scholarly journals Circles of Curvature at Points of Parabola in Isotropic Plane

2021 ◽  
Author(s):  
Vladimir Volenec ◽  
Marija Šimić Horvath ◽  
Ema Jurkin
Keyword(s):  
Isotropic Plane

The authors have studied the curvature of the focal conic in the isotropic plane and the form of the circle of curvature at its points has been obtained. Hereby, we discuss several properties of such circles of curvature at the points of a parabola in the isotropic plane.

A new methodology to obtain the exact solutions of isotropic plane beam subjected to arbitrary loads

2010 ◽  
Vol 37 (5) ◽  
pp. 476-483 ◽  
Author(s):  
Lang Zhang ◽  
Puyun Gao ◽  
Dongxu Li ◽  
Xue Wang
Keyword(s):  
Exact Solutions ◽  
Isotropic Plane

Bound state in a model of electromagnetic field interacting with a material plan

2020 ◽  
Vol 35 (21) ◽  
pp. 2050170
Author(s):  
Yu. M. Pismak ◽  
D. Shukhobodskaia
Keyword(s):  
Electromagnetic Field ◽  
Maxwell Equations ◽  
Singular Potential ◽  
Bound State ◽  
Material Object ◽  
Two Dimensional ◽  
Isotropic Plane ◽  
Chern Simons ◽  
Material Plane ◽  
State Of Field

In the model with Chern-Simons potential describing the coupling of electromagnetic field with a two-dimensional material, the possibility of the appearance of bound field states, vanishing at sufficiently large distances from interacting with its macro-objects, is considered. As an example of such two-dimensional material object we consider a homogeneous isotropic plane. Its interaction with electromagnetic field is described by a modified Maxwell equation with singular potential. The analysis of their solution shows that the bound state of field cannot arise without external charges and currents. In the model with currents and charges the Chern-Simons potential in the modified Maxwell equations creates bound state in the form of the electromagnetic wave propagating along the material plane with exponentially decreasing amplitude in the orthogonal to its direction.

scholarly journals Field of Stresses in an Isotropic Plane with Circular Inclusion under Tensile Stress

Engineering ◽  
2012 ◽  
Vol 04 (09) ◽  
pp. 583-589 ◽  
Author(s):  
Deryugin Ye Yevgeny ◽  
G. V. Lasko
Keyword(s):  
Tensile Stress ◽  
Circular Inclusion ◽  
Isotropic Plane

scholarly journals On Brocard Points of Harmonic Quadrangle in Isotropic Plane

KoG ◽  
2017 ◽  
pp. 11-18
Author(s):  
Ema Jurkin ◽  
Vladimir Volenec
Keyword(s):  
Isotropic Plane

U radu se prikazuju neki novi rezultati o Brocardovim točkama harmoničnog četverokuta u izotropnoj ravnini. Konstruiraju se novi harmonični četverokuti pridruženi danom četverokutu, te se proučavaju njihova svojstva vezana uz Brocardove točke.

scholarly journals On Solving Problems of Thermal Conductivity on an Anisotropic Plane with a Weakly Permeable Film

2021 ◽  
Vol 16 (3) ◽  
pp. 115-121
Author(s):  
Kholodovskii Svyatoslav Ye. ◽  
◽  
Orlov Aleksey O. ◽  
Keyword(s):  
Thermal Conductivity ◽  
Cauchy Problem ◽  
Initial Temperature ◽  
Practical Interest ◽  
Heat Propagation ◽  
Heat Sources ◽  
Fibrous Materials ◽  
Isotropic Plane ◽  
Fourier Expansions ◽  
Convolution Of Fourier Expansions

The problem of thermal conductivity on an anisotropic plane (x; y) divided into two halfplanes D1(1 < x < 0; y 2 R) and D2(0 < x < 1; y 2 R) by a weakly permeable film x = 0 is considered at given heat sources and a given initial temperature. The anisotropy ellipses are arbitrary (in magnitude and direction) and are the same at all points of the plane. Using the method of convolution of Fourier expansions, the solution of the problem is expressed in single quadratures through the well-known solution of the classical Cauchy problem on an isotropic plane without a film. The results obtained are of practical interest in the problems of heat propagation and conservation in materials with anisotropic properties (crystalline, fibrous materials), in the presence of a thermal insulation film.

scholarly journals Displacement Analytical Solution of a Circular Hole in Layered Composite Materials considering Shear Stress Effect

2017 ◽  
Vol 26 (3) ◽  
pp. 096369351702600
Author(s):  
Zhizeng Zhang ◽  
Xiaochang Li
Keyword(s):  
Shear Stress ◽  
Composite Materials ◽  
Analytical Solution ◽  
Circular Hole ◽  
Poisson Ratio ◽  
Transverse Isotropy ◽  
Layered Composite ◽  
Polar Coordinates ◽  
Stress Effect ◽  
Isotropic Plane

Layered composite materials can be treated as transverse isotropy in mechanics. According to basic equations of transverse isotropy, the compatibility equation in polar coordinates is firstly formulated. Then the analytical solution for a deep circular hole considering shear stress and two unequal normal stresses in layered composite materials is derived. The solution shows that the radial displacement is affected by the elastic modulus and Poisson ratio in both the isotropic plane and the direction of symmetry axis in spite of the hypothesis that the hole transect is parallel to the isotropic plane.

Determining the transverse isotropic rock’s static elastic moduli with cylindrical plugs: shortfalls, challenges and expected outcomes

Geophysics ◽  
2021 ◽  
pp. 1-59
Author(s):  
Luyi W. Shen ◽  
Tiffany Playter
Keyword(s):  
In Situ Stress ◽  
Isotropic Plane ◽  
Common Assumption ◽  
Young’S Moduli ◽  
Iterative Inversion ◽  
Transverse Isotropic ◽  
Proper Design ◽  
Complete Set ◽  
Static Elastic Moduli

Cylindrical shaped plugs can be tested using a Hoek-Cell like apparatus that allows for efficient and inexpensive measurements of a rock’s static elastic properties. However, when it comes to Transverse Isotropic material, this approach has a natural limitation due to the isotropic radial stresses; particular attention to the boundary conditions and the proper design of pressurization steps is warranted. Typical attempts to constrain the complete set of compliances ( S), using multiple plugs of different orientations, are impeded by the heterogeneity and pressure-dependent elasticities inherent to sedimentary rocks. Through stepwise pressure increases, we can constrain four normal compliances S 11, S 12, S 13, S 33 , describing two Young’s moduli and three Poison’s ratios using a single horizontal plug drilled parallel to the rock’s isotropic plane, contrary to the common assumption that at both horizontal and vertical plugs are needed. The measurement of the shear modulus S 44 needs to be obtained using a plug that is drilled oblique to the isotropic plane; replicating the in-situ stress environment is not possible using this approach. Lastly, the specimen’s anisotropic plane’s geometry is elliptical under isotropic radial stress; this causes a discrepancy between the strain gauge’s contraction and the actual strain. We propose an iterative inversion approach to account for this issue and calculate the exact strains useful for inferring S ij from measurements reported by strain gauges. The example included in this writing shows that without correction, inferred values of S ij may suffer errors of 20%.

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