An Interferometer Based Experimental Technique to Evaluate Large Strains and Springback on Sheet Metal

2013 ◽  
Author(s):  
Luis Rafael Sanchez ◽  
Shannon Peterson ◽  
Carl G. Simonsen ◽  
Abrar Satar
Keyword(s):  
Sheet Metal ◽  
Three Dimensional ◽  
Bending Moment ◽  
Large Strains ◽  
Two Dimensional ◽  
Strain Gages ◽  
Additional Information ◽  
Software Algorithms ◽  
Dimensional Measurements ◽  
Vertical Scanning Interferometry

A technique was successfully developed to measure large tensile, compressive strains, springback and strain reversal effects on sheet metal bent to small radii. Vertical Scanning Interferometry (VSI) was used to measure three dimensional data from surfaces with sides varying from 160 nm to 2 mm. Software algorithms were utilized to determine surface topography maps from three-dimensional curved locations and to represent them in a two dimensional plane. Fine reference marks were engraved on both sides of sample. The sample was bent /unbent to small radii under a pure bending moment. Outer strains were calculated from VSI two-dimensional measurements of the original and final lengths between the reference marks. Strain gages, applied at locations close to the reference marks, gave additional information at the elasto-plastic range. Experimental data collected included bending moment as a function of strain, 3-D curvature profiles, springback and reverse bending effects. The technique was proved useful for the experimental evaluation and theoretical validation of bending and springback properties of sheet metal. Experimental results for aluminum and steel alloys are presented.

Bending of an Infinite Beam on an Elastic Foundation

1937 ◽  
Vol 4 (1) ◽  
pp. A1-A7 ◽  
Author(s):  
M. A. Biot
Keyword(s):  
Elastic Foundation ◽  
Poisson Ratio ◽  
Elementary Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Concentrated Load ◽  
Elastic Continuum ◽  
Infinite Beam ◽  
A Value

Abstract The elementary theory of the bending of a beam on an elastic foundation is based on the assumption that the beam is resting on a continuously distributed set of springs the stiffness of which is defined by a “modulus of the foundation” k. Very seldom, however, does it happen that the foundation is actually constituted this way. Generally, the foundation is an elastic continuum characterized by two elastic constants, a modulus of elasticity E, and a Poisson ratio ν. The problem of the bending of a beam resting on such a foundation has been approached already by various authors. The author attempts to give in this paper a more exact solution of one aspect of this problem, i.e., the case of an infinite beam under a concentrated load. A notable difference exists between the results obtained from the assumptions of a two-dimensional foundation and of a three-dimensional foundation. Bending-moment and deflection curves for the two-dimensional case are shown in Figs. 4 and 5. A value of the modulus k is given for both cases by which the elementary theory can be used and leads to results which are fairly acceptable. These values depend on the stiffness of the beam and on the elasticity of the foundation.

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.

scholarly journals Automated three-dimensional measurements of version, inclination, and subluxation

2019 ◽  
Vol 12 (1) ◽  
pp. 31-37
Author(s):  
Dave R Shukla ◽  
Richard J McLaughlin ◽  
Julia Lee ◽  
Ngoc Tram V Nguyen ◽  
Joaquin Sanchez-Sotelo
Keyword(s):  
Computed Tomography ◽  
Image Analysis ◽  
Three Dimensional ◽  
Automated Image Analysis ◽  
Two Dimensional ◽  
Analysis Software ◽  
Glenoid Version ◽  
Image Analysis Software ◽  
Planning Software ◽  
Dimensional Measurements

Background Preoperative planning software has been developed to measure glenoid version, glenoid inclination, and humeral head subluxation on computed tomography (CT) for shoulder arthroplasty. However, most studies analyzing the effect of glenoid positioning on outcome were done prior to the introduction of planning software. Thus, measurements obtained from the software can only be extrapolated to predict failure provided they are similar to classic measurements. The purpose of this study was to compare measurements obtained using classic manual measuring techniques and measurements generated from automated image analysis software. Methods Ninety-five two-dimensional computed tomography scans of shoulders with primary glenohumeral osteoarthritis were measured for version according to Friedman method, inclination according to Maurer method, and subluxation according to Walch method. DICOM files were loaded into an image analysis software (Blueprint, Wright Medical) and the output was compared with values obtained manually using a paired sample t-test. Results Average manual measurements included 13.8° version, 13.2° inclination, and 56.2% subluxation. Average image analysis software values included 17.4° version (3.5° difference, p < 0.0001), 9.2° inclination (3.9° difference, p < 0.001), and 74.2% for subluxation (18% difference, p < 0.0001). Conclusions Glenoid version and inclination values from the software and manual measurement on two-dimensional computed tomography were relatively similar, within approximately 4°. However, subluxation measurements differed by approximately 20%.

scholarly journals Three-dimensional molar enamel distribution and thickness in Australopithecus and Paranthropus

2008 ◽  
Vol 4 (4) ◽  
pp. 406-410 ◽  
Author(s):  
A.J Olejniczak ◽  
T.M Smith ◽  
M.M Skinner ◽  
F.E Grine ◽  
R.N.M Feeney ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Cross Sectional ◽  
Enamel Thickness ◽  
Australopithecus Africanus ◽  
Interspecific Differences ◽  
Dimensional Measurements ◽  
Dimensional Distribution ◽  
History Of ◽  
Thickness Measurements

Thick molar enamel is among the few diagnostic characters of hominins which are measurable in fossil specimens. Despite a long history of study and characterization of Paranthropus molars as relatively ‘hyper-thick’, only a few tooth fragments and controlled planes of section (designed to be proxies of whole-crown thickness) have been measured. Here, we measure molar enamel thickness in Australopithecus africanus and Paranthropus robustus using accurate microtomographic methods, recording the whole-crown distribution of enamel. Both taxa have relatively thick enamel, but are thinner than previously characterized based on two-dimensional measurements. Three-dimensional measurements show that P. robustus enamel is not hyper-thick, and A. africanus enamel is relatively thinner than that of recent humans. Interspecific differences in the whole-crown distribution of enamel thickness influence cross-sectional measurements such that enamel thickness is exaggerated in two-dimensional sections of A. africanus and P. robustus molars. As such, two-dimensional enamel thickness measurements in australopiths are not reliable proxies for the three-dimensional data they are meant to represent. The three-dimensional distribution of enamel thickness shows different patterns among species, and is more useful for the interpretation of functional adaptations than single summary measures of enamel thickness.

Exact, Hierarchical Solutions for Localized Loadings in Isotropic, Laminated, and Sandwich Shells

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
E. Carrera ◽  
G. Giunta
Keyword(s):  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Application Area ◽  
Spherical Shells ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Transverse Pressure ◽  
Shell Models ◽  
Stress And Deformation

This paper presents closed form solutions for simply supported cylindrical and spherical shells subjected to uniform localized distributions of transverse pressure and bending moment. These distributions have been expanded in terms of Fourier’s series for which Navier type “exact” solutions have been found for the governing differential equations of the employed shell theories. Shells made of isotropic materials, composites laminates, and sandwich have been analyzed. Carrera’s unified formulation has been adopted in order to implement a large variety of two-dimensional theories. Classical, refined, zigzag, layerwise, and mixed theories are compared in order to evaluate the stress and deformation variables. Conclusions are drawn with respect to the accuracy of the various theories for the considered loadings and layouts. The importance of the refined shell models in order to describe accurately the three-dimensional stress state in the neighborhood of the localized loading application area is outlined.

Influence of vortex-pairing location on the three-dimensional evolution of plane mixing layers

2002 ◽  
Vol 462 ◽  
pp. 43-77 ◽  
Author(s):  
JORDI ESTEVADEORDAL ◽  
STANLEY J. KLEIS
Keyword(s):  
Time Evolution ◽  
Dimensional Space ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Secondary Structures ◽  
Two Dimensional ◽  
Vortex Pairing ◽  
Instability Modes ◽  
Dimensional Measurements ◽  
Large Plane

Detailed three-dimensional measurements of the first vortex pairing of a large plane mixing layer reveal excitation of several three-dimensional instability modes. Time evolution in three-dimensional space (x, y, z, t) shows how the two-dimensional rollers become three-dimensional as they approach each other and that the linear growth of at least two instability waves leads to a spanwise periodic pairing. The results are based on phase-locked measurements made in three-dimensional spatial grids, with a mesh spacing of 8.5% of the fundamental instability wavelength. Spanwise-uniform, periodic acoustic excitation stabilizes the most probable two-dimensional natural features – roll-up and first pairing. The second subharmonic is added to study the effect of alternate streamwise pairing locations on the three-dimensional characteristics of vortex pairing. Velocities are measured using hot-wire anemometry, and the coherent structures are reconstructed from the ensemble-averaged vorticity field.Vortex pairing is shown to initiate through local ‘bridging’ at the maxima of periodic spanwise undulations. The undulations result from linear amplification of various instability modes on pairing rollers having different strengths. Bridging results from the change of the relative phase between the spanwise undulations of the pairing rollers from in-phase (due to the initial translative mode) to out-of-phase (due to the amplification of bulging-like and non-axisymmetric modes). It is found that when pairing occurs sufficiently far upstream, only axisymmetric waves are amplified and the evolution results in axisymmetric merging. In contrast, when pairing occurs sufficiently far downstream, both axisymmetric and non-axisymmetric waves are amplified and the evolution results in non-axisymmetric merging.The results indicate that vortex pairing is accompanied by the counter-rotating pairs of secondary structures (‘streamwise vortices’ or ‘ribs’) located in the mixing-layer braids and residing in the valleys of the spanwise-roller waves. Time evolution of these secondary structures shows that they move in the transverse direction, following the rollers.

scholarly journals Softening the Complexity of Entropic Motion on Curved Statistical Manifolds

2012 ◽  
Vol 19 (01) ◽  
pp. 1250001 ◽  
Author(s):  
Carlo Cafaro ◽  
Adom Giffin ◽  
Cosmo Lupo ◽  
Stefano Mancini
Keyword(s):  
Statistical Model ◽  
Uncertainty Relation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Temporal Complexity ◽  
Additional Information ◽  
Statistical Manifolds ◽  
Higher Dimensional ◽  
Jacobi Vector ◽  
Minimum Uncertainty

We study the information geometry and the entropic dynamics of a three-dimensional Gaussian statistical model. We then compare our analysis to that of a two-dimensional Gaussian statistical model obtained from the higher-dimensional model via introduction of an additional information constraint that resembles the quantum mechanical canonical minimum uncertainty relation. We show that the chaoticity (temporal complexity) of the two-dimensional Gaussian statistical model, quantified by means of the information geometric entropy (IGE) and the Jacobi vector field intensity, is softened with respect to the chaoticity of the three-dimensional Gaussian statistical model.

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