The interaction between dislocation-type cracks III. Infinite periodic sequences of noncoplanar cracks

1966 ◽  
Vol 295 (1443) ◽  
pp. 429-439
Keyword(s):  
Plane Strain ◽  
Singular Integral Equations ◽  
Periodic Sequence ◽  
Periodic Sequences ◽  
Plane Strain Tension ◽  
Dislocation Type ◽  
The Stability ◽  
Different Characteristics ◽  
Strain Model

Earlier papers in this series have discussed the interaction between two coplanar dislocation-type cracks and between coplanar cracks that form an infinite periodic sequence, the stability criteria being determined. This paper examines the stability of an infinite periodic sequence of noncoplanar dislocation-type cracks, particular consideration being given to the determination of the complete fracture criterion. Unlike the situation that exists for coplanar dislocation-type cracks, some aspects of the results are radically different depending on whether the mode of deformation is anti-plane strain, plane strain shear, or plane strain tension, and the different characteristics of the three models are emphasized. With the anti-plane strain model exact solutions can be obtained, but with both plane strain shear and plane strain tension models, the governing singular integral equations can only be solved when the cracks are widely spaced.

The interaction between dislocation-type cracks II. The infinite periodic sequence of coplanar dislocation-type cracks

1966 ◽  
Vol 295 (1443) ◽  
pp. 421-428 ◽  
Keyword(s):  
Single Crystals ◽  
Magnesium Oxide ◽  
Periodic Sequence ◽  
Experimental Results ◽  
Continuous Distributions ◽  
Dislocation Type ◽  
Complete Fracture ◽  
The Stability

In a previous paper the interaction between two coplanar dislocation-type cracks was studied, the crack openings being described by continuous distributions of dislocations. A similar approach is used here to examine the stability of an infinite periodic sequence of coplanar dislocation-type cracks, each dislocation being such that its associated extra material is pointing in the same direction. Primary consideration is given to the criterion for the cracks to join up thereby causing complete fracture of the solid, and the characteristics of the model are applied to a very brief discussion of some experimental results on the deformation of magnesium oxide single crystals.

Study on the Influence of Pit Excavation on the Stability of Underground Openings Using Different Models

2013 ◽  
Vol 353-356 ◽  
pp. 1466-1469
Author(s):  
Ya Xin Yang ◽  
Guo Jian Shao ◽  
Jing Fu Yu ◽  
Guang Yuan Chen
Keyword(s):  
Finite Element Method ◽  
Plane Strain ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Dimensional Plane ◽  
Underground Openings ◽  
The Stability ◽  
D Model ◽  
Strain Model ◽  
Plane Strain Model

Simplified plane strain model and 3-D model were used to research the influence of pit excavation on the stability of underground openings using the finite element method (FEM). Conclusion from the 3-D FEM study is that the central region of the pit will have a large springback deformation and the openings will also float up at the same time because of large ranges of pit excavation. When using the simplified two-dimensional plane strain model for the analysis of this problem, the size of the excavation region leads directly to two completely inconsistent results. If the excavation region was wider than the openings the springback deformation would be obtained, while the settlement would be obtained if the opening was wider than the excavation region. Therefore the two-dimensional plane strain model is not proper for the analysis of the stability of the openings under this condition.

Determining the Norton’s Equivalent Model of Distribution System with Distributed Generation (DG) for Stability Analysis

2019 ◽  
Vol 12 (2) ◽  
pp. 190-198
Author(s):  
Sunny Katyara ◽  
Lukasz Staszewski ◽  
Faheem Akhtar Chachar
Keyword(s):  
Distributed Generation ◽  
Normal Condition ◽  
Distribution System ◽  
Distribution Networks ◽  
Equivalent Model ◽  
Stability Factor ◽  
Matlab Simulation ◽  
The Stability ◽  
Stability Issues

Background: Since the distribution networks are passive until Distributed Generation (DG) is not being installed into them, the stability issues occur in the distribution system after the integration of DG. Methods: In order to assure the simplicity during the calculations, many approximations have been proposed for finding the system’s parameters i.e. Voltage, active and reactive powers and load angle, more efficiently and accurately. This research presents an algorithm for finding the Norton’s equivalent model of distribution system with DG, considering from receiving end. Norton’s model of distribution system can be determined either from its complete configuration or through an algorithm using system’s voltage and current profiles. The algorithm involves the determination of derivative of apparent power against the current (dS/dIL) of the system. Results: This work also verifies the accuracy of proposed algorithm according to the relative variations in the phase angle of system’s impedance. This research also considers the varying states of distribution system due to switching in and out of DG and therefore Norton’s model needs to be updated accordingly. Conclusion: The efficacy of the proposed algorithm is verified through MATLAB simulation results under two scenarios, (i) normal condition and (ii) faulty condition. During normal condition, the stability factor near to 1 and change in dS/dIL was near to 0 while during fault condition, the stability factor was higher than 1 and the value of dS/dIL was away from 0.

Synthesis and solvatochromic studies of 2- amino-3-phenolazo1-(4-sulfophenyl)-3-methyi-5-pyrozolone and use it for the determination of trace amount of Nickel (II) in blood samples

2016 ◽  
Vol 5 (10) ◽  
pp. 4920
Author(s):  
Amar M. Ali ◽  
Hussain. J. Mohammed*
Keyword(s):  
Stability Constant ◽  
Trace Amount ◽  
Benzenesulfonic Acid ◽  
Determination Method ◽  
Blood Samples ◽  
Determination Of Nickel ◽  
Normal Human ◽  
The Stability ◽  
Normal Human Blood

A new, simple, sensitive and rapid spectrophotometric method is proposed for the determination of trace amount of Nickel (II). The method is based on the formation of a 1:2 complex with 4-(4-((2-hydroxy-6-nitrophenyl) diazenyl) -3-methyl-5-oxo-2, 5-dihydro-1H-pyrazol-1-yl) benzenesulfonic acid (2-ANASP) as a new reagent is developed. The complex has a maximum absorption at 516 nm and εmax of 1. 84 X 105 L. mol-1. cm-1. A linear correlation (0. 25 – 4. 0μg. ml-1) was found between absorbance at λmax and concentration. The accuracy and reproducibility of the determination method for various known amounts of Nickel (II) were tested. The results obtained are both precise (RSD was 1. 2 %) and accurate (relative error was 0. 787 %). The effect of diverse ions on the determination of Nickel (II) to investigate the selectivity of the method were also studied. The stability constant of the product was 0. 399 X 106 L. mol-1. The proposed method was successfully applied to the analysis of diabetes blood and normal human blood. 

scholarly journals Determination of Objective Weights Using a New Method Based on the Removal Effects of Criteria (MEREC)

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 525 ◽  
Author(s):  
Mehdi Keshavarz-Ghorabaee ◽  
Maghsoud Amiri ◽  
Edmundas Kazimieras Zavadskas ◽  
Zenonas Turskis ◽  
Jurgita Antucheviciene
Keyword(s):  
Essential Elements ◽  
New Method ◽  
Multi Criteria Decision Making ◽  
Analysis Of Means ◽  
Simulation Based ◽  
Criteria Weights ◽  
The Stability ◽  
Computational Analyses ◽  
Weighting Methods

The weights of criteria in multi-criteria decision-making (MCDM) problems are essential elements that can significantly affect the results. Accordingly, researchers developed and presented several methods to determine criteria weights. Weighting methods could be objective, subjective, and integrated. This study introduces a new method, called MEREC (MEthod based on the Removal Effects of Criteria), to determine criteria’ objective weights. This method uses a novel idea for weighting criteria. After systematically introducing the method, we present some computational analyses to confirm the efficiency of the MEREC. Firstly, an illustrative example demonstrates the procedure of the MEREC for calculation of the weights of criteria. Secondly, a comparative analysis is presented through an example for validation of the introduced method’s results. Additionally, we perform a simulation-based analysis to verify the reliability of MEREC and the stability of its results. The data of the MCDM problems generated for making this analysis follow a prevalent symmetric distribution (normal distribution). We compare the results of the MEREC with some other objective weighting methods in this analysis, and the analysis of means (ANOM) for variances shows the stability of its results. The conducted analyses demonstrate that the MEREC is efficient to determine objective weights of criteria.

scholarly journals Determination of Transverse Shear Stiffness of Sandwich Panels with a Corrugated Core by Numerical Homogenization

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1976
Author(s):  
Tomasz Garbowski ◽  
Tomasz Gajewski
Keyword(s):  
Transverse Shear ◽  
Shear Stiffness ◽  
The Finite Element Method ◽  
Homogenization Procedure ◽  
Plate Structures ◽  
Corrugated Board ◽  
Energy Equivalence ◽  
The Stability ◽  
Global Stiffness Matrix

Knowing the material properties of individual layers of the corrugated plate structures and the geometry of its cross-section, the effective material parameters of the equivalent plate can be calculated. This can be problematic, especially if the transverse shear stiffness is also necessary for the correct description of the equivalent plate performance. In this work, the method proposed by Biancolini is extended to include the possibility of determining, apart from the tensile and flexural stiffnesses, also the transverse shear stiffness of the homogenized corrugated board. The method is based on the strain energy equivalence between the full numerical 3D model of the corrugated board and its Reissner-Mindlin flat plate representation. Shell finite elements were used in this study to accurately reflect the geometry of the corrugated board. In the method presented here, the finite element method is only used to compose the initial global stiffness matrix, which is then condensed and directly used in the homogenization procedure. The stability of the proposed method was tested for different variants of the selected representative volume elements. The obtained results are consistent with other technique already presented in the literature.

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