scholarly journals Determination of the Stress State of a Piecewise Homogeneous Elastic Body with a Row of Cracks on an Interface Surface Subject to Antiplane Strains with Inclusions at the Tips

2015 ◽  
Vol 2015 ◽  
pp. 1-22 ◽  
Author(s):  
Ali Golsoorat Pahlaviani ◽  
Suren Mkhitaryan
Keyword(s):  
Stress State ◽  
Elastic Body ◽  
Linear Equations ◽  
The Body ◽  
Shear Stresses ◽  
Interface Surface ◽  
Special Cases ◽  
Crack Problems ◽  
Fourier Sine Series

The stress state of a bimaterial elastic body that has a row of cracks on an interface surface is considered. It is subjected to antiplane deformations by uniformly distributed shear forces acting on the horizontal sides of the body. The governing equations of the problem, the stress intensity factors, the deformation of the crack edges, and the shear stresses are derived. The solution of the problem via the Fourier sine series is reduced to the determination of a singular integral equation (SIE) and consequently to a system of linear equations. In the end, the problem is solved in special cases with inclusions. The results of this paper and the previously published results show that the used approach based on the Gauss-Chebyshev quadrature method can be considered as a generalized procedure to solve the collinear crack problems in mode I, II, or III loadings.

Study of the stress state of the sleeper base and sleepers of rail track with accounting variable conditions of their resting

2020 ◽  
pp. 200-217
Author(s):  
V.V. Hovorukha ◽  
◽  
A.V. Hovorukha ◽  
V.K. Kizilov ◽  
T.P. Sobko ◽  
...  
Keyword(s):  
Stress State ◽  
Mutual Influence ◽  
Shear Zones ◽  
Shear Resistance ◽  
Middle Part ◽  
Shear Stresses ◽  
Railway Transport ◽  
Base Stability ◽  
Resistance Forces

The live problem of the stress state of the sleeper base and rail sleepers is considered in the article with taking into account specific normal and specific shear stresses under variable conditions of the sleepers resting on the base. The methodology is aimed at the determination of the mutual influence of normal (compressive) and tangential (shear) specific stresses on formation of stability due to the displacement of individual parts of the base. Stability zones and shear zones of the sleeper base parts are also determined by the authors at different conditions of the sleeper resting on the base. Further, zones with insecure position of the base under the sleepers are found when they and their under-rail parts continuously rest on the base. It is stated that insecure position of the base is formed when specific shear stresses excess specific stresses of shear resistance, which consists of specific friction and specific cohesion between the parts in the base. It is also established that loss of stability of the ballast particles causes their displacement in the direction of the action of specific shear stresses. In these zones, density and rigidity of the sleeper base decreases leading to a gradual redistribution of reactive resistance of the base along the sleeper, and, depending on this redistribution, a change in the bending moments acting on the sleeper occurs. It is found that when the sleepers rest only by their under-rail parts, shear stresses and forces, as well as stresses and shear resistance forces under the middle part of the sleepers are distributed in such a way that shear forces exceed resistance forces up to the depth of 60 cm from the sleepers sole. This phenomenon leads to the displacement of ballast particles under the middle part of the sleeper, consolidation of the ballast and resting of the sleepers by their middle part with possible cracks formation. In the end sections of the sleepers, there is also a loss of ballast stability. Recommendations for improving stability indicators of the sleeper base and strength of the sleepers are given. The obtained results of the study can be used for the mine, industrial and railway transport.

Matrices of minimum norm satisfying certain prescribed band and spectral restrictions -- an extremal characterization of the discrete periodic Laplacian

2015 ◽  
Vol 30 ◽  
pp. 871-888
Author(s):  
Marcos Travaglia
Keyword(s):  
Linear Equations ◽  
Nearest Neighbors ◽  
Positive Semidefinite ◽  
Circulant Matrix ◽  
Numerical Illustration ◽  
Nonnegative Orthant ◽  
Special Cases ◽  
The Matrix

This paper has been motivated by the curiosity that the circulant matrix ${\rm Circ }(1/2, -1/4, 0, \dots, 0,-1/4)$ is the $n\times n$ positive semidefinite, tridiagonal matrix $A$ of smallest Euclidean norm having the property that $Ae = 0$ and $Af = f$, where $e$ and $f$ are, respectively, the vector of all $1$s and the vector of alternating $1$ and $-1$s. It then raises the following question (minimization problem): What should be the matrix $A$ if the tridiagonal restriction is replaced by a general bandwidth $2r + 1$ ($1\leq r \leq \tfrac{n}{2 } -1$)? It is first easily shown that the solution of this problem must still be a circulant matrix. Then the determination of the first row of this circulant matrix consists in solving a least-squares problem having $\tfrac{n}{2} \, - 1$ nonnegative variables (Nonnegative Orthant) subject to $\tfrac{n}{2} - r$ linear equations. Alternatively, this problem can be viewed as the minimization of the norm of an even function vanishing at the points $|i|>r$ of the set $\left\{-\tfrac{n}{2} + 1, \dots, -1, 0, 1, \dots ,\tfrac{n}{2} \right\}$, and whose Fourier-transform is nonnegative, vanishes at zero, and assumes the value one at $\tfrac{n}{2}$. Explicit solutions are given for the special cases of $r=\tfrac{n}{2}$, $r=\tfrac{n}{2} -1$, and $r=2$. The solution for the particular case of $r=2$ can be physically interpreted as the vibrational mode of a ring-like chain of masses and springs in which the springs link both the nearest neighbors (with positive stiffness) and the next-nearest neighbors (with negative stiffness). The paper ends wiih a numerical illustration of the six cases ($1\leq r \leq 6$)corresponding to $n=12$.

scholarly journals Determination of the body force of a two-dimensional isotropic elastic body

2009 ◽  
Vol 229 (1) ◽  
pp. 192-207 ◽  
Author(s):  
Dang Duc Trong ◽  
Pham Ngoc Dinh Alain ◽  
Phan Thanh Nam ◽  
Truong Trung Tuyen
Keyword(s):  
Elastic Body ◽  
Body Force ◽  
The Body ◽  
Two Dimensional ◽  
Isotropic Elastic Body

Gender determination of caucasoid hair using image analysis

1993 ◽  
Vol 51 ◽  
pp. 216-217
Author(s):  
T.B. Ball ◽  
W.M. Hess
Keyword(s):  
Image Analysis ◽  
Cross Sections ◽  
Scalp Hair ◽  
The Body ◽  
Equivalent Diameter ◽  
Cross Sectional ◽  
Hair Samples ◽  
Length Width ◽  
Morphological Differences

It has been demonstrated that cross sections of bundles of hair can be effectively studied using image analysis. These studies can help to elucidate morphological differences of hair from one region of the body to another. The purpose of the present investigation was to use image analysis to determine whether morphological differences could be demonstrated between male and female human Caucasian terminal scalp hair.Hair samples were taken from the back of the head from 18 caucasoid males and 13 caucasoid females (Figs. 1-2). Bundles of 50 hairs were processed for cross-sectional examination and then analyzed using Prism Image Analysis software on a Macintosh llci computer. Twenty morphological parameters of size and shape were evaluated for each hair cross-section. The size parameters evaluated were area, convex area, perimeter, convex perimeter, length, breadth, fiber length, width, equivalent diameter, and inscribed radius. The shape parameters considered were formfactor, roundness, convexity, solidity, compactness, aspect ratio, elongation, curl, and fractal dimension.

Determination of Lead Content in Red Colored Lipsticks from Mandalay Market by Flame Atomic Absorption Spectrophotometer

2018 ◽  
Vol 30 (3) ◽  
pp. 167-173
Keyword(s):  
Sampling Procedure ◽  
The Body ◽  
Lead Content ◽  
Social Psychological ◽  
Allowable Limit ◽  
Flame Atomic Absorption ◽  
Therapeutic Benefits ◽  
Flame Atomic Absorption Spectrophotometer ◽  
Exposure Levels

Red colored lipstick is the most widely used cosmetic product. Although lipstick gives a lot of social, psychological and therapeutic benefits, it may harm the consumers. Because some lipsticks contain a considerable amount of heavy metal especially lead. Lead is being used in lipstick mainly for the pigments required to obtain needed colors. Lead accumulates in the body over time and lead-containing lipstick applied several times a day, every day, combined with lead in water and other sources, could add up to significant exposure levels. Therefore, this study was aimed to determine lead content in red colored lipsticks from market. This study was laboratorybased, analytical study by using 25 lipstick samples. Red colored lipsticks were bought from Mandalay Market by random sampling procedure and they were completely coded to avoid the bias. Then, lead content in coded samples was determined by Flame AAS according to International Conference on Harmonization (ICH) guideline. Lead contents of 88% of the lipsticks samples were more than specified limit (20 ppm) of Food and Drug Administration, United States. All of them, lead content was highest in counterfeit lipsticks group. Among the tested lipstick samples, lipstick with lowest lead content was LE-RL 01 (15.74 ppm) and the lipstick with highest lead content was CF-RL 01(60.09 ppm). In conclusion, lead contents of red colored lipsticks (22 out of 25) from market samples were higher than allowable limit (20 ppm).

Fast Method for the Determination of Residual Solvents in Radiopharmaceutical Products

2017 ◽  
Vol 68 (4) ◽  
pp. 666-670 ◽  
Author(s):  
Mirela Mihon ◽  
Catalin Stelian Tuta ◽  
Alina Catrinel Ion ◽  
Dana Niculae ◽  
Vasile Lavric
Keyword(s):  
Gas Chromatography ◽  
Control Method ◽  
Limit Of Detection ◽  
The Body ◽  
Biologically Active ◽  
Injection Technique ◽  
Fast Method ◽  
Residual Solvent ◽  
Residual Solvents

The aim of this work was the development and validation of a fast analytical method to determine the residual solvents content in radiopharmaceuticals such as: 18F-Fluorodeoxyglucose (18F-FDG), 18F-Fluoroestradiol (18F-FES), 18F-Fluorothymidine (18F-FLT),18F-Fluoromisonidazole (18F-FMISO). Radiopharmaceuticals are radioactive preparations for medical purposes used in nuclear medicine as tracers in diagnostic imaging and treatment of certain diseases. Positron Emission Tomography (PET) is a medical imaging technique that consists in introducing into the body of a small amount of a biologically active chemical compound labelled with a short lived positron-emitting radioisotope (18F, 11C, 68Ga). Residual solvents are critical impurities in radiopharmaceuticals that can affect labelling, stability and physicochemical properties of drugs. Therefore, the determination of these solvents is essential for quality control of radiopharmaceuticals. Validation of the control method for residual solvents by gas chromatography is referred by the European Pharmacopoeia using a special injection technique (head space). The parameters of the method, which comply with International Conference on Harmonization guidelines, are: accuracy, precision, linearity, limit of detection, limit of quantification and robustness. The proposed method (direct gas chromatography injection) proved to be linear, precise, accurate and robust. Good linearity was achieved for all the solvents and correlation coefficients (R2) for each residual solvent were found more than 0.99.

scholarly journals Movement of a finite body in channel flow

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160164 ◽  
Author(s):  
Frank T. Smith ◽  
Edward R. Johnson
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Flow Instability ◽  
Flow Direction ◽  
Finite Size ◽  
The Body ◽  
Thin Body ◽  
Shear Stresses ◽  
Unsteady Interaction ◽  
High Reynolds

A body of finite size is moving freely inside, and interacting with, a channel flow. The description of this unsteady interaction for a comparatively dense thin body moving slowly relative to flow at medium-to-high Reynolds number shows that an inviscid core problem with vorticity determines much, but not all, of the dominant response. It is found that the lift induced on a body of length comparable to the channel width leads to differences in flow direction upstream and downstream on the body scale which are smoothed out axially over a longer viscous length scale; the latter directly affects the change in flow directions. The change is such that in any symmetric incident flow the ratio of slopes is found to be cos ⁡ ( π / 7 ) , i.e. approximately 0.900969, independently of Reynolds number, wall shear stresses and velocity profile. The two axial scales determine the evolution of the body and the flow, always yielding instability. This unusual evolution and linear or nonlinear instability mechanism arise outside the conventional range of flow instability and are influenced substantially by the lateral positioning, length and axial velocity of the body.

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