Shear-stress function approach of hydration layer based on the Green-Kubo formula

2015 ◽  
Vol 91 (3) ◽  
Author(s):  
Bongsu Kim ◽  
Soyoung Kwon ◽  
Geol Moon ◽  
Wonho Jhe
Keyword(s):  
Shear Stress ◽  
Stress Function ◽  
Function Approach ◽  
Kubo Formula ◽  
Hydration Layer ◽  
Shear Stress Function

Numerical Analysis of Wall Slip Effects on Flow of Newtonian and Non-Newtonian Fluids in Macro and Micro Contraction Channels

2006 ◽  
Vol 129 (1) ◽  
pp. 23-30 ◽  
Author(s):  
Alfeus Sunarso ◽  
Takehiro Yamamoto ◽  
Noriyasu Mori
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Wall Shear Stress ◽  
Newtonian Fluid ◽  
Stress Function ◽  
Slip Velocity ◽  
Wall Slip ◽  
Average Shear ◽  
Wall Shear ◽  
Shear Stress Function

We performed numerical simulation to investigate the effects of wall slip on flow behaviors of Newtonian and non-Newtonian fluids in macro and micro contraction channels. The results show that the wall slip introduces different vortex growth for the flow in micro channel as compared to that in macro channel, which are qualitatively in agreement with experimental results. The effects of slip on bulk flow behaviors depend on rheological property of the fluid. For Newtonian fluid, the wall slip always reduces the vortex length, while for non-Newtonian fluid, the strength of the slip determines whether the vortex length is reduced or increased. Analyses on the velocity and stress fields confirm the channel size dependent phenomena, such as the reduction of wall shear stress with the decrease in channel size. With the increase in average shear rate, the Newtonian fluid shows the reduction of wall shear stress that increases in the same trend with slip velocity-wall shear stress function, while for non-Newtonian fluid, the effect of the slip is suppressed by shear thinning effect and, therefore, the reduction of wall shear stress is less sensitive to the change in average shear rate and slip velocity-wall shear stress function.

scholarly journals Theoretical Analysis of Radiative Effects on Transient Free Convection Heat Transfer past a Hot Vertical Surface in Porous Media

2008 ◽  
Vol 13 (4) ◽  
pp. 419-432 ◽  
Author(s):  
S. K. Ghosh ◽  
O. Anwar Beg
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Shear Stress ◽  
Free Convection ◽  
Thermal Radiation ◽  
Stress Function ◽  
Dimensionless Time ◽  
Permeability Parameter ◽  
Shear Stress Function

The purpose of the present investigation deals with the unsteady free convective flow of a viscous incompressible gray, absorbing-emitting but non-scattering, optically-thick fluid occupying a semi-infinite porous regime adjacent to an infinite moving hot vertical plate with constant velocity. We employ a Darcian viscous flow model for the porous medium. The momentum and thermal boundary layer equations are non-dimensionalized using appropriate transformations and then solved subject to physically realistic boundary conditions using the Laplace transform technique. Thermal radiation effects are simulated via a radiation-conduction parameter, Kr, based on the Rosseland diffusion approximation. The influence of Grashof (free convection) number, radiation-conduction parameter (Kr), inverse permeability parameter (Kp) and dimensionless time (t) are studied graphically. We observe that increasing thermal radiation parameter causes a noticeable increase in the flow velocity, u. Temperature, θ, is significantly increased within the boundary layer with a rise in Kr since the latter represents the relative contribution of thermal radiation heat transfer to thermal conduction heat transfer. Increased radiation therefore augments heat transfer, heats the fluid and increases the thickness of the momentum and thermal boundary layers. Velocity is found to decrease with an increase in Kp (inverse permeability parameter) as are shear stress function ( ∂u/∂y | y=0) magnitudes owing to greater resistance of the porous medium for lower permeabilities, which decelerate the flow. An increase in Kr however boosts the shear stress function magnitudes i.e. serves to accelerate the flow. Temperature gradient, ∂θ/∂y | y=0 is also positively affected by an increase in thermal radiation (Kr) and with time. The present study has applications in geological convection, forest fire propagation, glass heat treatment processes at high temperature, metallurgical processing etc.

scholarly journals Nonlinear Finite Element Analysis Formulation for Shear in Reinforced Concrete Beams

2019 ◽  
Vol 9 (17) ◽  
pp. 3503 ◽  
Author(s):  
Sang-Ho Kim ◽  
Sun-Jin Han ◽  
Kang Kim
Keyword(s):  
Shear Stress ◽  
Reinforced Concrete ◽  
Stress Function ◽  
Shear Stresses ◽  
Rc Beams ◽  
Test Results ◽  
Proposed Model ◽  
Load Displacement ◽  
Shear Stress Function ◽  
Column Element

This study suggests a novel beam-column element formulation that utilizes an equilibrium-driven shear stress function. The beam shear is obtained from the bi-axial states of micro-planes, through matrix condensation and zero vertical traction assumptions. This properly remedies the shear stiffening of a one-dimensional beam-column element, keeping its degrees of freedom to a minimum. For verification of the proposed method, a total of seven shear test results of reinforced concrete (RC) beams were collected from the literature, in which the key variables were the reinforcement ratio, the presence of shear reinforcement, and section shape. The advantages are clearly shown in the shear stresses distributions being accurately described and the global load-displacement relations being successfully obtained and matching well with various test results. The proposed model shows satisfactory descriptions of the monotonic load-displacement response of the RC beams failing in multiple modes that vary from diagonal-tension to flexural-compression. In addition, more accurate and reliable information of sectional responses including sectional shear deformation and stresses is collected, leading to better prediction of a potential shear failure mode. Finally, the advantages of the proposed model are demonstrated by comparing the analysis results of an RCT-beam by using the different shear assumptions that include the constant and parabolic shear strains, constant shear flow, and the proposed shear stress function.

A two-term stress function approach to evaluate stress distributions in bonded joints of different geometries

2002 ◽  
Vol 37 (5) ◽  
pp. 385-398 ◽  
Author(s):  
P Lazzarin ◽  
M Quaresimin ◽  
P Ferro
Keyword(s):  
Elastic Properties ◽  
Stress Function ◽  
Function Approach ◽  
Design Parameters ◽  
Bonded Joints ◽  
Stress Distributions ◽  
Singular Stress ◽  
Generalized Stress Intensity Factors ◽  
Singular Stress Field ◽  
Singular Stress Fields

The paper presents a method for the evaluation of the singular stress fields in bonded joints of different geometries. The stress distributions are represented by a two-term stress expansion, under the hypothesis that both the first and the second terms are in the variable separable form. The method is based on the stress function approach, where the formulation is completed analytically and the resulting set of ordinary differential equations is solved numerically. The capability of the formulation to account for the actual elastic properties of the substrates allows an accurate description of the singular stress field to be obtained even in the case of joints made of materials with comparable elastic properties. The influence of adhesive joint design parameters such as the type of joint, geometry and material properties on the generalized stress intensity factors will also be presented and discussed.

Alternative Derivation of Marguerre’s Displacement Solution in Plane Isotropic Elasticity

1999 ◽  
Vol 67 (2) ◽  
pp. 419-421 ◽  
Author(s):  
X.-L. Gao
Keyword(s):  
Stress Function ◽  
Present Approach ◽  
Function Approach ◽  
Airy Stress Function ◽  
Green's Theorem ◽  
Alternative Derivation ◽  
Green’S Theorem ◽  
Isotropic Elasticity

An alternative derivation of Marguerre’s solution for displacements in plane isotropic elasticity is provided. It is shown that the present approach, which is based on Green’s theorem and parallel to the Airy stress function approach, is straightforward. Also, the current derivation establishes the completeness of the Marguerre solution. [S0021-8936(00)00302-0]

Stress Solutions of some Axisymmetric and Non-Axisymmetric Cases with the Principles of Elasticity: A Review

2012 ◽  
Vol 215-216 ◽  
pp. 1026-1032
Author(s):  
Suhas Ankalkhope ◽  
Nilesh Jadhav ◽  
Sunil Bhat
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shear Stress ◽  
Excellent Agreement ◽  
Stress Function ◽  
Structural Member ◽  
Numerical Results ◽  
Airy’S Stress Function ◽  
Element Method

Stress solutions are reviewed for some typical cases of axisymmetric and non-axisymmetric loads over a structural member with the principles of elasticity. A curved bar is chosen for the analysis. Tangential, radial and shear stress are determined analytically using Airy’s stress function. The curved bar is also modelled by finite element method to obtain numerical values of stress. Analytical and numerical results are in excellent agreement with each other.

scholarly journals Solution of the Boussinesq’s problem in evaluating ratio between shear stress and contact pressure

2020 ◽  
pp. 139-151
Author(s):  
Е.Г. Хитров ◽  
А.В. Андронов ◽  
Е.В. Нестерова
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Normal Stress ◽  
Contact Pressure ◽  
Stress Function ◽  
Average Pressure ◽  
Normal Stress Distribution ◽  
Contact Patch ◽  
Wide Range ◽  
Boussinesq’S Problem

Решение фундаментальной задачи Буссинеска широко используется в технических науках и позволяет эффективно решать широкий спектр задач науки о лесозаготовительном производстве. На его основе удается получить практически значимые результаты в области оценки распределения напряжений, возникающих в обрабатываемом материале под воздействием рабочего органа. Цель нашего исследования - проанализировать результаты расчетов и установить соотношение максимального значения касательного напряжения и среднего значения давления по пятну контакта рабочего органа с обрабатываемом материалом. Теоретическую основу работы составляют уравнения распределения нормальных и касательных напряжений, возникающих в упругом полупространстве при вдавливании в него жесткого клина. В результате анализа теоретических расчетов показано, что характер затухания нормального напряжения по глубине деформируемого массива материала с высокой точностью аппроксимируется квадратичной функцией (на основе полученной приближенной функции выполнено сопоставление среднего давления по пятну контакта индентора с массивом и нормального напряжения по глубине массива). При этом, как показали результаты расчетов, функция распространения касательного напряжения в деформируемом массиве имеет экстремум. Выполнено сопоставление полученных данных по значению экстремума функции касательного напряжения со значением приближенной функции нормального напряжения на границе контакта индентора сдеформируемым массивом. В результате показано, что максимальное по модулю касательное напряжение составляет 11-12% среднего контактного давления. Расчеты проведены при варьировании коэффициента Пуассона материала массива, установленное соотношение остается практически неизменным. Solution of fundamental Boussinesq’s problem is widely used in technical sciences and allows effectively solving a wide range of problems in forestry science. On its basis, it is possible to obtain practically significant results in the field of assessing the distribution of stresses arising in processed material under the influence of a working body. The purpose of our study is to analyze the results of calculations and establish the ratio of the maximum value of the shear stress and the average pressure over the contact patch of the working body with the material being processed. The theoretical basis of the work is formed by the equations for the distribution of normal and tangential stresses arising in an elastic half-space when a rigid cone is pressed into it. As a result of the analysis of the results of theoretical calculations, it was shown that the character of the normal stress distribution over the depth of the deformed massif of material is approximated with high accuracy by a quadratic function (based on the obtained approximate function, the average pressure over the contact patch of the indenter with the massif and the normal stress over the depth of the massif were compared). In this case, as shown by the results of calculations, the function of the shear stress distribution in the deformed massif has the extremum. Comparison of the obtained data on the value of the extremum of the shear stress function with the value of the approximate normal stress function at the interface of the indenter contact with the deformable mass is performed. As a result, it is shown that the maximum shear stress in absolute value is 11-12% of the average contact pressure. The calculations were carried out with varying Poisson's ratio of the massif material; the established ratio remains practically unchanged.

Sign in / Sign up

Export Citation Format

Share Document