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.

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.

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

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

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