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Journal articles on the topic 'Critical plane'

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Published: 4 June 2021
Last updated: 1 February 2022

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1

Norton, Alec, and Charles Pugh. "Critical sets in the plane." Michigan Mathematical Journal 38, no. 3 (1991): 441–59. http://dx.doi.org/10.1307/mmj/1029004393.

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2

Jensen, Iwan, and Anthony J. Guttmann. "Critical exponents of plane meanders." Journal of Physics A: Mathematical and General 33, no. 21 (May 18, 2000): L187—L192. http://dx.doi.org/10.1088/0305-4470/33/21/101.

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3

Karolczuk, Aleksander, and Ewald Macha. "Critical Planes in Multiaxial Fatigue." Materials Science Forum 482 (April 2005): 109–14. http://dx.doi.org/10.4028/www.scientific.net/msf.482.109.

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The paper includes a review of literature on the multiaxial fatigue failure criteria based on the critical plane concept. The criteria were divided into three groups according to the distinguished fatigue damage parameter used in the criterion, i.e. (i) stress, (ii) strain and (iii) strain energy density criteria. Each criterion was described mainly by the applied the critical plane position. The multiaxial fatigue criteria based on two critical planes seem to be the most promising. These two critical planes are determined by different fatigue damage mechanisms (shear and tensile mechanisms).
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4

Bobroff, Norman. "Critical alignments in plane mirror interferometry." Precision Engineering 15, no. 1 (January 1993): 33–38. http://dx.doi.org/10.1016/0141-6359(93)90276-g.

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5

AKAMA, Makoto, Hiroyuki MATSUDA, Hisayo DOI, and Masahiro TSUJIE. "F405 Fatigue crack initiation life prediction of rails using theory of critical distance and critical plane approach." Proceedings of The Computational Mechanics Conference 2011.24 (2011): _F—54_—_F—57_. http://dx.doi.org/10.1299/jsmecmd.2011.24._f-54_.

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6

Zhou, Y., and R. A. Antonia. "Critical points in a turbulent near wake." Journal of Fluid Mechanics 275 (September 25, 1994): 59–81. http://dx.doi.org/10.1017/s0022112094002284.

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Velocity data were obtained in the turbulent wake of a circular cylinder with an orthogonal array of sixteen X-wires, eight in the (x, y)-plane and eight in the (x, z)-plane. By applying the phase-plane technique to these data, three types of critical points (where the velocity is zero and the streamline slope is indeterminate) were identified. Of these, foci and saddle points occurred most frequently, although a significant number of nodes was also found. Flow topology and properties associated with these points were obtained in each plane. Saddle-point regions associated with spanwise vortices provide the dominant contribution to the Reynolds shear stress and larger contributions to the normal stresses than focal regions. The topology was found to be in close agreement with that obtained from other methods of detecting features of the organized motion. The inter-relationship between critical points simultaneously identified in the two planes can provide some insight into the three-dimensionality of the organized motion. Foci in the (x, z)-plane correspond, with relatively high probability and almost negligible streamwise separation, to saddle points in the (x, y)-plane and are interpreted in terms of ribs aligned with the diverging separatrix between consecutive spanwise vortex rolls. Foci in the (x, z)-plane which correspond, with relatively weak probability, to foci in the (x, y)-plane seem consistent with a distortion of the vortex rolls in the (y, z)-plane.
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7

Holec, D., and Colin J. Humphreys. "Calculations of Equilibrium Critical Thickness for Non-Polar Wurtzite InGaN/GaN Systems." Materials Science Forum 567-568 (December 2007): 209–12. http://dx.doi.org/10.4028/www.scientific.net/msf.567-568.209.

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We investigate critical thicknesses of InGaN epilayers grown on GaN substrates with the growth-plane not being the c-plane. In particular, we focus on non-polar orientations with growth planes being the m- and a-planes. We have taken into account the proper hexagonal symmetry of wurtzite GaN. We have found that there is only a small difference in the critical thickness for the cplane and the a-plane material; however, in the case of the m-plane material, we predict a quite different behaviour along the (in-plane) c-axis and the perpendicular (in-plane) a-direction.
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8

Raskin, Igor, and John Roorda. "In-Plane and Out-of-Plane Buckling of Triangulated Grids." International Journal of Space Structures 10, no. 1 (March 1995): 57–63. http://dx.doi.org/10.1177/026635119501000103.

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The stability of plane, triangulated, uniformly compressed grids with rigid nodes is considered. The lowest critical loads for grids of hexagonal, triangular and rhombic overall layout are calculated for the case of in-plane buckling and associated modes are obtained. The lower and upper bounds for these critical loads related to the behaviour of a single triangular cell are given. The connection between symmetry of the buckled configurations and the multiplicity of corresponding critical points is discussed and illustrated by the example of out-of-plane buckling of hexagonal grid.
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9

Langlais, T. "Multiaxial cycle counting for critical plane methods." International Journal of Fatigue 25, no. 7 (July 2003): 641–47. http://dx.doi.org/10.1016/s0142-1123(02)00148-2.

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10

Wang, Lei, Tian Zhong Sui, Yu Ma, and Yan Sun. "Determination of the Critical Plane under the Multiaxial Complex Loading." Advanced Materials Research 544 (June 2012): 182–87. http://dx.doi.org/10.4028/www.scientific.net/amr.544.182.

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Engineering components and structures in service are generally subjected to the multiaxial complex loads. The approach of critical plane has been widely accepted by most researchers as the best method in the multiaxial fatigue research field. It can be used well in the constant multiaxial fatigue loads, but not in the complex loads. Basis on analyzing characteristics of shear strain on material planes, the concept of weight-averaged maximum shear strain plane is proposed. A procedure is presented to determine the critical plane under multiaxial random loading. The angle values of the planes that experience peak values of maximum shear strains are averaged by employing the weight function, which is assumed to take into account the main factors of influencing the fatigue behavior, e.g. fatigue damage. The proposed algorithm is applied to the multiaxial in- and out-of-phase experiments to assess the correlation between the weight-averaged maximum shear strain direction and the position of the experimental fatigue crack initiation plane.
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11

Dasari, Venkat R., Brian Jalaian, and Saleil Bhat. "Programmable control plane for mission critical wireless networks." Journal of Defense Modeling and Simulation: Applications, Methodology, Technology 15, no. 2 (August 24, 2017): 245–54. http://dx.doi.org/10.1177/1548512917715808.

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The control plane is an essential element to manage the data plane communications in wired and wireless networks. In a traditional network architecture, the control plane is embedded in the hardware and it lacks programmability. Military wireless networks are historically heterogeneous in nature and require complicated manual setups to create interoperability because of a discontinuous control plane. In the present work, we describe a simple programmable control plane model along with associated network abstractions to create a unified control plane interface that can communicate across heterogeneous wireless networks. We chose an ns-3 based network simulation engine to create, test, and validate the functional fidelity of our models. In addition to the network objects and interfaces available in ns-3, we modified ns-3 codes to capture the characteristics of our proposed model. Furthermore, we proposed a tractable mathematical framework to optimize the performance of the proposed control plane model.
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12

Naik, Rajiv A., Daniel P. DeLuca, and Dilip M. Shah. "Critical Plane Fatigue Modeling and Characterization of Single Crystal Nickel Superalloys." Journal of Engineering for Gas Turbines and Power 126, no. 2 (April 1, 2004): 391–400. http://dx.doi.org/10.1115/1.1690768.

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Single crystal nickel-base superalloys deform by shearing along 〈111〉 planes, sometimes referred to as “octahedral” slip planes. Under fatigue loading, cyclic stress produces alternating slip reversals on the critical slip systems which eventually results in fatigue crack initiation along the “critical” octahedral planes. A “critical plane” fatigue modeling approach was developed in the present study to analyze high cycle fatigue (HCF) failures in single crystal materials. This approach accounted for the effects of crystal orientation and the micromechanics of the deformation and slip mechanisms observed in single crystal materials. Three-dimensional stress and strain transformation equations were developed to determine stresses and strains along the crystallographic octahedral planes and corresponding slip systems. These stresses and strains were then used to calculate several multiaxial critical plane parameters to determine the amount of fatigue damage and also the “critical planes” along which HCF failures would initiate. The computed fatigue damage parameters were used along with experimentally measured fatigue lives, at 1100°F, to correlate the data for different loading orientations. Microscopic observations of the fracture surfaces were used to determine the actual octahedral plane (or facet) on which fatigue initiation occurred. X-ray diffraction measurements were then used to uniquely identify this damage initiation facet with respect to the crystal orientation in each specimen. These experimentally determined HCF initiation planes were compared with the analytically predicted “critical planes.”
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13

Chu, C. C. "Fatigue Damage Calculation Using the Critical Plane Approach." Journal of Engineering Materials and Technology 117, no. 1 (January 1, 1995): 41–49. http://dx.doi.org/10.1115/1.2804370.

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The critical plane approach is applied to model material fatigue behavior under any constant amplitude proportional loading. The most critical plane and the largest damage parameter are determined in closed form for six damage criteria that have been proposed in the literature. The correct procedures of utilizing these closed-form solutions to construct the damage parameter versus fatigue life curve are outlined. It is shown that the common practice of characterizing the material’s fatigue behavior by plotting the damage parameter evaluated on the maximum shear plane against the observed fatigue life violates the principle of the critical plane approach, a problem which can arise during the calibration of any biaxial type of damage criterion. The study emphasizes that the critical plane approach should be consistently applied to both the initial calibration and the subsequent fatigue analysis.
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14

Bai-Mao, Lei, Tran Van-Xuan, Hu Xiang-Hong, and Li Qian. "Critical Plane Orientation Under Biaxial Fatigue Loading Conditions." Procedia Engineering 133 (2015): 72–83. http://dx.doi.org/10.1016/j.proeng.2015.12.625.

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15

Chicone, Carmen, and Marc Jacobs. "Bifurcation of critical periods for plane vector fields." Transactions of the American Mathematical Society 312, no. 2 (February 1, 1989): 433. http://dx.doi.org/10.1090/s0002-9947-1989-0930075-2.

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16

Mao, Z. Q., Y. Maeno, S. NishiZaki, T. Akima, and T. Ishiguro. "In-Plane Anisotropy of Upper Critical Field inSr2RuO4." Physical Review Letters 84, no. 5 (January 31, 2000): 991–94. http://dx.doi.org/10.1103/physrevlett.84.991.

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17

Mars, William V., Yintao Wei, Wang Hao, and Mark A. Bauman. "Computing Tire Component Durability via Critical Plane Analysis." Tire Science and Technology 47, no. 1 (March 1, 2019): 31–54. http://dx.doi.org/10.2346/tire.19.150090.

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ABSTRACT Tire developers are responsible for designing against the possibility of crack development in each of the various components of a tire. The task requires knowledge of the fatigue behavior of each compound in the tire, as well as adequate accounting for the multiaxial stresses carried by tire materials. The analysis is illustrated here using the Endurica CL fatigue solver for the case of a 1200R20 TBR tire operating at 837 kPa under loads ranging from 66 to 170% of rated load. The fatigue behavior of the tire's materials is described from a fracture mechanical viewpoint, with care taken to specify each of the several phenomena (crack growth rate, crack precursor size, strain crystallization, fatigue threshold) that govern. The analysis of crack development is made by considering how many cycles are required to grow cracks of various potential orientations at each element of the model. The most critical plane is then identified as the plane with the shortest fatigue life. We consider each component of the tire and show that where cracks develop from precursors intrinsic to the rubber compound (sidewall, tread grooves, innerliner) the critical plane analysis provides a comprehensive view of the failure mechanics. For cases where a crack develops near a stress singularity (i.e., belt-edge separation), the critical plane analysis remains advantageous for design guidance, particularly relative to analysis approaches based upon scalar invariant theories (i.e., strain energy density) that neglect to account for crack closure effects.
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18

Pacoste, Costin, and Anders Eriksson. "Element behavior in post-critical plane frame analysis." Computer Methods in Applied Mechanics and Engineering 125, no. 1-4 (September 1995): 319–43. http://dx.doi.org/10.1016/0045-7825(95)00813-g.

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19

Zhang, Yongming. "Critical transition Reynolds number for plane channel flow." Applied Mathematics and Mechanics 38, no. 10 (July 14, 2017): 1415–24. http://dx.doi.org/10.1007/s10483-017-2245-6.

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20

Kleinbock, Dmitry, Anurag Rao, and Srinivasan Sathiamurthy. "Critical loci of convex domains in the plane." Indagationes Mathematicae 32, no. 3 (May 2021): 719–28. http://dx.doi.org/10.1016/j.indag.2021.03.003.

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21

Andrianopoulos, N. P., and V. C. Boulougouris. "On an intrinsic relationship between plane stress and plane strain critical stress intensity factors." International Journal of Fracture 67, no. 1 (May 1994): R9—R12. http://dx.doi.org/10.1007/bf00032369.

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22

Fokkema, Jacob T., and Anton Ziolkowski. "The critical reflection theorem." GEOPHYSICS 52, no. 7 (July 1987): 965–72. http://dx.doi.org/10.1190/1.1442365.

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In predictive deconvolution of seismic data, it is assumed that the response of the earth is white. Any nonwhite components are presumed to be caused by the source wavelet or by unwanted multiples. We show that this whiteness assumption is invalid at precritical incidence. We consider plane waves incident on a layered acoustic half‐space. At exactly critical incidence at any interface in the half‐space, the lower layer acts similar to a rigid plate. The response of the half‐space is then all‐pass, or white. This result we call the critical reflection theorem. The response is also white if the waves are postcritically incident on the lower half‐space. In normal data processing these postcritical components are removed by muting. Thus the whiteness assumption is normally applied to exactly that part of the data where it is invalid. The demarcation between precritical and postcritical incidence can be exploited for the purposes of deconvolution, provided the data can be decomposed into plane waves. To develop this application, we consider the response of a point source in the uppermost layer of the layered half‐space, with a free surface above. The response is simply a superposition of the plane‐wave responses already studied, with complications introduced by the source and receiver ghosts and by multiples in the upper layer. At postcritical incidence the earth response is white for all plane‐wave components; the source spectrum may be estimated from the postcritical plane‐wave components after removing the effects of ghosts and multiples in the upper layer. If the source signature is already known, the demarcation criterion can be used to separate intrinsic absorption effects from attenuation effects caused by scattering.
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23

Revyakina, M. G., M. A. Obolenskii, A. V. Bondarenko, and V. A. Shklovskij. "Temperature dependence and anisotropy due to twin planes of the critical current inab-plane." Czechoslovak Journal of Physics 46, S3 (March 1996): 1771–72. http://dx.doi.org/10.1007/bf02563000.

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24

Palin-Luc, Thierry, and Franck Morel. "Critical plane concept and energy approach in multiaxial fatigue." Materials Testing 47, no. 5 (May 2005): 278–86. http://dx.doi.org/10.3139/120.100660.

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25

Brighenti, Roberto, and Andrea Carpinteri. "Damage Mechanics and Critical Plane Approach to Multiaxial Fatigue." Key Engineering Materials 592-593 (November 2013): 239–45. http://dx.doi.org/10.4028/www.scientific.net/kem.592-593.239.

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The mechanical behaviour of structural components subjected to multiaxial fatigue loading is very important in modern design. Several approaches have been introduced in recent decades to analyse this problem. The so-called critical plane approach, based on the stresses acting on the plane where the crack nucleation is expected to occur, is widely used. This criterion can give us a fatigue damage measurement, which can be used to evaluate fatigue life. On the other hand, fatigue life under general multiaxial stress histories can also be assessed by applying the damage accumulation method. In such a method, a scalar damage parameter is quantified through the damage increments which develop during the fatigue process up to the critical damage value corresponding to the final failure of the structures. The damage increment approach to fatigue has recently been discussed and connected to the classical crack propagation approach. In the present paper, the interpretation of the critical plane approach based on the continuum damage mechanics concepts is examined. In particular, the physical meaning of the critical plane approach is shown, that is, such an approach can be interpreted as a damage method which takes into account the scalar damage parameter evaluated along preferential directions. Finally, the fatigue behaviour of a metallic material under multiaxial cyclic load histories is analysed through the two above approaches.
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26

Wang, Yingyu, and Luca Susmel. "Critical plane approach to multiaxial variable amplitude fatigue loading." Frattura ed Integrità Strutturale 9, no. 33 (June 19, 2015): 345–56. http://dx.doi.org/10.3221/igf-esis.33.38.

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27

Révész, Pál. "Clustering of the critical branching process on the plane." Studia Scientiarum Mathematicarum Hungarica 38, no. 1-4 (May 1, 2001): 357–66. http://dx.doi.org/10.1556/sscmath.38.2001.1-4.26.

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Let be a Poisson random field in R d . Attimet= 0 a critical branching Wiener process is startingfrom eachP 2. It turns out that after a time the particles will be located in dense, small clusters and between these clusters empty domains are located.
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28

Albinmousa, Jafar. "Multiaxial fatigue crack path prediction using critical plane concept." Frattura ed Integrità Strutturale 10, no. 35 (December 29, 2015): 182–86. http://dx.doi.org/10.3221/igf-esis.35.21.

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29

Ge, Min, Lei Zhang, Jiyu Fan, Changjin Zhang, Li Pi, Shun Tan, and Yuheng Zhang. "Critical behavior of the in-plane weak ferromagnet Sr2IrO4." Solid State Communications 166 (July 2013): 60–65. http://dx.doi.org/10.1016/j.ssc.2013.05.007.

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30

Iglói, Ferenc. "Nonuniversal and surface critical behavior near a defect plane." Physical Review B 40, no. 7 (September 1, 1989): 5187–89. http://dx.doi.org/10.1103/physrevb.40.5187.

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31

Anes, V., M. de Freitas, and L. Reis. "The damage scale concept and the critical plane approach." Fatigue & Fracture of Engineering Materials & Structures 40, no. 8 (June 20, 2017): 1240–50. http://dx.doi.org/10.1111/ffe.12653.

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32

Cuccoli, Alessandro, Valerio Tognetti, Paola Verrucchi, and Ruggero Vaia. "Critical behavior of the two‐dimensional easy‐plane ferromagnet." Journal of Applied Physics 76, no. 10 (November 15, 1994): 6362–64. http://dx.doi.org/10.1063/1.358267.

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33

Chen, Charng‐Ning, and Tommy S. W. Wong. "Critical Rainfall Duration for Maximum Discharge from Overland Plane." Journal of Hydraulic Engineering 119, no. 9 (September 1993): 1040–45. http://dx.doi.org/10.1061/(asce)0733-9429(1993)119:9(1040).

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34

Rao, Achanta Ramakrishna, and Gopu Sreenivasulu. "DESIGN OF PLANE SEDIMENT BED CHANNELS AT CRITICAL CONDITION." ISH Journal of Hydraulic Engineering 12, no. 2 (January 2006): 94–117. http://dx.doi.org/10.1080/09715010.2006.10514834.

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35

Mikhalkin, V. N., S. P. Medvedev, A. E. Mailkov, and S. V. Khomik. "Critical Conditions for Plane-to-Cylindrical Detonation Wave Transformation." Russian Journal of Physical Chemistry B 13, no. 4 (July 2019): 621–25. http://dx.doi.org/10.1134/s1990793119040249.

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36

Fruchter, L., D. Colson, and V. Brouet. "Magnetic critical properties and basal-plane anisotropy of Sr2IrO4." Journal of Physics: Condensed Matter 28, no. 12 (March 2, 2016): 126003. http://dx.doi.org/10.1088/0953-8984/28/12/126003.

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37

Mladenov, K. A. "On the critical and postcritical behaviour of plane frames." Journal of Constructional Steel Research 21, no. 1-3 (January 1992): 97–113. http://dx.doi.org/10.1016/0143-974x(92)90021-6.

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38

Jóhannsson, Hjörtur, Jacob Østergaard, and Arne Hejde Nielsen. "Identification of critical transmission limits in injection impedance plane." International Journal of Electrical Power & Energy Systems 43, no. 1 (December 2012): 433–43. http://dx.doi.org/10.1016/j.ijepes.2012.05.050.

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39

Bruno, Alexander Dmitrievich, and Alexander Borisovich Batkhin. "Level lines of a polynomial in the plane." Keldysh Institute Preprints, no. 57 (2021): 1–24. http://dx.doi.org/10.20948/prepr-2021-57.

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We propose a method for computing the position of all level lines of a real polynomial in the real plane. To do this, it is necessary to compute its critical points and critical curves, and then to compute critical values of the polynomial (there are finite number of them). Now finite number of critical levels and one representative of noncritical level corresponding to a value between two neighboring critical ones enough to compute. We propose a scheme for computing level lines based on polynomial computer algebra algorithms: Gröbner bases, primary ideal decomposition. Software for these computations are pointed out. Nontrivial examples are considered.
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40

Liao, Ding, Shun-Peng Zhu, and Guian Qian. "Multiaxial fatigue analysis of notched components using combined critical plane and critical distance approach." International Journal of Mechanical Sciences 160 (September 2019): 38–50. http://dx.doi.org/10.1016/j.ijmecsci.2019.06.027.

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41

CATHALA, J. C. "ON CRITICAL CURVES IN TWO-DIMENSIONAL ENDOMORPHISMS." International Journal of Bifurcation and Chaos 11, no. 03 (March 2001): 821–39. http://dx.doi.org/10.1142/s021812740100247x.

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Properties of the critical curves of noninvertible maps are studied using the representation of the plane in the form of sheets. In such a representation, every sheet is associated with a well-defined determination of the inverse map which leads to a foliation of the plane directly related to fundamental properties of the map. The paper describes the change of the plane foliation occurring in the presence of parameter variations, leading to a modification of the nature of the map by crossing through a foliation bifurcation. The degenerated map obtained at the foliation bifurcation is characterized by the junction of more than two sheets on a critical curve segment. Examples illustrating these situations are given.
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42

Foda, Omar. "Off-critical local height probabilities on a plane and critical partition functions on a cylinder." Nuclear Physics B 928 (March 2018): 279–306. http://dx.doi.org/10.1016/j.nuclphysb.2018.01.011.

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43

Mencinger, Matej. "Stability Analysis of Critical Points in Quadratic Systems inR3Which Contain a Plane of Critical Points." Progress of Theoretical Physics Supplement 150 (2003): 388–92. http://dx.doi.org/10.1143/ptps.150.388.

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44

Wang, Xiao-Wei, De-Guang Shang, and Yu-Juan Sun. "A weight function method for multiaxial low-cycle fatigue life prediction under variable amplitude loading." Journal of Strain Analysis for Engineering Design 53, no. 4 (March 27, 2018): 197–209. http://dx.doi.org/10.1177/0309324718763671.

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A weight function method based on strain parameters is proposed to determine the critical plane in low-cycle fatigue region under both constant and variable amplitude tension–torsion loadings. The critical plane is defined by the weighted mean maximum absolute shear strain plane. Combined with the critical plane determined by the proposed method, strain-based fatigue life prediction models and Wang-Brown’s multiaxial cycle counting method are employed to predict the fatigue life. The experimental critical plane orientation and fatigue life data under constant and variable amplitude tension–torsion loadings are used to verify the proposed method. The results show that the proposed method is appropriate to determine the critical plane under both constant and variable amplitude loadings.
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45

Wei, H., and Y. Liu. "A critical plane-energy model for multiaxial fatigue life prediction." Fatigue & Fracture of Engineering Materials & Structures 40, no. 12 (April 27, 2017): 1973–83. http://dx.doi.org/10.1111/ffe.12614.

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46

Syngellakis, Stavros, and Esmat S. Kameshki. "Elastic Critical Loads for Plane Frames by Transfer Matrix Method." Journal of Structural Engineering 120, no. 4 (April 1994): 1140–57. http://dx.doi.org/10.1061/(asce)0733-9445(1994)120:4(1140).

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47

Alobaidi, Ghada, and Roland Mallier. "Critical Layer Analysis of Stuart Vortices in a Plane Jet." Mathematical Problems in Engineering 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/137253.

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Asymptotic techniques are used to model quasi-steady-state vortices in the plane (Bickley) inviscid jet. A nonlinear critical layer analysis is used to find a family of steady-state finite amplitude two-dimensional vortices which are based on the Stuart vortex.
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48

Ushaksaraei, R., and S. Pietruszczak. "Failure Criterion for Structural Masonry based on Critical Plane Approach." Journal of Engineering Mechanics 128, no. 7 (July 2002): 769–78. http://dx.doi.org/10.1061/(asce)0733-9399(2002)128:7(769).

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49

Mei, Xiao, Shihao Ge, and Ying Zheng. "Research of Fatigue Crack Growth Based on Critical Plane Method." MATEC Web of Conferences 67 (2016): 03020. http://dx.doi.org/10.1051/matecconf/20166703020.

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50

Combescot, R., and X. Leyronas. "Plane-chain coupling inYBa2Cu3O7: Impurity effect on the critical temperature." Physical Review B 54, no. 6 (August 1, 1996): 4320–30. http://dx.doi.org/10.1103/physrevb.54.4320.

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