scholarly journals The limiting state of bodies during separation in the case of the general plane problem

2021 ◽  
pp. 47-55
Author(s):  
Алёна Николаевна Матвеева ◽  
Сергей Владимирович Матвеев
Keyword(s):  
Plane Problem ◽  
Average Pressure ◽  
Limiting State ◽  
Characteristic Equations ◽  
Main Stress ◽  
General Plane ◽  
Limiting Values ◽  
Limiting Value

Работа посвящена решению общей плоской задачи, связанной с определением предельного состояния тел при отрыве. Уравнения, определяющие условия предельного состояния принимаются функциями, зависящими от среднего давления и направлений отрыва. В результате вычислений были получены характеристические уравнения для двух случаев: при достижении предельных значений отрыва двумя главными напряжениями и при достижении предельного значения отрыва одним главным напряжением. Для двух рассмотренных случаев были получены уравнения характеристик и соотношения вдоль них. The work is devoted to the solution of the general plane problem related to the determination of the limiting state of bodies during separation. The equations defining the conditions for the limiting state are taken as functions that depend on the average pressure and directions of separation. As a result of calculations, the characteristic equations were determined for two cases: when the limiting values of separation by two main stresses are reached and when the limiting value of separation by one main stress is reached. For the two considered cases, equations of characteristics and relations along them were obtained.

scholarly journals Determination of the limiting state of bodies during separation in the case of the general plane problem

2021 ◽  
Vol 2094 (2) ◽  
pp. 022037
Author(s):  
A N Matveeva ◽  
S V Matveev ◽  
A A Andreeva
Keyword(s):  
Principal Stress ◽  
Plane Problem ◽  
Average Pressure ◽  
Principal Stresses ◽  
Limiting State ◽  
Characteristic Equations ◽  
General Plane ◽  
Limiting Value

Abstract The paper considers the general plane problem of determining the limiting state of bodies during separation. The conditions for reaching the limiting state are considered to depend on the average pressure and the direction of separation. The paper defines the characteristic equations for two cases of separation: equality of two principal stresses to the limiting value of separation and equality of one principal stress to the limiting value of separation. Equations of characteristics’ lines and relations along them are determined.

On the determination of a velocity field for a perfectly plastic flow: The case of the general plane problem

2001 ◽  
Vol 46 (8) ◽  
pp. 596-601 ◽  
Author(s):  
D. D. Ivlev ◽  
L. A. Maksimova ◽  
R. I. Nepershin
Keyword(s):  
Velocity Field ◽  
Plastic Flow ◽  
Plane Problem ◽  
Perfectly Plastic ◽  
General Plane

Statistical method of steepest improvement of response

2018 ◽  
Vol 84 (11) ◽  
pp. 74-87
Author(s):  
V. B. Bokov
Keyword(s):  
Statistical Method ◽  
Linear Model ◽  
Response Prediction ◽  
Initial Experiment ◽  
First Order ◽  
Prediction Response ◽  
Conditional Extremum ◽  
Order Polynomial ◽  
Limiting Values

A new statistical method for response steepest improvement is proposed. This method is based on an initial experiment performed on two-level factorial design and first-order statistical linear model with coded numerical factors and response variables. The factors for the runs of response steepest improvement are estimated from the data of initial experiment and determination of the conditional extremum. Confidence intervals are determined for those factors. The first-order polynomial response function fitted to the data of the initial experiment makes it possible to predict the response of the runs for response steepest improvement. The linear model of the response prediction, as well as the results of the estimation of the parameters of the linear model for the initial experiment and factors for the experiments of the steepest improvement of the response, are used when finding prediction response intervals in these experiments. Kknowledge of the prediction response intervals in the runs of steepest improvement of the response makes it possible to detect the results beyond their limits and to find the limiting values of the factors for which further runs of response steepest improvement become ineffective and a new initial experiment must be carried out.

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

scholarly journals The shrinkage of soils

1917 ◽  
Vol 8 (3) ◽  
pp. 312-330 ◽  
Author(s):  
H. A. Tempany
Keyword(s):  
Linear Relationship ◽  
Pore Space ◽  
Linear Shrinkage ◽  
Fine Silt ◽  
Leeward Islands ◽  
Physical Composition ◽  
Colloidal Clay ◽  
Internal Pore ◽  
Limiting Value

1. By determination of the internal pore space in blocks of soils and comparison with the observed value for the linear shrinkage it is found that a linear relationship appears to exist between the two values.2. By extrapolating the curve thus obtained an approximation for the limiting value of the shrinkage in the case of pure colloidal clay is arrived at amounting to approximately 23 per cent.3. On this assumption it becomes possible to calculate the approximate content of colloidal material in any soil from a knowledge of the linear shrinkage.4. Results are adduced, showing the values obtained for the shrinkage in the case of separated fine silt and clay fractions in the case of two soils of known shrinkage and physical composition, and compared with the values calculated from previous assumptions.5. The results of the calculation of the content of colloidal clay in the foregoing manner in the case of 16 Leeward Islands soils are appended.

The Estimation of Long-Range Internal Stress Fields by Spectral-Acoustic Method

2014 ◽  
Vol 1013 ◽  
pp. 121-126 ◽  
Author(s):  
Aleksandr Smirnov ◽  
Nikolai Ababkov ◽  
Aleksandra Glinka
Keyword(s):  
Conceptual Model ◽  
Physical And Mechanical Properties ◽  
Acoustic Method ◽  
Electron Microscopic ◽  
Limiting State ◽  
Acoustic Characteristics ◽  
Complex Criterion ◽  
Microscopic Studies ◽  
Hazardous Production

A conceptual model consisting of diagrams, text and terminology dictionary, made in a formalized way and representations of functions, each of which reflects the real state of the long-running metal at all stages of the life cycle. Based on the developed conceptual model, analysis of the results of electron microscopic studies measuring the acoustic characteristics and determination of physical and mechanical properties of the complex criterion limiting state long working metal technical devices hazardous production facilities.

Pore Structure, Permeability, And Chloride Diffusion In Fly Ash-And Slag-Containing Pastes And Mortars

1988 ◽  
Vol 137 ◽  
Author(s):  
R. I. A. Malek ◽  
D. M. Roy ◽  
Y. Fang
Keyword(s):  
Chloride Diffusion ◽  
Fly Ashes ◽  
Chloride Permeability ◽  
Cement Pastes ◽  
Granulated Blast Furnace Slag ◽  
Transport Of Ions ◽  
Diffusion Rates ◽  
Different Sources ◽  
Limiting Value

AbstractThe transport of ions through cement pastes and mortars with variable contents of fly ashes and granulated blast-furnace slag from different sources and with variable composition has been investigated. The research included the determination of chloride diffusion rate and chloride permeability in relation to microstructure development. The median pore size generally was much diminished in mature blended material compared with Portland cement (PC) pastes and mortars. It appears that, at the same age, a finer microstructure is generally developed in blended specimens compared to PC specimens. Also, it was found that the microstructure approaches a limiting value at longer ages of hydration. That limiting value may be reached at earlier ages with the blends. The chloride diffusion rates and permeabilities in the blends were significantly lower than PC mixes. A comparison between the blends containing fly ashes and those containing slag was made.

Determination of transport constants of isolated Nitella cell walls

1968 ◽  
Vol 46 (4) ◽  
pp. 317-327 ◽  
Author(s):  
M. T. Tyree
Keyword(s):  
Activation Energy ◽  
Cell Wall ◽  
Diffusion Coefficient ◽  
Cell Walls ◽  
Transport Coefficients ◽  
Irreversible Thermodynamics ◽  
Kcal Mole ◽  
Limiting Value ◽  
Nitella Flexilis

Transport coefficients LPP, LPE, LEP, and LEE for electrokinetic equations according to irreversible thermodynamics, the Onsager coefficients, were measured for isolated Nitella flexilis cell walls in KCl solutions ranging from 10−4 to 100 normal. LPP and LPE (= LEP) were found to be independent of KCl concentration and equal to 1.4 × 10−6 cm3 sec−1 cm−2 (joule cm−3)−1 cm and 6 × 10−5 cm3 sec−1 cm−2 volt−1 cm respectively. LEE was a function of the salt concentration, reaching a limiting value of about 1.2 × 10−3 mho cm−1 in 10−4 N KCl. The activation energy for movement of KCl in cell walls was found to be 4.33 Kcal mole−1; the diffusion coefficient for KCl in cell walls was calculated by two methods to be 8 × 10−6 cm2 sec−1; and the concentration of the fixed ions in Nitella cell walls from the above data was estimated at greater than 0.04 equivalent per liter of cell wall. Electroosmosis in Nitella membranes is re-examined in the light of the measured transport coefficients and it is concluded that under proper conditions the cell wall of Nitella can contribute significantly (~20% or more) to the observed electroosmosis of living Nitella cells.

An analytical and experimental investigation of the velocities of particles entrained by the gas flow in nozzles

1968 ◽  
Vol 33 (1) ◽  
pp. 131-149 ◽  
Author(s):  
John H. Neilson ◽  
Alastair Gilchrist
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Particle Velocity ◽  
Flow Rate ◽  
Relative Velocity ◽  
Gas Flow ◽  
Wall Surface ◽  
Erosion Damage ◽  
Limiting Value

Among the parameters which determine the erosion damage sustained by the walls of a nozzle, in which a mixture of gas and particles is flowing is the speed attained by the particle before collision with the wall surface. This work is concerned with the determination of the particle velocity, and a number of relationships are given from which the variation in particle velocity can be obtained for a variety of gas conditions. The changes of state and velocity of the gas, occasioned by the interchange of heat and work between the gas and the particles are dependent on the ratio of the mass flow rate of particles to the mass flow rate of gas. It is shown that if this ratio is small the particle velocity may be obtained without serious error by assuming that the gas conditions are not affected by the presence of particles. Figures for the limiting value of this ratio for certain flows are given. The effects of particle size, density and initial relative velocity are investigated analytically and experimentally.

The determination of the orientation of section planes of meteoritic irons

1942 ◽  
Vol 26 (176) ◽  
pp. 141-166 ◽  
Author(s):  
Max H. Hey
Keyword(s):  
Direct Method ◽  
Plane Section ◽  
General Plane ◽  
Meteoritic Iron ◽  
Crystallographic Axes

The Widmanstetter figures on a general plane section of a meteoritic iron of the octahedrite class consist of kamacite bands running in four directions, the traces of the four planes of the octahedron, while tessellated octahedrites show three more sets of bands, the traces of the cube planes. The angles which these bands make with one another give data which are in principle sufficient to define the crystallographic axes of the iron, but in practice there does not appear to be any simple direct method of effecting this definition. In the following, two simpler cases are first discussed, followed by a method for the general case somewhat shorter than any published method I am aware of, and by methods for orientation from the Neumann lines and from inclusions.

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