scholarly journals Flow of a new class of non-Newtonian fluids in tubes of non-circular cross-sections

2019 ◽  
Vol 377 (2144) ◽  
pp. 20180069 ◽  
Author(s):  
Juan P. Gomez-Constante ◽  
Kumbakonam R. Rajagopal
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Cross Section ◽  
Cross Sections ◽  
Applied Mathematics ◽  
Constitutive Relations ◽  
Maximum Shear Stress ◽  
Circular Cross Section ◽  
Secondary Flows ◽  
Shear Stresses

Fluids described by constitutive relations wherein the symmetric part of the velocity gradient is a function of the stress can be used to describe the flows of colloids and suspensions. In this paper, we consider the flow of a fluid obeying such a constitutive relation in a tube of elliptic and other non-circular cross-sections with the view towards determining the velocity field and the stresses that are generated at the boundary of the tube. As tubes are rarely perfectly circular, it is worthwhile to study the structure of the velocity field and the stresses in tubes of non-circular cross-section. After first proving that purely axial flows are possible, that is, there are no secondary flows as in the case of many viscoelastic fluids, we determine the velocity profile and the shear stresses at the boundaries. We find that the maximum shear stress is attained at the co-vertex of the ellipse. In general tubes of non-circular cross-section, the maximum shear stress occurs at the point on the boundary that is closest to the centroid of the cross-section. This article is part of the theme issue ‘Rivlin's legacy in continuum mechanics and applied mathematics’.

Determining of Shear Modulus for the Samples Circular and Hollow Circular Cross-Section

2016 ◽  
Vol 862 ◽  
pp. 298-304
Author(s):  
Eva Labašová ◽  
Rastislav Ďuriš ◽  
Vladimír Labaš
Keyword(s):  
Shear Stress ◽  
Shear Modulus ◽  
Cross Section ◽  
Theoretical Basis ◽  
Maximum Shear Stress ◽  
Circular Cross Section ◽  
Static Method ◽  
Strength Theory ◽  
Modulus Maximum ◽  
System Quantum

The contribution is focused on estimating the shear modulus of the samples of circular and hollow circular sections by static method. The samples were loaded by simple torsion, individual sections were stressed by shear stress. Theoretical basis are determined by linear elasticity and strength theory and they define the relation between shear modulus, maximum shear stress and relative strains. Relative strains are determined by using measurement apparatus and measurement system Quantum X MX 840.

Stresses in a Reinforced Monocoque Cylinder Under Concentrated Symmetric Transverse Loads

1944 ◽  
Vol 11 (4) ◽  
pp. A235-A239
Author(s):  
N. J. Hoff
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Cross Section ◽  
Maximum Shear Stress ◽  
Circular Cross Section ◽  
Bending Moment ◽  
Normal Stress Distribution ◽  
Transverse Loads ◽  
Conventional Analysis ◽  
Analysis Application

Abstract The stresses in the sheet covering, stringers, and rings of a reinforced monocoque cylinder of circular cross section are calculated for the case of a loading consisting of concentrated symmetric forces applied to the rings in the planes of the rings. The conventional assumptions of a linear normal stress distribution and a corresponding shear-stress distribution in the bent cylinder are replaced by a least-work analysis. Application of the theory to the numerical example of a cantilever monocoque cylinder yields a maximum shear stress in the sheet covering and a maximum bending moment in the ring amounting to 900 per cent and 33 per cent, respectively, of the values obtained by the conventional analysis.

The Analysis of Al-Cu Bimetallic Bars Bond Layers Joined by the Explosive Method

2013 ◽  
Vol 199 ◽  
pp. 508-513 ◽  
Author(s):  
Seweryn Wąsek ◽  
Sebastian Mróz ◽  
Grzegorz Stradomski ◽  
Konrad Błażej Laber
Keyword(s):  
Shear Stress ◽  
Cross Section ◽  
Cross Sections ◽  
Maximum Shear Stress ◽  
Explosion Welding ◽  
Outer Diameter ◽  
Technological Parameters ◽  
Explosive Cladding ◽  
Microhardness Distribution ◽  
Explosion Method

The paper presents investigation results for obtaining a semi-finished product in the form of round Al-Cu bimetallic bars by the explosion method. The systems and technological parameters of explosion welding were selected in such a manner as to obtain finished bimetallic bars of an outer diameter of approx. 22 mm and a copper area fraction of the bimetal cross-section of approx. 15 and 30%. In this work was made an analysis of microstructure changes and the microhardness distribution on the cross-sections of the stock materials. There were also made tests of layers connections quality by determining the maximum shear stress on the joint boundary. The results show that the explosive cladding method guarantee a permanent connection of copper layers and aluminum core.

An Improved Method for Predicting Shear Stress in Rectangular Shafts Based on Optimization Polynomials

1995 ◽  
Author(s):  
T. E. Shoup ◽  
L. A. Sanchez
Keyword(s):  
Shear Stress ◽  
Cross Section ◽  
Maximum Shear Stress ◽  
Merit Function ◽  
Shear Stresses ◽  
Optimization Approach ◽  
Improved Method ◽  
Approximate Methods ◽  
The Cross

Abstract This paper presents several new approximations for the coefficients associated with the shear stresses in rectangular shafts. The new results are developed using an optimization approach based on a polynomial merit function to predict the maximum shear stress along the center of the long side of the cross section. The results are shown to be more accurate than existing approximate methods that are now in the literature.

scholarly journals Asymptotic Behavior of Stable Structures Made of Beams

2021 ◽  
Author(s):  
Georges Griso ◽  
Larysa Khilkova ◽  
Julia Orlik ◽  
Olena Sivak
Keyword(s):  
Asymptotic Behavior ◽  
Cross Section ◽  
Cross Sections ◽  
Linear Elasticity ◽  
Circular Cross Section ◽  
Linear Elasticity Theory ◽  
Linear Elastic ◽  
The Cross ◽  
Small Rotation ◽  
Stable Structures

AbstractIn this paper, we study the asymptotic behavior of an $\varepsilon $ ε -periodic 3D stable structure made of beams of circular cross-section of radius $r$ r when the periodicity parameter $\varepsilon $ ε and the ratio ${r/\varepsilon }$ r / ε simultaneously tend to 0. The analysis is performed within the frame of linear elasticity theory and it is based on the known decomposition of the beam displacements into a beam centerline displacement, a small rotation of the cross-sections and a warping (the deformation of the cross-sections). This decomposition allows to obtain Korn type inequalities. We introduce two unfolding operators, one for the homogenization of the set of beam centerlines and another for the dimension reduction of the beams. The limit homogenized problem is still a linear elastic, second order PDE.

scholarly journals Effect of liquid cooling on PCR performance with the parametric study of cross-section shapes of microchannels

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yousef Alihosseini ◽  
Mohammad Reza Azaddel ◽  
Sahel Moslemi ◽  
Mehdi Mohammadi ◽  
Ali Pormohammad ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Heat Sink ◽  
Evaluation Criteria ◽  
Circular Cross Section ◽  
Microchannel Heat Sink ◽  
Liquid Cooling ◽  
Maximum Heat ◽  
Maximum Heat Transfer

AbstractIn recent years, PCR-based methods as a rapid and high accurate technique in the industry and medical fields have been expanded rapidly. Where we are faced with the COVID-19 pandemic, the necessity of a rapid diagnosis has felt more than ever. In the current interdisciplinary study, we have proposed, developed, and characterized a state-of-the-art liquid cooling design to accelerate the PCR procedure. A numerical simulation approach is utilized to evaluate 15 different cross-sections of the microchannel heat sink and select the best shape to achieve this goal. Also, crucial heat sink parameters are characterized, e.g., heat transfer coefficient, pressure drop, performance evaluation criteria, and fluid flow. The achieved result showed that the circular cross-section is the most efficient shape for the microchannel heat sink, which has a maximum heat transfer enhancement of 25% compared to the square shape at the Reynolds number of 1150. In the next phase of the study, the circular cross-section microchannel is located below the PCR device to evaluate the cooling rate of the PCR. Also, the results demonstrate that it takes 16.5 s to cool saliva samples in the PCR well, which saves up to 157.5 s for the whole amplification procedure compared to the conventional air fans. Another advantage of using the microchannel heat sink is that it takes up a little space compared to other common cooling methods.

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

Numerical Investigation of Cross-Section on Aluminum A6063 Thin-Walled Structures under Low-Velocity Impact Loading

2014 ◽  
Vol 1019 ◽  
pp. 96-102
Author(s):  
Ali Taherkhani ◽  
Ali Alavi Nia
Keyword(s):  
Energy Absorption ◽  
Cross Section ◽  
Cross Sections ◽  
Peak Load ◽  
Circular Cross Section ◽  
Absorption Capacity ◽  
Energy Absorption Capacity ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Crush Strength

In this study, the energy absorption capacity and crush strength of cylindrical thin-walled structures is investigated using nonlinear Finite Elements code LS-DYNA. For the thin-walled structure, Aluminum A6063 is used and its behaviour is modeled using power-law equation. In order to better investigate the performance of tubes, the simulation was also carried out on structures with other types of cross-sections such as triangle, square, rectangle, and hexagonal, and their results, namely, energy absorption, crush strength, peak load, and the displacement at the end of tubes was compared to each other. It was seen that the circular cross-section has the highest energy absorption capacity and crush strength, while they are the lowest for the triangular cross-section. It was concluded that increasing the number of sides increases the energy absorption capacity and the crush strength. On the other hand, by comparing the results between the square and rectangular cross-sections, it can be found out that eliminating the symmetry of the cross-section decreases the energy absorption capacity and the crush strength. The crush behaviour of the structure was also studied by changing the mass and the velocity of the striker, simultaneously while its total kinetic energy is kept constant. It was seen that the energy absorption of the structure is more sensitive to the striker velocity than its mass.

A critical look at the Wallace-Bott hypothesis in fault-slip analysis

2013 ◽  
Vol 184 (4-5) ◽  
pp. 299-306 ◽  
Author(s):  
Richard J. Lisle
Keyword(s):  
Shear Stress ◽  
Maximum Shear Stress ◽  
Fault Slip ◽  
Shear Stresses ◽  
Homogeneous State ◽  
Slip Direction ◽  
Fault Surface ◽  
State Of Stress ◽  
Simultaneous Movement

AbstractThe assumption is widely made that slip on faults occurs in the direction of maximum resolved shear stress, an assumption known as the Wallace-Bott hypothesis. This assumption is used to theoretically predict slip directions from known in situ stresses, and also as the basis of palaeostress inversion from fault-slip data. This paper examines different situations in relation to the appropriateness of this assumption. Firstly, it is shown that the magnitude of the shear stress resolved within a plane is a function with a poorly defined maximum direction, so that shear stress values greater than 90% of the maximum occur within a wide angular range (± 26°) degrees. The situation of simultaneous movement on pairs of faults requires slip on each fault to be parallel to their mutual line of intersection. However, the resolved shear stresses arising from a homogeneous state of stress do not accord with such a slip arrangement except in the case of pairs of perpendicular faults. Where fault surfaces are non-planar, the directions of resolved shear stress in general give, according to the Wallace-Bott hypothesis, a set of slip directions of rigid fault blocks, which is generally kinematically incompatible. Finally, a simple model of a corrugated fault suggests that any anisotropy of the shear strength of the fault such as that arising from fault surface topography, can lead to a significant angular difference between the directions of maximum shear stress and the slip direction.These findings have relevance to the design of procedures used to estimate palaeostresses and the amount of data required for this type of analysis.

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