scholarly journals Two interacting non-elliptical rigid harmonic inclusions loaded by couples

2019 ◽  
Vol 46 (2) ◽  
pp. 157-171
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Conformal Mapping ◽  
Tangential Stress ◽  
Geometric Parameters ◽  
Mean Stress ◽  
The Matrix ◽  
Mapping Techniques ◽  
The Moment ◽  
Hoop Stresses ◽  
Inclusion Matrix ◽  
Two Inclusions

We use conformal mapping techniques to design two interacting non-elliptical rigid inclusions, each of which is loaded by a couple, which ensure the so-called ?harmonic condition? in which the original mean stress in the matrix remains undisturbed after the introduction of the inclusions. We show that for prescribed Poisson?s ratio and corresponding geometric parameters, several restrictions are necessary on the external loadings to ensure the harmonic condition. It is seen from our analysis that: (i) the interfacial and hoop stresses are uniformly distributed along each of the inclusion-matrix interfaces; (ii) the interfacial normal and hoop stresses along the two interfaces are completely determined by the Poisson?s ratio and the constant mean stress in the matrix whilst the interfacial tangential stress along the two interfaces can be completely determined by the moments of the couples and the areas of the two inclusions; (iii) the existence of the applied couples will influence the non-elliptical shapes of the two rigid harmonic inclusions when the moment to area ratios for the two inclusions differ.

A circular Eshelby inclusion interacting with a non-parabolic open inhomogeneity with internal uniform anti-plane stresses

2019 ◽  
Vol 25 (3) ◽  
pp. 573-581 ◽  
Author(s):  
Xu Wang ◽  
Ping Yang ◽  
Peter Schiavone
Keyword(s):  
Stress Field ◽  
Conformal Mapping ◽  
Stress Distributions ◽  
Uniform Stress ◽  
Elastic Deformations ◽  
Surrounding Matrix ◽  
Eshelby Inclusion ◽  
The Matrix ◽  
Uniform Stress Field ◽  
Mapping Techniques

Using conformal mapping techniques and analytic continuation, we prove that when subjected to anti-plane elastic deformations, a non-parabolic open inhomogeneity continues to admit an internal uniform stress field when a circular Eshelby inclusion is placed in its vicinity and the surrounding matrix is subjected to uniform remote stresses. Explicit expressions for the non-uniform stress distributions in the matrix and in the circular Eshelby inclusion are obtained. The internal uniform stress field is independent of the shape of the inhomogeneity and the presence of the circular Eshelby inclusion, whereas the existence of the circular Eshelby inclusion exerts a significant influence on the shape of the non-parabolic open inhomogeneity as well as on the non-uniform stress distributions in the matrix and in the circular Eshelby inclusion itself.

Pinocytotic-Like Forms of Mitochondria From Rat Anterior Pituitary

1968 ◽  
Vol 26 ◽  
pp. 146-147
Author(s):  
Burton B. Silver
Keyword(s):  
Electron Micrographs ◽  
Conformational Changes ◽  
Anterior Pituitary ◽  
Dynamic State ◽  
Surrounding Cell ◽  
The Matrix ◽  
The Moment ◽  
Cell Medium ◽  
Sectioned Tissue ◽  
State Of Activity

Sectioned tissue rarely indicates evidence of what is probably a highly dynamic state of activity in mitochondria which have been reported to undergo a variety of movements such as streaming, divisions and coalescence. Recently, mitochondria from the rat anterior pituitary have been fixed in a variety of configurations which suggest that conformational changes were occurring at the moment of fixation. Pinocytotic-like vacuoles which may be taking in or expelling materials from the surrounding cell medium, appear to be forming in some of the mitochondria. In some cases, pores extend into the matrix of the mitochondria. In other forms, the remains of what seems to be pinched off vacuoles are evident in the mitochondrial interior. Dense materials, resembling secretory droplets, appear at the junction of the pores and the cytoplasm. The droplets are similar to the secretory materials commonly identified in electron micrographs of the anterior pituitary.

scholarly journals D-Optimal Slope Design for Second Degree Kronecker Model Mixture Experiment With Three Ingredients

2020 ◽  
Vol 9 (2) ◽  
pp. 30
Author(s):  
Ngigi Peter Kung’u ◽  
J. K. Arap Koske ◽  
Josphat K. Kinyanjui
Keyword(s):  
Information Matrix ◽  
Coefficient Matrix ◽  
Three Dimensions ◽  
Matrix Means ◽  
The Matrix ◽  
Optimal Values ◽  
The Moment ◽  
Product Algebra ◽  
Slope Design ◽  
Second Degree

This study presents an investigation of an optimal slope design in the second degree Kronecker model for mixture experiments in three dimensions. The study is restricted to weighted centroid designs, with the second degree Kronecker model. A well-defined coefficient matrix is used to select a maximal parameter subsystem for the model since its full parameter space is inestimable. The information matrix of the design is obtained using a linear function of the moment matrices for the centroids and directly linked to the slope matrix. The discussion is based on Kronecker product algebra which clearly reflects the symmetries of the simplex experimental region. Eventually the matrix means are used in determining optimal values of the efficient developed design.

An elastic harmonic inclusion near a rigid harmonic inclusion loaded by a couple

2019 ◽  
Vol 84 (3) ◽  
pp. 555-566
Author(s):  
Xu Wang ◽  
Liang Chen ◽  
Peter Schiavone
Keyword(s):  
Rigid Inclusion ◽  
Elastic Inclusion ◽  
Complex Loading ◽  
Solution Procedure ◽  
External Loading ◽  
Surrounding Matrix ◽  
The Matrix ◽  
Mapping Techniques ◽  
Loading Parameter ◽  
Harmonic Inclusion

AbstractWe use conformal mapping techniques to solve the inverse problem concerned with an elastic non-elliptical harmonic inclusion in the vicinity of a rigid non-elliptical harmonic inclusion loaded by a couple when the surrounding matrix is subjected to remote uniform stresses. Both a size-independent complex loading parameter and a size-dependent real loading parameter are introduced as part of the solution procedure. The stress field inside the elastic inclusion is uniform and hydrostatic; the interfacial normal and tangential stresses as well as the hoop stress on the matrix side are uniform along each one of the two inclusion–matrix interfaces. The tangential stress along the interface of the elastic inclusion (free of external loading) vanishes, whereas that along the interface of the rigid inclusion (loaded by the couple) does not. A novel method is proposed to determine the area of the rigid inclusion.

scholarly journals A Simplified Method for the Design of Steel Beam-to-column Connections

2017 ◽  
Vol 48 (2) ◽  
pp. 79-86
Author(s):  
Imola Kristóf ◽  
Zsanett Novák ◽  
Dezső Hegyi
Keyword(s):  
Failure Modes ◽  
Steel Structures ◽  
Simple Calculation ◽  
Geometric Parameters ◽  
End Plate ◽  
Simplified Method ◽  
Eurocode 3 ◽  
Steel Sections ◽  
The Moment ◽  
Hot Rolled

The moment resistance of beam-to-column connections is frequently utilised in steel structures. Eurocode 3 suggests the component method to analyse such connections, and it implements the equivalent T-stub method to determine the resistance of the end plate of the beam. The latter method requires tedious and concentrated work. A simplified method is suggested to reduce the number of calculations and enable the designer to focus on construction aspects in the pre-design phase, or in education.The resistance of the T-stub covers three possible failure modes: the yield of the plate, the failure of the of the bolt and simultaneous yield. The yield of the plate and simultaneous yield depend on numerous parameters, and they are verified by multiple equations. The failure of the bolts are more easily checked.In the present paper, requirements for geometric ratios are defined for the widely used steel sections to assure failure of the bolts at a lower level of the load than the yield of the plate. These parameters facilitate the simple calculation of the resistance of the bolts instead of the tedious work needed for the end plate resistance.The paper presents a proper explanation for the design rules and the effect of the geometric parameters on the resistance of the end plate. Geometric parameters are suggested for the widely used hot rolled and typical welded beam sections. All the parameters fulfil the requirements of the equivalent T-stub method of Eurocode 3.

scholarly journals Novel cloaking lamellar structures for a screw dislocation dipole, a circular Eshelby inclusion and a concentrated couple

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200095
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Conformal Mapping ◽  
Screw Dislocation ◽  
Lamellar Structure ◽  
Stress Fields ◽  
Uniform Stress ◽  
Dislocation Dipole ◽  
Lamellar Structures ◽  
Eshelby Inclusion ◽  
Mapping Techniques ◽  
Concentrated Couple

Using conformal mapping techniques, we design novel lamellar structures which cloak the influence of any one of a screw dislocation dipole, a circular Eshelby inclusion or a concentrated couple. The lamellar structure is composed of two half-planes bonded through a middle coating with a variable thickness within which is located either the dislocation dipole, the circular Eshelby inclusion or the concentrated couple. The Eshelby inclusion undergoes either uniform anti-plane eigenstrains or uniform in-plane volumetric eigenstrains. As a result, the influence of any one of the dislocation dipole, the circular Eshelby inclusion or the concentrated couple is cloaked in that their presence will not disturb the prescribed uniform stress fields in both surrounding half-planes.

Influence of the pressure relief door area and aspect ratio on discharge and force characteristics

2019 ◽  
Vol 92 (2) ◽  
pp. 107-116
Author(s):  
Shiyu Feng ◽  
Chenchen Wang ◽  
Xiaotian Peng ◽  
Yan Yan ◽  
Yang Deng ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Discharge Coefficient ◽  
Geometric Parameters ◽  
Pressure Relief ◽  
Thrust Coefficient ◽  
Content Type ◽  
Moment Coefficient ◽  
The Moment ◽  
Compartment Pressures ◽  
Force Characteristics

Purpose The purpose of this paper is to analyze the effects of the PRD geometric parameters, including the area and aspect ratio, on the discharge and force characteristics of pressure relief process under various plenum compartment pressures and Mach numbers. Design/methodology/approach Under various plenum compartment pressures and Mach numbers, the effect of the area and aspect ratio on the discharge and force characteristics of the PRD are numerically investigated via a three-dimensional steady Reynolds-averaged Navier–Stokes equations solver based on structured grid technology. Findings When the aspect ratio remains constant, the discharge coefficient CD, thrust coefficient CT and moment coefficient CM are not affected by the PRD. When the area is constant, the aspect ratio dramatically impacts the discharge and force characteristics because the aspect ratio increases, the discharge coefficient CD of the PRD decreases, and the thrust coefficient CT and the moment coefficient CM both increase. When the aspect ratio is 2, the discharge coefficient CD decreases by 14.7 per cent, the thrust coefficient CT increases by 10-15 per cent, and the moment coefficient CM increases by 10-23 per cent compared with when the aspect ratio is 1. Practical implications This study provides detailed data and conclusions for nacelle PRD researchers and actual engineering applications. Originality/value On the basis of considering the influence of operating conditions on the discharge and force characteristics of the nacelle PRD, the impact of geometric parameters, including the area and aspect ratio on the discharge and force characteristics is comprehensively considered.

Internal uniform hydrostatic stresses in a three-phase non-elliptical inclusion subjected to a nearby concentrated couple

2019 ◽  
Vol 24 (9) ◽  
pp. 2931-2943 ◽  
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Stress Field ◽  
Conformal Mapping ◽  
Hydrostatic Stress ◽  
Geometric Parameters ◽  
Interphase Layer ◽  
Infinite Matrix ◽  
Elliptical Inclusion ◽  
Three Phase ◽  
Uniform Hydrostatic Stress Field ◽  
Concentrated Couple

We apply conformal mapping techniques with analytic continuation to study the existence of a uniform hydrostatic stress field inside a non-elliptical inclusion bonded to an infinite matrix via a finite thickness interphase layer when the matrix is simultaneously subjected to a concentrated couple as well as uniform remote in-plane stresses. We show that the desired internal uniform hydrostatic stress field is possible for given material and geometric parameters provided a certain constraint is placed on the remote loading. Subsequently, when the single loading parameter, five material parameters and three geometric parameters are prescribed, all of the unknown complex coefficients appearing in the series representing the corresponding conformal mapping function can be uniquely determined from a set of nonlinear recurrence relations. We find that the internal uniform hydrostatic stress field, the constant mean stress in the interphase layer and the hoop stress along the inner interface on the interphase layer side are all unaffected by the existence of the concentrated couple whereas the non-elliptical shape of the (three-phase) inclusion is attributed solely to the influence of the nearby concentrated couple.

Effect of Deep Cryogenic Process on the Microstructure and Hardness and Wear Resistance of High Carbon Tool Steel

2018 ◽  
Vol 934 ◽  
pp. 100-104
Author(s):  
Yuan Ching Lin ◽  
Ji Wei Gong
Keyword(s):  
Wear Resistance ◽  
Tool Steel ◽  
Cryogenic Treatment ◽  
Wear Test ◽  
High Carbon ◽  
Deep Cryogenic Treatment ◽  
Treatment Conditions ◽  
The Matrix ◽  
Cryogenic Process ◽  
The Moment

In this investigation, the effects of different heat treatment conditions on the mechanical properties of high carbon tool steel (SK2) were explored. Experimental results indicated that immediately doing deep cryogenic treatment can effectively reduce retained austenite after quenching. The moment of the holding time for the cryogenic treatment was extended can promote the fine carbides precipitated, and thus increased its hardness. The results of X-ray diffraction showed that the carbides in the matrix included Fe3C and Fe7C3.The wear test results demonstrated that the specimen with Q-T1hr-C24hr-T1hr treatment has the highest wear resistance than the others, which was caused by the effect of several tempering processes to improve toughness of the matrix and to precipitate considerable quantities of the fine carbides.

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