Journal articles: 'Displacement fields'

1

Epstein, J. S., W. G. Reuter, and D. D. Keiser. "Crack embrittlement displacement fields." Optics and Lasers in Engineering 13, no. 1 (1990): 3–16. http://dx.doi.org/10.1016/0143-8166(90)90036-9.

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TAEPRASARTSIT, SOMPON. "USING VON KARMAN NONLINEAR DISPLACEMENT FUNCTIONS IN THE FINITE ELEMENT ANALYSIS OF FUNCTIONALLY GRADED COLUMN." International Journal of Computational Methods 09, no. 03 (2012): 1250042. http://dx.doi.org/10.1142/s0219876212500429.

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This paper focuses on deriving the exact displacement fields of a functionally graded column (FGC) subjected to mechanical and thermal loads under the assumptions of the Timoshenko beam theory and von Karman strains. Valid only when an axial load is present, the obtained displacement fields are, therefore, not applicable in pure bending analysis. These displacement fields are used as the interpolation functions for formulating static finite element equations whose DOFs are arbitrary constants rather than nodal displacements. The element is super-convergent in von Karman nonlinear analysis, and its superiority over beam elements formulated by using linear exact displacement fields is shown in two examples: (1) the buckling analysis of a stepped FGC, and (2) an FGC subjected to a thermal load. Also investigated is the efficiency of using von Karman nonlinear displacement fields as the interpolation functions for analyzing cases in which the level of nonlinearity is higher than that of the von Karman strain.

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Xia, Yong Jun, and Qian Miao. "Large Deformation Geometric Nonlinear Beam Element Based on U.L. Format." Advanced Materials Research 446-449 (January 2012): 3596–603. http://dx.doi.org/10.4028/www.scientific.net/amr.446-449.3596.

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Based on the geometric deformation of the Euler-Bernoulli beam element, the geometric nonlinear Euler-Bernoulli beam element based on U.L. formulation is derived. The element’s transverse first-order displacement field is constructed using the cubic Hermite interpolation polynomial, and the first-order Lagrange interpolation polynomial is used for the axial displacement field. Then the additional displacements induced from the rotation of the elemental are included into the transverse and longitudinal displacement fields, so those displacement fields are expressed as the quadratic function of nodal displacement. Afterwards the nonlinear finite element formulas of Euler-Bernoulli beam element under the form of U.L. formulation are derived using Cauchy strain tensor and the principle of virtual displacements. The total equilibrium equation and tangent stiffness for large displacement geometric nonlinear analysis of frame are obtained in the total coordinate system. The correctness of this element is proved by typical example.

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Honório, Leonardo M., Milena F. Pinto, Maicon J. Hillesheim, Francisco C. de Araújo, Alexandre B. Santos, and Delfim Soares. "Photogrammetric Process to Monitor Stress Fields Inside Structural Systems." Sensors 21, no. 12 (2021): 4023. http://dx.doi.org/10.3390/s21124023.

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This research employs displacement fields photogrammetrically captured on the surface of a solid or structure to estimate real-time stress distributions it undergoes during a given loading period. The displacement fields are determined based on a series of images taken from the solid surface while it experiences deformation. Image displacements are used to estimate the deformations in the plane of the beam surface, and Poisson’s Method is subsequently applied to reconstruct these surfaces, at a given time, by extracting triangular meshes from the corresponding points clouds. With the aid of the measured displacement fields, the Boundary Element Method (BEM) is considered to evaluate stress values throughout the solid. Herein, the unknown boundary forces must be additionally calculated. As the photogrammetrically reconstructed deformed surfaces may be defined by several million points, the boundary displacement values of boundary-element models having a convenient number of nodes are determined based on an optimized displacement surface that best fits the real measured data. The results showed the effectiveness and potential application of the proposed methodology in several tasks to determine real-time stress distributions in structures.

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Konvisar, A. M., V. O. Mikhailov, M. S. Volkova, and V. B. Smirnov. "Model of the Seismic Rupture Surface of the Chignik Earthquake (Alaska, USA) 07.29.2021 Based on SAR Interferometry and GNSS Data." Вулканология и сейсмология 17, no. 5 (2023): 74–83. http://dx.doi.org/10.31857/s0203030623700256.

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The paper presents a new rupture model for the Mw = 8.2 “Chignik” earthquake, which occurred off the coast of the Alaska Peninsula on 29.07.2021. The model is based on the Earth’s surface displacement fields obtained by InSAR (Interferometric synthetic aperture radar) method using images of the ESA Sentinel-1 satellites from 17.07 to 10.08.2021 and data on horizontal displacements at nearest permanent GPS sites from 18.07 to 08.08.2021. Obtained displacement fields include both coseismic and part of postseismic displacements. When constructing a model of the seismic rupture surface, we used F. Pollitz’s solution of the problem of the displacement fields at the surface of a spherical radially stratified planet caused by displacements on a rectangular discontinuity located inside it. For the regularization of the inverse problem, we added the condition that the direction of slip on each element of the fault plane is close to the rake angle, determined from seismological data. In the constructed model, the seismic rupture area was approximated by a single plane with a length of 225 km along the strike, 126 km along the dip, divided into 48 identical rectangles. According to the constructed model, the type of displacements is almost pure thrust, and displacements, in general, occurred throughout all the source area. The maximum displacement was 5.7 m, with an average displacement over the entire plane of 2.2 m, which is close to the USGS and GCMT estimates derived from seismological data.

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Tukiainen, Pekka, and Mark Hughes. "The fracture behavior of birch and spruce in the radial-tangential crack propagation direction at the scale of the growth ring." Holzforschung 67, no. 6 (2013): 673–81. http://dx.doi.org/10.1515/hf-2012-0139.

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Abstract Crack-tip displacement fields have been computed based on digital image correlation for spruce (Picea abies [L.] Karst.) and birch (Betula pendula Roth.) wood, which were submitted to pure mode I loading in the RT-direction under both green and air-dried conditions. Moreover, crack propagation was modeled based on both linear elastic fracture mechanics (LEFM) and nonlinear fracture mechanics, relying on the fictitious crack model (FCM). The measured and modeled load versus the crack-mouth opening displacement (CMOD) curves and displacement fields were compared. In the case of spruce, the load-CMOD curves simulated by the FCM coincide well with the measured ones. On the contrary, measured near crack-tip displacement fields in both green and air-dried spruce are better comparable with the LEFM predictions than with the FCM predictions. In the case of green birch, the simulated FCM curve follows the measured curve quite well, but in air-dried birch the simulated FCM curve has a better fit than the LEFM-curve only before maximum load. In birch, the FCM predicts the displacement fields better than the LEFM. In both species, moisture content has a big effect on the softening behavior. In both spruce and birch, the FCM overestimates the displacements ahead of crack tip, whereas the LEFM model underestimates the displacements.

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7

Ayasse, Jörg, and Heinrich Müller. "Sculpturing on Discrete Displacement Fields." Computer Graphics Forum 21, no. 3 (2002): 431–40. http://dx.doi.org/10.1111/1467-8659.00603.

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8

Yang, Xue-Min, and Paul M. Davis. "Deformation due to a rectangular tension crack in an elastic half-space." Bulletin of the Seismological Society of America 76, no. 3 (1986): 865–81. http://dx.doi.org/10.1785/bssa0760030865.

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Abstract Closed, analytic expressions are given for the displacement fields, their derivatives, and stresses from a rectangular crack in an elastic half-space having Burger's vector normal to its surface. Displacements are found by integration of Volterra's formula over the crack area using Mindlin's (1936) point force solutions for the elastic half-space. Differentiation of the displacement fields yields expressions for calculating stress and strain throughout the medium. Contours of stresses and displacements are given for selected geometries. The expressions for displacements give identical values to those calculated using angular dislocations (Comninou and Dundurs, 1975). All solutions are presented as a FORTRAN subroutine to facilitate practical implementation.

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9

Lee, M. W. "Particle displacements on the wall of a borehole from incident plane waves." GEOPHYSICS 52, no. 9 (1987): 1290–96. http://dx.doi.org/10.1190/1.1442389.

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Particle displacements from incident plane waves at the wall of a fluid‐filled borehole are formulated by applying the seismic reciprocity theorem to far‐field displacement fields. Such displacement fields are due to point forces acting on a fluid‐filled borehole under the assumption of long wavelengths. The displacement fields are analyzed to examine the effect of the borehole on seismic wave propagation, particularly for vertical seismic profiling (VSP) measurements. When the shortest wavelength of interest is approximately 25 times longer than the borehole’s diameter, the scattered displacements are proportional to the first power of incident frequency and borehole diameter. The maximum scattered energy occurs when an incident P‐wave propagates perpendicular to the borehole. Borehole effects on VSP measurements, such as waveform distortion, amplitude variation, and time delay, have been analyzed using the concept of a transfer function. When the shortest wavelength of interest is about 40 times longer than the borehole’s diameter, borehole effects on VSP measurements using a wall‐locking geophone are negligible.

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10

Feng, Ruitao, Qingyun Du, Huanfeng Shen, and Xinghua Li. "Region-by-Region Registration Combining Feature-Based and Optical Flow Methods for Remote Sensing Images." Remote Sensing 13, no. 8 (2021): 1475. http://dx.doi.org/10.3390/rs13081475.

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While geometric registration has been studied in remote sensing community for many decades, successful cases are rare, which register images allowing for local inconsistency deformation caused by topographic relief. Toward this end, a region-by-region registration combining the feature-based and optical flow methods is proposed. The proposed framework establishes on the calculation of pixel-wise displacement and mosaic of displacement fields. Concretely, the initial displacement fields for a pair of images are calculated by the block-weighted projective model and Brox optical flow estimation, respectively in the flat- and complex-terrain regions. The abnormal displacements resulting from the sensitivity of optical flow in the land use or land cover changes, are adaptively detected and corrected by the weighted Taylor expansion. Subsequently, the displacement fields are mosaicked seamlessly for subsequent steps. Experimental results show that the proposed method outperforms comparative algorithms, achieving the highest registration accuracy qualitatively and quantitatively.

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11

Sciammarella, Cesar A., Federico M. Sciammarella, and Luciano Lamberti. "Determination of Displacement Fields at the Sub-Nanometric Scale." Materials 12, no. 11 (2019): 1804. http://dx.doi.org/10.3390/ma12111804.

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Macroscopic behavior of materials depends on interactions of atoms and molecules at nanometer/sub-nanometer scale. Experimental mechanics (EM) can be used for assessing relationships between the macro world and the atomic realm. Theoretical models developed at nanometric and sub-nanometric scales may be verified using EM techniques with the final goal of deriving comprehensive but manageable models. Recently, the authors have carried out studies on EM determination of displacements and their derivatives at the macro and microscopic scales. Here, these techniques were applied to the analysis of high-resolution transmission electron microscopy patterns of a crystalline array containing dislocations. Utilizing atomic positions as carriers of information and comparing undeformed and deformed configurations of observed area, displacements and their derivatives, as well as stresses, have been obtained in the Eulerian description of deformed crystal. Two approaches are introduced. The first establishes an analogy between the basic crystalline structure and a 120° strain gage rosette. The other relies on the fact that, if displacement information along three directions is available, it is possible to reconstruct the displacement field; all necessary equations are provided in the paper. Remarkably, the validity of the Cauchy-Born conjecture is proven to be correct within the range of observed deformations.

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12

Timofeev, V. Yu, D. G. Ardyukov, and A. V. Timofeev. "Variation of displacement fields and Gorny Altai seismic regime." Vulkanologiâ i sejsmologiâ, no. 4 (December 16, 2024): 54–69. https://doi.org/10.31857/s0203030624040048.

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More than twenty years of crust motion measurements by space geodesy method include different epochs of Gorny Altai seismic process. Our study aims at investigating the fields of displacement and deformation in the Gorny Altai region, where we have 20 points-net, situated on big territory, from Novosibirsk in North to Molgolian border at South, and from Kazahstan border at West, to Sayan Mountains at East. Chuya earthquake (September, 2003) separated study period (2000‒2022) to several epochs: pre-seismic – 2000‒2003; 2003‒2004 co-seismic period for epicentral zone; 2004‒2013 post-seismic period for epicentral zone and 2000‒2022 period for far-zone without of earthquake influence. Long term data analyses by modern special program. Anomalous behavior features are discovered in the displacement orientations, as well as in the distribution of velocities and deformation in the zone of the future earthquake. The spatial displacement pattern defined for the period of coseismic displacements corresponds to the right‐lateral strike‐slip along the vertical fault. Elastic and viscoelastic models (2D and 3D modification) used for interpretation. Depth of hypocenter was estimated as 14 km with 2 m relative shift on the seismic fault. In frame of two layers model the viscosity of lower crust ranges 5·1019‒1.1·1020 Pa·s for different elastic modulus parameters. The results of our study show that modern horizontal displacements occur in the NNW direction at the rate of 0.8 mm/y for mountain part outside the Chuya earthquake epicenters zone. Velocity of area deformation at mountain part was 2·10–8/y and it is one order more than the value at flat territory situated to North from Gorny Altai.

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13

Souza, Simone, A. T. Avelar, J. M. C. Malbouisson, and B. Baseia. "Conditional displacement operator for traveling fields." Optics Communications 281, no. 10 (2008): 2864–67. http://dx.doi.org/10.1016/j.optcom.2008.01.056.

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14

Tereschenko, T. V., P. B. Sokolov, and O. A. Goncharov. "Graphic-motor adaptation to computer distortions between coordinates of the visual and motor fields." Experimental Psychology (Russia) 11, no. 1 (2018): 92–113. http://dx.doi.org/10.17759/exppsy.2018110106.

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The article presents. The paper is devoted to perceptual-motor coordination and adaptation in the conditions of computer distortion between the coordinates of motor and visual fields. We studied experimentally changes and relationship between the speed and accuracy of motor execution at different angular displacements of the computer mouse movement, adaptation to the changed conditions of the cursor movement perception, gender differences in speed and quality of the graphic-motor task. The experiment was carried out in a computer version. It is used nine conditions of angular displacements (from 0° to 180°). 25 subjects participated in the experiment: 12 women and 13 men aged 17-25 years. According to the results, speed and accuracy of the graphic-motor task are decreasing with increasing angular displacement (p&lt;0,001). We identified three groups of angular displacement according to the degree of accuracy and adaptation. The largest range of values and errors is observed at the angular displacement in 135°. At small angular displacements (less 75°) the increase of execution time leads to accuracy improvement, but at the angles more than 90° it leads to accuracy decline. Gender differences were at the level of statistical trend (p=0,087) — men performed tasks faster and more accurately than women, but adaptation to the changed conditions was almost equal

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15

Geers, M. G. D., R. De Borst, and W. A. M. Brekelmans. "Computing strain fields from discrete displacement fields in 2D-solids." International Journal of Solids and Structures 33, no. 29 (1996): 4293–307. http://dx.doi.org/10.1016/0020-7683(95)00240-5.

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16

Pan, Bing, Hui Min Xie, Tao Hua, Wei Ning Wang, and Yan Fang. "Displacement Smoothing and Strain Estimation Using Savitaky-Golay Filters in Digital Image Correlation." Key Engineering Materials 326-328 (December 2006): 135–38. http://dx.doi.org/10.4028/www.scientific.net/kem.326-328.135.

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Recently, many research works were concentrated on how to improve the accuracy of displacement fields in digital image correlation (DIC). However, the original displacement fields calculated at discrete locations using DIC are unavoidably contaminated by noises. If the strain fields are directly computed by differentiating the original displacement fields, the noises will be amplified even at a higher level and the resulting strain fields are untrustworthy. To acquire reliably estimation of strain fields, in this paper, Savitaky-Golay (SG) filters are introduced to obtain smoothed displacement fields and reasonable strain estimation. The principle of two-dimensional SG filters is described in detail first. Then images of uniaxial tensile and three-point bending experiments were used to verify the proposed approach. The resulting smoothed displacement fields and strain fields clearly show that the proposed method is simple and effective.

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Luo, P.-F., and F. C. Huang. "An experimental study on the mixed-mode crack tip deformation fields in polymethyl methacrylate." Journal of Strain Analysis for Engineering Design 38, no. 4 (2003): 313–28. http://dx.doi.org/10.1243/03093240360692904.

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Stereo vision was used to measure the full three-dimensional deformation field around the crack tip region of a compact tension shear (CTS) specimen made of polymethyl methacrylate (PMMA) subjected to mixed-mode (I/II) loading. The stress intensity factors (SIF), K1 and KII, were then estimated using both measured in-plane and out-of-plane deformation fields. The KI and KII values determined from in-plane displacements are in very good agreement with those determined from out-of-plane displacement. The far-field J integral values computed using the line integral are compared with those evaluated using the measured KI and KII values. The extent of the region near a mixed-mode crack tip where the plane stress solutions can reasonably predict the in-plane and out-of-plane displacements was investigated. Experimental results indicate that the solution of the out-of-plane displacement derived on the basis of the plane stress condition does not provide a good approximation to the experimental data for distances from the crack tip within half the specimen thickness. However, there is good agreement between the in-plane displacement measurements and the computed results, even for r/h < 0.5.

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Butler, James P., Iva Marija Tolić-Nørrelykke, Ben Fabry, and Jeffrey J. Fredberg. "Traction fields, moments, and strain energy that cells exert on their surroundings." American Journal of Physiology-Cell Physiology 282, no. 3 (2002): C595—C605. http://dx.doi.org/10.1152/ajpcell.00270.2001.

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Adherent cells exert tractions on their surroundings. These tractions can be measured by observing the displacements of beads embedded on a flexible gel substrate on which the cells are cultured. This paper presents an exact solution to the problem of computing the traction field from the observed displacement field. The solution rests on recasting the relationship between displacements and tractions into Fourier space, where the recovery of the traction field is especially simple. We present two subcases of the solution, depending on whether or not tractions outside the observed cell boundaries are set to be zero. The implementation is computationally efficient. We also give the solution for the traction field in a representative human airway smooth muscle cell contracted by treatment with histamine. Finally, we give explicit formulas for reducing the traction and displacement fields to contraction moments, the orientation of the principal axes of traction, and the strain energy imparted by the cell to the substrate.

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19

Li, Chenglong, Guohong Zhang, Xinjian Shan, Dezheng Zhao, and Xiaogang Song. "Geometric Variation in the Surface Rupture of the 2018 Mw7.5 Palu Earthquake from Subpixel Optical Image Correlation." Remote Sensing 12, no. 20 (2020): 3436. http://dx.doi.org/10.3390/rs12203436.

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We obtained high-resolution (10 m) horizontal displacement fields from pre- and post-seismic Sentinel-2 optical images of the 2018 Mw7.5 Palu earthquake using subpixel image correlation. From these, we calculated the curl, divergence, and shear strain fields from the north-south (NS) and east-west (EW) displacement fields. Our results show that the surface rupture produced by the event was distributed within the Sulawesi neck (0.0974–0.6632°S) and Palu basin (0.8835–1.4206°S), and had a variable strike of 313.0–355.2° and strike slip of 2.00–6.62 m. The NS and EW displacement fields within the Palu basin included fine-scale displacements in both the near- and far-fault, the deformation patterns included a small restraining bend (localized shortening), a distributed rupture zone, and a major releasing bend (net extension) from the curl, divergence, and shear strain. Surface rupture was dominated by left-lateral strike-slip from initiation to termination, with a localized normal slip component peaking at ~3.75 m. The characteristics and geometric variation of the ruptured fault controlled both the formation of these surface deformation patterns and sustained supershear rupture.

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20

Skok, Gregor. "A New Spatial Distance Metric for Verification of Precipitation." Applied Sciences 12, no. 8 (2022): 4048. http://dx.doi.org/10.3390/app12084048.

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Precipitation is an essential meteorological variable affecting the biosphere and human societies. At the same time, precipitation is notoriously difficult to predict and verify. A new spatial distance metric for verification of precipitation is presented. It is called the Precipitation Smoothing Distance (PSD). The aim was to develop a measure that would provide a good and meaningful approximation of the displacement of precipitation events in the two fields. An estimate of spatial displacement is very appealing for forecast interpretation because it is easy to understand and mimics how humans tend to judge fields by eye. Contrary to most other distance metrics, the new metric does not require thresholding and can thus be used to analyze binary and non-binary fields (e.g., continuous or multi-level). The analysis of idealized situations showed that the new metric provides a meaningful approximation of the displacement. Typically the estimate of displacement provided by PSD was better than the results provided by most other metrics. The measure is also not overly sensitive to noise, its results are directly related to the actual displacements of precipitation events, and the events with a larger magnitude have a bigger influence on the resulting value. The analysis of ECMWF precipitation forecasts over Europe and North Africa confirmed that the new metric provides a meaningful approximation of the displacement even in more complex real-world situations.

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21

Mittelstedt, Christian, and Wilfried Becker. "Thermoelastic Fields in Boundary Layers of Isotropic Laminates." Journal of Applied Mechanics 72, no. 1 (2005): 86–101. http://dx.doi.org/10.1115/1.1827247.

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An approximate approach to the calculation of displacements, strains, and stresses near edges and corners in symmetric rectangular layered plates of dissimilar isotropic materials under thermal load is presented. In the thickness direction the plate is discretized into an arbitrary number of sublayers/mathematical layers. A layerwise linear displacement field is formulated such that the terms according to classical laminate plate theory are upgraded with unknown in-plane functions and a linear interpolation scheme through the layer thickness in order to describe edge and corner perturbations. By virtue of the principle of minimum potential energy the governing coupled Euler–Lagrange differential equations are derived, which in the case of free-edge effects allow a closed-form solution for the unknown inplane functions. Free-corner effects are investigated by combining the displacement formulations of the two interacting free-edge effects. Hence, all state variables in the plate are obtained in a closed-form manner. Boundary conditions of traction free plate edges are satisfied in an integral sense. The present methodology is easily applied and requires only reasonable computational expenses.

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Vahidi, M., V. Jafari, M. H. Abyaneh, and SH Vahdani. "Displacement Field Approximations for Force-Based Elements in Large Displacement Analyses." Journal of Applied Mathematics 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/516290.

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This paper investigates different approximation techniques for planar beam column elements in force-based methods. The three fields, introduced in this review, are: curvature-based displacement interpolation (CBDI) used in matrix-based flexibility formulations, linear displacement approximation applied in state space, and higher-order displacement approximation utilized again in state space. Using these three approximation fields, the responses and their accuracies in some systems are compared in examples. Finally, focusing on the accuracy and regarding the performed analyses, it seems that the computational cost is reduced and accuracy of responses is elevated in many engineering problems using the higher-order approximation field in state space.

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Beretta, S., L. Patriarca, and S. Rabbolini. "Stress Intensity Factor calculation from displacement fields." Frattura ed Integrità Strutturale 11, no. 41 (2017): 269–76. http://dx.doi.org/10.3221/igf-esis.41.36.

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Sciammarella, Cesar A., Bartolomeo Trentadue, and Federico M. Sciammarella. "Observations Of Displacement Fields In Particulate Composites." Materials Technology 18, no. 4 (2003): 229–33. http://dx.doi.org/10.1080/10667857.2003.11753048.

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Flemming, T., M. Hertwig, and R. Usinger. "Speckle interferometry for highly localized displacement fields." Measurement Science and Technology 4, no. 8 (1993): 820–25. http://dx.doi.org/10.1088/0957-0233/4/8/004.

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Yates, J. R., M. Zanganeh, and Y. H. Tai. "Quantifying crack tip displacement fields with DIC." Engineering Fracture Mechanics 77, no. 11 (2010): 2063–76. http://dx.doi.org/10.1016/j.engfracmech.2010.03.025.

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Karacali, B., and C. Davatzikos. "Estimating Topology Preserving and Smooth Displacement Fields." IEEE Transactions on Medical Imaging 23, no. 7 (2004): 868–80. http://dx.doi.org/10.1109/tmi.2004.827963.

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Hao Bi and Wai-Yip Chan. "Rate-distortion optimization of hierarchical displacement fields." IEEE Transactions on Circuits and Systems for Video Technology 8, no. 1 (1998): 18–24. http://dx.doi.org/10.1109/76.660825.

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Georgsen, Frode, Per Røe, Anne Randi Syversveen, and Oddvar Lia. "Fault displacement modelling using 3D vector fields." Computational Geosciences 16, no. 2 (2012): 247–59. http://dx.doi.org/10.1007/s10596-011-9257-z.

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Kovalev, V. F., and I. P. Mel'nichenko. "Biharmonic potentials and plane isotropic displacement fields." Ukrainian Mathematical Journal 40, no. 2 (1988): 197–99. http://dx.doi.org/10.1007/bf01056476.

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PESTOV, A. B., and BIJAN SAHA. "ON THE NATURAL GAUGE FIELDS OF MANIFOLDS." Modern Physics Letters A 15, no. 32 (2000): 1991–2005. http://dx.doi.org/10.1142/s0217732300002504.

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The gauge symmetry inherent in the concept of manifold has been discussed. Within the scope of this symmetry the linear connection or displacement field can be considered as a natural gauge field on the manifold. The gauge-invariant equations for the displacement field have been derived. It has been shown that the energy–momentum tensor of this field conserves and hence the displacement field can be treated as one that transports energy and gravitates. To show the existence of the solutions of the field equations, we have derived the general form of the displacement field in Minkowski space–time which is invariant under rotation and space and time inversion. With this ansatz we found spherically-symmetric solutions of the equations in question.

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32

Timofeev, V. Yu, D. G. Ardyukov, A. V. Timofeev, and E. V. Boiko. "MODERN MOVEMENTS OF THE CRUST SURFACE IN GORNY ALTAI FROM GPS DATA." Geodynamics & Tectonophysics 10, no. 1 (2019): 123–46. http://dx.doi.org/10.5800/gt-2019-10-1-0407.

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In 2000–2017, the GPS technology was first applied to study inter-seismic, co-seismic and post-seismic processes in the crust of the Altai Mountains (Gorny Altai). Our study aims at investigating the fields of displacement and deformation in the Gorny Altai region as a part of Asia.The 3D displacement fields are reconstructed for the period before the M 7.3 Chuya earthquake that occurred in the southern sector of the Altai GPS network (49° to 55°N, and 81° to 89°E)on 27 September 2003.Anomalous behavior features are discovered in the displacement orientations, as well as in the distribution of velocities and deformation in the zone of the future earthquake.The spatial displacement pattern defined for the period of co-seismic displacements corresponds to the right-lateral strike-slip along the vertical fault. The fault depth is estimated using the elastic model and the experimental data (change in displacement from 0.30 m to 0.02 m at the distances of 14 km and 84 km from the fault, respectively); it amounts to 8–10 km.The co-seismic deformation field is investigated.In the post-seismic stage (2004–2017), displacements revealedin the epicentral zone show the right-lateral strike-slip along the fault at the rate of 2 mm/yr. Therefore, two-layer viscoelastic models can be considered. The estimated viscosity of the lower crust ranges from 6×1019to 3×1020Pa×s, and the elastic upper crust thickness is 25 km. Analyzed are modern movements in the Gorny Altai region outside the Chuya earthquake area.The results of our study show that modern horizontal displacements occur in the NNW direction at the rate of 1.1 mm/yr, which is twice lower than the displacement rate before the earthquake.

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Feng, Y., T. M. Abney, R. J. Okamoto, R. B. Pless, G. M. Genin, and P. V. Bayly. "Relative brain displacement and deformation during constrained mild frontal head impact." Journal of The Royal Society Interface 7, no. 53 (2010): 1677–88. http://dx.doi.org/10.1098/rsif.2010.0210.

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This study describes the measurement of fields of relative displacement between the brain and the skull in vivo by tagged magnetic resonance imaging and digital image analysis. Motion of the brain relative to the skull occurs during normal activity, but if the head undergoes high accelerations, the resulting large and rapid deformation of neuronal and axonal tissue can lead to long-term disability or death. Mathematical modelling and computer simulation of acceleration-induced traumatic brain injury promise to illuminate the mechanisms of axonal and neuronal pathology, but numerical studies require knowledge of boundary conditions at the brain–skull interface, material properties and experimental data for validation. The current study provides a dense set of displacement measurements in the human brain during mild frontal skull impact constrained to the sagittal plane. Although head motion is dominated by translation, these data show that the brain rotates relative to the skull. For these mild events, characterized by linear decelerations near 1.5 g ( g = 9.81 m s −2 ) and angular accelerations of 120–140 rad s −2 , relative brain–skull displacements of 2–3 mm are typical; regions of smaller displacements reflect the tethering effects of brain–skull connections. Strain fields exhibit significant areas with maximal principal strains of 5 per cent or greater. These displacement and strain fields illuminate the skull–brain boundary conditions, and can be used to validate simulations of brain biomechanics.

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Nehrkorn, Thomas, Bryan Woods, Thomas Auligné, and Ross N. Hoffman. "Application of Feature Calibration and Alignment to High-Resolution Analysis: Examples Using Observations Sensitive to Cloud and Water Vapor." Monthly Weather Review 142, no. 2 (2014): 686–702. http://dx.doi.org/10.1175/mwr-d-13-00164.1.

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Abstract Alignment errors [i.e., cases where coherent structures (“features”) of clouds or precipitation in the background have position errors] can lead to large and non-Gaussian background errors. Assimilation of cloud-affected radiances using additive increments derived by variational and/or ensemble methods can be problematic in these situations. To address this problem, the Feature Calibration and Alignment technique (FCA) is used here for correcting position errors by displacing background fields. A set of two-dimensional displacement vectors is applied to forecast fields to improve the alignment of features in the forecast and observations. These displacement vectors are obtained by a nonlinear minimization of a cost function that measures the misfit to observations, along with a number of additional constraints (e.g., smoothness and nondivergence of the displacement vectors) to prevent unphysical solutions. The method was applied in an idealized case using Weather Research and Forecasting Model (WRF) forecast fields for Hurricane Katrina. Application of the displacement vectors to the three-dimensional WRF fields resulted in improved predicted hurricane positions in subsequent forecasts. When applied to a set of high-resolution forecasts of deep moist convection over the central United States, displacements are able to efficiently characterize part of the ensemble spread. To test its application as an analysis preprocessor, FCA was applied to a real-data case of cloud-affected radiances of one of the Atmospheric Infrared Sounder (AIRS) channels. The displaced background resulted in an improved fit to the AIRS observations in all cloud-sensitive channels.

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Woo, Kwang Sung, Yoo Mi Kwon, Dong Woo Lee, and Hee Joong Kim. "LEFM Analysis of V-Notched Aluminum Plates Using Higher-Order Layerwise Model." Advanced Materials Research 898 (February 2014): 355–58. http://dx.doi.org/10.4028/www.scientific.net/amr.898.355.

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Higher-order layerwise model is proposed to determine stress intensity factors using virtual crack closure technique for V-notched plates. Present method is based on p-convergent approach and adopts the concept of subparametric element. In assumed displacement field, strain-displacement relations and 3-D constitutive equations of a layer are obtained by combination of 2-D and 1-D higher-order shape functions. Thus, it allows independent implementation of p-refinement for in-plane and transversal displacements. In the proposed elements, the integrals of Legendre polynomials and Gauss-Lobatto technique are employed to interpolate displacement fields and to implement numerical quadrature, respectively.

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Takeda, Nobuo, Shinji Ogihara, Satoshi Suzuki, and Akira Kobayashi. "Evaluation of Microscopic Deformation in CFRP Laminates with Delamination by Micro-Grid Methods." Journal of Composite Materials 32, no. 1 (1998): 83–100. http://dx.doi.org/10.1177/002199839803200105.

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Micro-grid methods were applied to measure displacements in 90° ply in CFRP cross-ply laminates with only transverse cracks or with both transverse cracks and delaminations. The COD (crack opening displacement) of the transverse cracks were also measured. Micro-grids were printed on the specimen edge surfaces by using the photo-lithography technique. The displacement fields of the specimen edge surface obtained from the experiment were compared with McCartney's [1] and Lee et al.'s [2] analyses which predicted the displacement field of a cross-ply laminate with only transverse cracks. Furthermore these analyses were modified to consider the existence of delamination.

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Sarode, A. P., and O. H. Mahajan. "Displacement fields of a Cuboid crystal in a Photoacoustic Cell: Mathematical aspects." Bulletin of the Karaganda University. "Physics" Series 101, no. 1 (2021): 6–11. http://dx.doi.org/10.31489/2021ph1/6-11.

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Photo acoustic effect is popular due to a minimal sample preparation during execution, the ability to examine scattering and opaque sample along with the capability to access depth profile. These features enable Photoacoustic spectroscopy to be used in depth-resolved characterization of solids. Thermal interaction is a basic perspective in solid state physics research regarding industrial devices and components. It is a key factor of fabrication and performance of such devices and components. Today, crystalline solids are widely studied due to their wide scientific and industrial applications. Displacement field resulting in thermal stresses is one of the important aspects of premature failure of industrial components and devices. In this paper, displacement fields in photoacoustic effect with solid cuboid crystal are mathematically presented. According to our opinion, displacement fields in photoacoustic effect in three dimensional analysis are not reported earlier. Hence that will be a major contribution of this paper. For a simple cuboid homogeneous crystal kept in a photoacoustic cell, an airy stress function is determined based on laser interaction with surface of the crystal. By applying the finite Marchi-Fasulo integral transform method within the crystal size limitations, displacement field is exactly determined.

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38

Beom, H. G., and Y. Y. Earmme. "The Elastic Field of an Elliptic Cylindrical Inclusion in a Laminate With Multiple Isotropic Layers." Journal of Applied Mechanics 66, no. 1 (1999): 165–71. http://dx.doi.org/10.1115/1.2789143.

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An elliptic cylindrical inclusion with an eigenstrain in an infinite laminate composed of multiple isotropic layers is analyzed. The problem is formulated by using the classical laminated plate theory in which displacement fields in the laminated plate are expressed in terms of in-plane displacements on the main plane and transverse displacement. Employing a method based on influence functions, an integral type solution to the equilibrium equation is expressed in terms of the eigenstrain. Closed-Form solutions for the elastic fields are obtained by evaluating the integrals explicitly for interior points and exterior points of the ellipse. The elastic fields caused by an elliptic cylindrical inhomogeneity with an eigenstrain in the infinite laminate are determined by the equivalent eigenstrain method. Solutions for a finite laminate with an eigenstrain in a circular cylindrical inhomogeneity are also obtained in terms of material and geometric parameters for each layer composing the laminate.

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Chao, C. C., T. P. Tung, and H. H. Li. "3-D Stress Analysis of Cross-Ply Laminated Composites." Journal of Energy Resources Technology 116, no. 3 (1994): 240–49. http://dx.doi.org/10.1115/1.2906449.

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A consistent higher-order theory is presented for static deformation and stress analysis of cross-ply thick laminates. Emphasis is placed on consistence with the 3-D boundary conditions and interlaminar stress continuity, exterior and interior, respectively, to the simply supported rectangular plate. All edges and lateral surfaces are considered stress-free, while surface traction and applied load equilibrium is maintained in the loading area. Individual layer displacement fields are expressed in terms of in-plane double Fourier series and cubic polynomials in thickness coordinates with continuity of interlaminar displacements and transverse stresses observed. A system of equations is derived with all these necessary conditions satisfied by means of the higher-order terms of the displacement fields in the extended Rayleigh-Ritz procedure. 3-D displacement and stress components, as compared well with exact solution cases available, can be found throughout the plate for 3-D analysis of localized damage. Thickness shrinking is noted with no mid-surface symmetry of stress distribution.

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Woo, Kwang S., and Jae S. Ahn. "Implementation of Virtual Crack Closure Technique for Damaged Composite Plates Using Higher-Order Layerwise Model." Advances in Materials Science and Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/684065.

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A higher-order layerwise model is proposed to determine stress intensity factors using virtual crack closure technique for single-edge-crack aluminum plates with patch repairs. The present method is based onp-convergent approach and adopts the concept of subparametric elements. In assumed displacement fields, strain-displacement relations and three-dimensional constitutive equations of layers are obtained by combination of two- and one-dimensional shape functions. Thus, it allows independent implementation ofp-refinement for in-plane and transversal displacements. In the proposed elements, the integrals of Legendre polynomials and Gauss-Lobatto technique are employed to interpolate displacement fields and to implement numerical quadrature, respectively. For verification of the present model, not only single-edge-crack plates but also V-notch aluminum plates are first analyzed. For patched aluminum plate with behavior of complexity, the accuracy and simplicity of the present model are shown with comparison of the results with previously published papers using the conventional three-dimensional finite elements based onh-refinement.

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Elshan Aliyev, Azer Gasimli, Elshan Aliyev, Azer Gasimli. "ON DEVELOPMENT OF OIL FIELDS." ETM - Equipment, Technologies, Materials 21, no. 03 (2024): 04–10. http://dx.doi.org/10.36962/etm21032024-01.

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Using a literature review, the article concludes that the displacement of oil by surfactants affects interrelated factors: by affecting the surface tension at the oil-water-rock interface, SAM adsorption occurs on the surface of pore channels, rock surface water and oil wetting changes, the oil layer is broken up and washed from the rock surface, the dispersion of oil in water stabilizes, the phase permeability of the porous medium changes, and finally, the forced displacement of oil by the water phase occurs. Keywords: gravity, elastic, capillary forces, adhesion, adsorption.

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Bastawros, A. F., and A. S. Voloshin. "Thermal Strain Measurements in Electronic Packages Through Fractional Fringe Moire´ Interferometry." Journal of Electronic Packaging 112, no. 4 (1990): 303–8. http://dx.doi.org/10.1115/1.2904382.

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Fractional Fringe Moire´ Interferometry (FFMI)—a new experimental methodology to measure accurately deformations and consequently strains—has been successfully implemented to determine thermally induced strains in a specimen made from an AT&T 1MB DRAM device. The specimen was heated uniformly from room temperature to 90° C. Resulting moire´ fringe patterns were recorded, analyzed using digital-image-processing and in plane displacements in the device were determined. Strain components were computed by simple differentiation of the displacement fields. The technique proved to be successful in detecting full displacement fields with submicron resolution. Contour maps showing actual thermo/mechanical strain components in the specimen were constructed. Those maps can provide an excellent tool realistic for strain analysis of microelectronic devices regardless of the structural and material complexity.

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Walker, C. A., and Jamasri. "Mixed-mode stress intensity factors in finite, edge-cracked orthotropic plates." Journal of Strain Analysis for Engineering Design 30, no. 2 (1995): 83–90. http://dx.doi.org/10.1243/03093247v302083.

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A generalized experimental method for measuring mixed-mode stress intensity factors is described for use in orthotropic materials. Moiré interferometry has been used to record the whole field surface displacements of double-edge cracked specimens made from unidirectional laminated composites. The moiré patterns were subsequently used to determine mode I and mode II stress intensity factors ( KI and KII) by utilizing the displacement fields around the crack tip. The equations expressing KI and KII as functions of the displacement fields were reformulated to encompass the orthotropic material constants. A method for deriving these has been described. The accuracy of the results was found to depend on the precision in determining the location of the crack tip, as well as the measurement of the fringe spacing.

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Guo, Yapeng, Peng Zhong, Yi Zhuo, Fanzeng Meng, Hao Di, and Shunlong Li. "Displacement Field Calculation of Large-Scale Structures Using Computer Vision with Physical Constraints: An Experimental Study." Sustainability 15, no. 11 (2023): 8683. http://dx.doi.org/10.3390/su15118683.

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In recent years, computer vision-based structural displacement acquisition technique has received wide attention and research due to the advantages of easy deployment, low-cost, and non-contact. However, the displacement field acquisition of large-scale structures is a challenging topic as a result of the contradiction of camera field-of-view and resolution. This paper presents a large-scale structural displacement field calculation framework with integrated computer vision and physical constraints using only one camera. First, the full-field image of the large-scale structure is obtained by processing the multi-view image using image stitching technique; second, the full-field image is meshed and the node displacements are calculated using an improved template matching method; and finally, the non-node displacements are described using shape functions considering physical constraints. The developed framework was validated using a scaled bridge model and evaluated by the proposed evaluation index for displacement field calculation accuracy. This paper can provide an effective way to obtain displacement fields of large-scale structures efficiently and cost-effectively.

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Antony, S. J., and Zuhair Kadhim Jahanger. "Local Scale Displacement Fields in Grains–Structure Interactions Under Cyclic Loading: Experiments and Simulations." Geotechnical and Geological Engineering 38, no. 2 (2019): 1277–94. http://dx.doi.org/10.1007/s10706-019-01088-5.

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Abstract Soils encounter cyclic loading conditions in situ, for example during the earthquakes and in the construction sequences of pavements. Investigations on the local scale displacements of the soil grain and their failure patterns under the cyclic loading conditions are relatively scarce in the literature. In this study, the local displacement fields of a dense sand layer interacting with a rigid footing under the plane-strain condition are examined using both experiments and simulations. Three commonly used types of cyclic loading conditions were applied on the footing. Digital particle image velocimetry (DPIV) is used to measure the local scale displacement fields in the soil, and to understand the evolution of the failure envelopes in the sand media under the cyclic loading conditions. The experimental results are compared with corresponding finite element analysis (FEA), in which experimentally-characterised constitutive relations are fed as an input into the FEM simulations. For comparison purposes, the case of footing subjected to the quasi-static loading condition was also studied. In general, the results show a good level of agreement between the results of the experiments and simulations conducted here. Overall, relatively shallower but wider displacement fields are observed under the cyclic loading, when compared with that of the quasi-static load test. The vorticity regions are highly localized at the shear bands in the sand media under the ultimate load. The research contributes to new understanding on the local scale displacement fields and their link to the bearing capacity of the footing under the cyclic loading environments.

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Dahmen, U., C. J. D. Hetherington, and K. H. Westmacott. "A technique for measuring small atomic displacements in HREM images." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 4 (1990): 338–39. http://dx.doi.org/10.1017/s0424820100174825.

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An important problem in materials science is the measurement of elastic strain fields, lattice rotations and rigid body shifts. High resolution microscopy is a simple and direct means of mapping displacement fields near defects, interfaces or precipitates. Large and highly localized atomic relaxations such as those found near the core of dislocations or structural units in grain boundaries are sensitive to thickness and defocus conditions and must be interpreted with the use of image simulations. However, displacements of small magnitude or displacement fields that vary slowly enough to allow only a gradual change of the periodic interatomic distance avoid artifacts caused by oscillations of the contrast transfer function. Such displacements are accurately reflected in the position of atomic column images under most imaging conditions and can be measured directly and without the aid of image simulations. Spot-to-spot measurements can be performed directly on a high resolution image, but such measurements are tedious and of low accuracy. Plane-to-plane measurements are more accurate but require the use of a microdensitometer. The present contribution introduces an alternative method based on interference effects between two overlaid images or lattices to produce Moiré patterns that display the displacement field in a graphic and accurate manner. The method makes use of the fact that small violations of perfect translation, rotation and mirror symmetries will give rise to large changes in the periodicity of the Moirés.

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Lee, Kwang Ho, and Gap Su Ban. "Stress and Displacement Fields at a Transient Crack Tip Propagating in Functionally Graded Materials." Key Engineering Materials 345-346 (August 2007): 481–84. http://dx.doi.org/10.4028/www.scientific.net/kem.345-346.481.

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Stress and displacement fields for a transient crack tip propagating along gradient in functionally graded materials (FGMs) with an exponential variation of shear modulus and density under a constant Poisson's ratio are developed. The equations of transient motion in nonhomogeneous materials are developed using displacement potentials and the solution to the displacement fields and the stress fields for a transient crack propagating at nonuniform speed though an asymptotic analysis.

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GÓIS, WESLEY, and SERGIO PERSIVAL BARONCINI PROENÇA. "GENERALIZED FINITE ELEMENT METHOD ON NONCONVENTIONAL HYBRID-MIXED FORMULATION." International Journal of Computational Methods 09, no. 03 (2012): 1250038. http://dx.doi.org/10.1142/s0219876212500387.

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The generalized finite element method (GFEM) is applied to a nonconventional hybrid-mixed stress formulation (HMSF) for plane analysis. In the HMSF, three approximation fields are involved: stresses and displacements in the domain and displacement fields on the static boundary. The GFEM–HMSF shape functions are then generated by the product of a partition of unity associated to each field and the polynomials enrichment functions. In principle, the enrichment can be conducted independently over each of the HMSF approximation fields. However, stability and convergence features of the resulting numerical method can be affected mainly by spurious modes generated when enrichment is arbitrarily applied to the displacement fields. With the aim to efficiently explore the enrichment possibilities, an extension to GFEM–HMSF of the conventional Zienkiewicz-Patch-Test is proposed as a necessary condition to ensure numerical stability. Finally, once the extended Patch-Test is satisfied, some numerical analyses focusing on the selective enrichment over distorted meshes formed by bilinear quadrilateral finite elements are presented, thus showing the performance of the GFEM–HMSF combination.

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Barber, J. R. "Surface Displacements due to a Steadily Moving Point Force." Journal of Applied Mechanics 63, no. 2 (1996): 245–51. http://dx.doi.org/10.1115/1.2788856.

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Closed-form expressions are obtained for the normal surface displacements due to a normal point force moving at constant speed over the surface of an elastic half-space. The Smirnov-Sobolev technique is used to reduce the problem to a linear superposition of two-dimensional stress and displacement fields.

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Yadav, Ramhit. "Variation of Displacement Fields for Great Earthquakes due to Rectangular Fault System." Orchid Academia Siraha 1, no. 1 (2022): 1–12. http://dx.doi.org/10.3126/oas.v1i1.52064.

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The expressions for the displacement fields produced by a finite rectangular fault associated with great earthquakes are explained by elastic theory of dislocation. The variation of displacement fields has been estimated by considering the elastic half-space in contact with traction free boundary and varying depth, distance from top to bottom of the fault. It is also carried out in an infinite elastic medium. Also, the variation of displacement fields with the distance from fault especially for strike slip fault shows that even if different fault length and approximately equal magnitudes, the variation of displacement fields with the distance from the fault is almost the same in the case of great earthquakes viz. San Francisco (1906) and Bihar-Nepal (1934).

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Journal articles on the topic 'Displacement fields'

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