Photo-elasticity

Coker, E. G.

doi:10.1016/s0016-0032(25)90236-0

Cited by 13 publications

(7 citation statements)

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“…Finally, we might wonder whether there is any more information to be retrieved from the ray transforms Iw and Iu, or alternatively Ï and Í, as so far we could only reconstruct one tensor component from these data. The answer is no: As proven in [13], if any two stress tensors σ (1) and σ (2) satisfy (26, 27) and σ (1) 33 = σ (2) 33 then they produce the same ray transforms, Iw (1) = Iw (2) and Iu (1) = Iu (2) . As a consequence, the retrieval of one tensor component is the maximum information to be gleaned from a ray transform which is performed for horizontal lines only.…”

Section: Longitudinal and Transverse Tensor Componentsmentioning

confidence: 99%

“…A transparent optical medium which initially is isotropic and homogeneous with respect to light propagation may become birefringent when subjected to external strain, an effect which is known as Photoelasticity [1,2]. The spatially varying tensor of refraction then reflects the presence of stresses within the material, opening up the possibility of examining internal stresses by means of the change in the state of polarization of light beams passing through the strained medium.…”

Section: Introductionmentioning

confidence: 99%

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Application of Sharafutdinov?s Ray Transform in Integrated Photoelasticity

Hammer¹,

Lionheart²

2004

J Elasticity

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Abstract. We explain the main concepts centered around Sharafutdinov's ray transform, its kernel, and the extent to which it can be inverted. It is shown how the ray transform emerges naturally in any attempt to reconstruct optical and stress tensors within a photoelastic medium from measurements on the state of polarization of light beams passing through the strained medium. The problem of reconstruction of stress tensors is crucially related to the fact that the ray transform has a nontrivial kernel; the latter is described by a theorem for which we provide a new proof which is simpler and shorter as in Sharafutdinov's original work, as we limit our scope to tensors which are relevant to Photoelasticity. We explain how the kernel of the ray transform is related to the decomposition of tensor fields into longitudinal and transverse components. The merits of the ray transform as a tool for tensor reconstruction are studied by walking through an explicit example of reconstructing the σ33-component of the stress tensor in a cylindrical photoelastic specimen. In order to make the paper self-contained we provide a derivation of the basic equations of Integrated Photoelasticity which describe how the presence of stress within a photoelastic medium influences the passage of polarized light through the material.

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Section: Longitudinal and Transverse Tensor Componentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application of Sharafutdinov?s Ray Transform in Integrated Photoelasticity

Hammer¹,

Lionheart²

2004

J Elasticity

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“…Previous work on the problem of a plate with a circular hole loaded by a pin includes a photoelastic investigation by Coker and an empirical analysis by Bickley [1]. 2 These investigations were confined to umeinforced holes.…”

Section: Introductionmentioning

confidence: 99%

“…2 These investigations were confined to umeinforced holes. 1 Presented before Sevent h International Congress for Applied Mechanics, London, Sept. 1948.…”

Section: Introductionmentioning

confidence: 99%

Stress distribution near reinforced circular hole loaded by pin

Lévy¹,

Smith²

1949

J. RES. NATL. BUR. STAN.

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This paper presents a theoretical analysis for the stress distribution in a flat plate near a reinforced circular hole loaded by a pin, and a comparison of the theory with test results for a plate of sandwich construction. It is a ss umed t hat an auxiliary reinforcement at the edge of the hole is so rigid t hat no d istortion of the shape of the hole occurs du e to the load. The plate is reinforced in the vic ini ty of the hole by circular "doubler" plates. The theor y and experiment are found t o be in good agreement.

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“…These problems are best treated by using a bipolar coordinate system. The detailed introduction of the bipolar coordinate system can be referred to [1] and [9].…”

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confidence: 99%

Influences of surface on the interaction between holes or edge

Zhang

Shen

2010

Arch Appl Mech

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The effects of surface energy on the interaction between holes or edge are investigated. Three typical problems are discussed: (1) an infinite plate containing two holes of unequal size subjected to an all-round tension, (2) a circle disc containing an eccentric hole subjected to uniform pressure on either external or internal surface, (3) a semi-infinite plate containing an unstressed circular hole subjected to a uniform tension parallel to its straight edge. The problems are solved by series expansion in bipolar coordinates. The results show that the surface energy significantly affects the stress concentrations around the holes as the size of the holes shrinks to nanometers. Meanwhile, the interaction between the holes or edge influences the stress distribution around the holes or edge, which becomes evident as the holes or edge close to each other and is affected by the surface effect significantly.

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Photo-elasticity

Cited by 13 publications

References 0 publications

Application of Sharafutdinov?s Ray Transform in Integrated Photoelasticity

Application of Sharafutdinov?s Ray Transform in Integrated Photoelasticity

Stress distribution near reinforced circular hole loaded by pin

Influences of surface on the interaction between holes or edge

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