is removed and confidence in the calculated results may be improved

scholarly journals New method of deriving stresses graphically from photo-elastic observations

1933 ◽  
Vol 141 (844) ◽  
pp. 314-324 ◽  
Keyword(s):  
Principal Stress ◽  
Plane Stress ◽  
Polarized Light ◽  
New Method ◽  
Considerable Time ◽  
Principal Stresses ◽  
Graphical Integration ◽  
The Difference ◽  
General Relations

In transparent bodies under plane stress the difference and directions of the two principal stresses are obtained by observations with polarized light. To separate the stresses either additional measurements can be used, for instance changes of thickness; or we may resort to any method of graphical integration. Although several different methods exist, all are based upon the equations of equilibrium and involve considerable time. A new method, which has now been worked out by the writer, based entirely upon elastic equations , enables us to trace those lines, along which the sum of the principal stresses has a constant value. Since we can assign to each line its appropriate parameter, we know in this way the sum of the principal stresses at any point of the plate. This method is very accurate and is carried out quite simply as follows. (I) Theory. (1) General Relations. The lines of principal stress 1 and 2, fig. 1, give at all points the directions of the two principal stresses (σ 1 and σ 2 ); where ϕ is the angle between the directions 1 and Y, or 2 and Z respectively (Y-Z are Cartesian co-ordinates).

Principal Stress Separation Using a Combination of Photoelasticity and Thermoelastic Stress Analysis under Biaxial Stress

2005 ◽  
Vol 297-300 ◽  
pp. 1214-1219
Author(s):  
Akira Shimamoto ◽  
Hiroshi Ohkawara ◽  
Sung Mo Yang
Keyword(s):  
Principal Stress ◽  
Integration Method ◽  
Stress Measurement ◽  
Thermoelastic Stress ◽  
Uniaxial Stress ◽  
Biaxial Stress ◽  
Combined Method ◽  
Principal Stresses ◽  
Stress Separation ◽  
The Difference

Today, stress measurement methods by thermography and by photoelasticity are widely used to make stress distribution visible. However, it is difficult to separate principal stresses using only one of these methods because only the difference of principal stresses is measured in photoelasticity, and only the sum of the principal stresses is measured in thermograpy. Therefore, the inverse analysis problem must be solved to separate the principal stress in the thermoelastic method and the shear difference integration method must be used for the photoelastic method. Although there are some reports separation of the principal stresses under uniaxial stress by combining the two methods, little research under the biaxial stress has been reported due to the difficulty of experimentation. In this research, the principal stresses under biaxial stress are separated by a combined method. Moreover, it is verified that the thermoelastic stress measurement method is effective to evaluate the stress concentration factor.

Photoelastic Separation of Principal Stresses by Oblique Incidence

1943 ◽  
Vol 10 (3) ◽  
pp. A156-A160
Author(s):  
D. C. Drucker
Keyword(s):  
Oblique Incidence ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Fringe Order ◽  
Principal Stresses ◽  
Significant Magnitude ◽  
Oblique Position ◽  
Theoretical Evidence

Abstract Rotation of a two-dimensional model about an axis in its plane is suggested as a simple and quite rapid means of obtaining p and q separately. A determination of retardation (fringe order) in an oblique position is all that is required in addition to the usual photoelastic measurements. Experimental and theoretical evidence is presented to show that accurate results can easily be obtained when the principal stress is of significant magnitude. The method can also be applied in three-dimensional studies.

Calculation of Elastic Displacements From Photoelastic Curves

1953 ◽  
Vol 20 (3) ◽  
pp. 375-380
Author(s):  
H. Poritsky ◽  
R. P. Jerrard
Keyword(s):  
Principal Stress ◽  
Beam Theory ◽  
Dimensional Case ◽  
Stress Difference ◽  
Two Dimensional ◽  
Principal Stresses ◽  
Fringe Patterns

Abstract A method of utilizing photoelastic fringe patterns for purposes of calculating elastic displacements of stressed members is developed. This method utilizes only the lines of constant principal stress difference and does not require knowledge of the directions of the principal stresses. The method developed should prove useful in many cases where measurements of elastic displacements cannot be carried out conveniently but photoelastic fringe patterns are readily available. As an example, the two-dimensional case of a beam in bending with a change in thickness is treated. The correction that must be applied to simple beam theory is determined.

Calculation of the Ion Optical Properties of Inhomogeneous Magnetic Sector Fields Part 3: Oblique Incidence and Exit at Curved Boundaries

1959 ◽  
Vol 14 (9) ◽  
pp. 822-827 ◽  
Author(s):  
H. A. Tasman ◽  
A. J. H. Boerboom ◽  
H. Wachsmuth
Keyword(s):  
Oblique Incidence ◽  
Normal Incidence ◽  
Second Order ◽  
Resolving Power ◽  
High Mass ◽  
Curved Boundaries ◽  
Magnetic Sector ◽  
Mass Resolving Power ◽  
Mass Dispersion ◽  
Fringing Fields

In previous papers 1.2we presented the radial second order imaging properties of inhomogeneous magnetic sector fields with normal incidence and exit at plane boundaries. These fields may provide very high mass resolving power and mass dispersion without increase in radius or decrease of slit widths. In the present paper the calculations are extended to include the effect of oblique incidence and exit at curved boundaries. The influence of the fringing fields on axial focusing when the boundaries are oblique, is accounted for. It is shown that the second order angular aberration may Le eliminated by appropriate curvature of the boundaries.

Diffraction of a pulse by a resistive half-plane. I. Normal incidence

1960 ◽  
Vol 255 (1283) ◽  
pp. 538-549 ◽  
Keyword(s):  
Time Dependence ◽  
Half Plane ◽  
Wave Diffraction ◽  
Diffraction Problem ◽  
Normal Incidence ◽  
Step Function ◽  
Two Dimensional ◽  
Dynamic Similarity ◽  
Function Time ◽  
Dimensional Wave

The two-dimensional wave diffraction problem, acoustic or electromagnetic, in which a pulse of step-function time dependence is diffracted by a resistive half-plane is solved by assuming dynamic similarity in the solution.

Application of Moire Methods to the Determination of Transient Stress and Strain Distributions

1962 ◽  
Vol 29 (1) ◽  
pp. 23-29 ◽  
Author(s):  
W. F. Riley ◽  
A. J. Durelli
Keyword(s):  
Strain Distribution ◽  
Stress And Strain ◽  
Two Dimensional ◽  
Distribution Problem ◽  
Principal Stresses ◽  
Transient Stress ◽  
Optical Phenomenon ◽  
Moiré Effect ◽  
Fringe Patterns

When two arrays of lines are superimposed an optical phenomenon known as the moire effect is observed under certain conditions. This moire effect is used by the authors to determine the distribution of transient strains on the surface of two-dimensional bodies. The method can be used to solve completely the strain-distribution problem or it can be used in combination with photoelasticity to separate the principal stresses. The methods used in interpreting the moire fringe patterns and the techniques used to produce the patterns are described in the paper. Two applications are discussed.

scholarly journals Determination of the Paleostress Orientations and Magnitudes for Missan Structures, Southeastern Iraq

2018 ◽  
Vol 26 (10) ◽  
pp. 213-233
Author(s):  
Atheer Edan Khalil AL- Hachem ◽  
Mustafa Rasheed Salih Al – Obaidi
Keyword(s):  
Principal Stress ◽  
Graphical Methods ◽  
Principal Stresses ◽  
Unstable Region ◽  
Diagram Method ◽  
Stress Orientations

        The use of  Right dihedral method and Mohr diagram method allow determination of the paleostress orientation and its magnitude in Missan structures, Southeastern Iraq. The principal stress orientations and its magnitudes have been determined by the measure of the striation on the faults planes. The measurement of orientation of the principal stress was deduced by different graphical methods, the horizontal maximum principal stresses (σ1) magnitudes were (3600, 4360,4650, 4750 and 5700) bars, the horizontal  intermediate  principal stresses (σ2) magnitudes   were (1528, 1842,1962.5, 1998.5 and 2390.5) bars and the vertical minimum principal stresses (σ3) magnitudes were (544, 676,725, 753 and 919) bars. This study shows that area is located within the unstable region since the poles of measured faults lie in the area of reactivated faults in Mohr diagram.

scholarly journals Three-Dimensional Coordination Number from Two-Dimensional Measurements: A New Method

1986 ◽  
Vol 32 (112) ◽  
pp. 391-396 ◽  
Author(s):  
Richard B. Alley
Keyword(s):  
Coordination Number ◽  
Three Dimensional ◽  
New Method ◽  
Two Dimensional ◽  
Shape Factors ◽  
Important Measure ◽  
Dimensional Measurements ◽  
Average Bond

AbstractThe average three-dimensional coordination number, n3, is an important measure of firn structure. The value of n3 can be estimated from n2, the average measured two-dimensional coordination number, and from a function, Γ, that depends only on the ratio of average bond radius to grain radius in the sample. This method is easy to apply and does not require the use of unknown shape factors or tunable parameters.

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