scholarly journals Response Due to Concentrated Force in Micropolar Elastic Solid with Voids

2014 ◽  
Vol 19 (4) ◽  
pp. 755-769
Author(s):  
R. Singh ◽  
K. Singh
Keyword(s):  
Fourier Transforms ◽  
Normal Force ◽  
Volume Fraction ◽  
Tangential Force ◽  
Elastic Solid ◽  
Normal Displacement ◽  
Laplace And Fourier Transforms ◽  
Concentrated Force ◽  
Eigen Value ◽  
Stress Components

Abstract The eigen value approach, following Laplace and Fourier transforms has been employed to find the general solution of the field equation in a micropolar elastic solid with voids for the plane strain problem. An application of an infinite space with impulsive force has been taken to illustrate the utility of the approach. The integral transformations have been inverted by using a numerical inversion technique to get result in physical domain. The result in the form of normal displacement, volume fraction, normal force stress, tangential force stress and tangential couple stress components has been obtained numerically and illustrated graphically to depict the effect of micropolarity and voids.

scholarly journals Response Due To Impulsive Force In Generalized Thermomicrostretch Elastic Solid

2015 ◽  
Vol 20 (3) ◽  
pp. 487-502
Author(s):  
V. Kumar ◽  
R. Singh
Keyword(s):  
Fourier Transforms ◽  
Normal Force ◽  
Elastic Solid ◽  
Integral Transforms ◽  
Normal Displacement ◽  
Impulsive Force ◽  
Field Equations ◽  
Laplace And Fourier Transforms ◽  
Eigen Value ◽  
Plain Strain

Abstract A two dimensional Cartesian model of a generalized thermo-microstretch elastic solid subjected to impulsive force has been studied. The eigen value approach is employed after applying the Laplace and Fourier transforms on the field equations for L-S and G-L model of the plain strain problem. The integral transforms have been inverted into physical domain numerically and components of normal displacement, normal force stress, couple stress and microstress have been illustrated graphically.

scholarly journals Eigen Value Approach in Micropolar Elastic Medium with Voids

2013 ◽  
Vol 18 (2) ◽  
pp. 521-536
Author(s):  
R. Singh ◽  
K. Singh
Keyword(s):  
Elastic Medium ◽  
Normal Force ◽  
Volume Fraction ◽  
Tangential Force ◽  
Normal Displacement ◽  
Physical Domain ◽  
Field Equations ◽  
Hankel Transformation ◽  
Eigen Value ◽  
Stress Components

The eigen value approach, following the Laplace and Hankel transformation has been employed to find a general solution of the field equations in a micropolar elastic medium with voids for an axisymmetric problem. An infinite space with the mechanical source has been applied to illustrate the utility of the approach. The integral transformations has been inverted by using a numerical inversion technique to get the result in physical domain. The results in the form of normal displacement, volume fraction, normal force stress, tangential force stress and tangential couple stress components have been obtained numerically and illustrated graphically.

Response of ramp-type heating in a monoclinic generalized thermoelastic material

2020 ◽  
Vol 16 (6) ◽  
pp. 1373-1384
Author(s):  
Leena Rani ◽  
Sushant Shekhar
Keyword(s):  
Half Space ◽  
Thermal Loading ◽  
Fourier Transforms ◽  
Generalized Thermoelasticity ◽  
Normal Displacement ◽  
Linear Temperature ◽  
Content Type ◽  
Wide Range ◽  
Eigen Value ◽  
Thermally Conducting

PurposeThe two-dimensional deformation of a homogeneous, thermally conducting, monoclinic material has been studied by using Laplace and Fourier transforms technique. A linear temperature ramping function is used to more realistically model: thermal loading of the half-space surface. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating and loading. The displacements, stresses and temperature distribution so obtained in the physical domain are computed numerically and illustrated graphically. The comparison for Lord-Shulman (L-S), Green and Lindsay (G–L), Green and Naghdi (G–N) and Chandrasekharaiah and Tzou (CTU) theories have been shown graphically to estimate the effect of ramping parameter of heating for an insulated and temperature gradient boundaries.Design/methodology/approachThe design of the study is eigenvalue approachFindingsHomogeneous, thermally conducting monoclinic material has been taken under consideration to study the effect of linear temperature ramping parameter on temperature and normal displacement field. It is observed that magnitude of field quantities is large near the point of application of source for the non-dimensional values of time in all the four models. The numerical values for the field quantities are computed graphically for a wide range of values of finite pulse rise-time in the two situations t0 < t, t0 > t for generalized thermoelasticity theories.Originality/value(1) Governing equations for homogeneous, t0 thermally conducting, monoclinic material are described and solved. (2) Eigen value approach is used to solve the problem. (3) The effect of ramping parameter of heating has been studied for various models of the thermoelasticity to show the comparision between them.

scholarly journals Interaction Due to Mechanical Source in Generalized Thermo Microstretch Elastic Medium

2014 ◽  
Vol 19 (2) ◽  
pp. 347-363
Author(s):  
R. Singh ◽  
V. Kumar
Keyword(s):  
Elastic Medium ◽  
Couple Stress ◽  
Axisymmetric Problem ◽  
Normal Force ◽  
Normal Displacement ◽  
Physical Domain ◽  
Field Equations ◽  
Hankel Transformation ◽  
Integral Transformations ◽  
Eigen Value

Abstract The eigen value approach, following the Laplace and Hankel transformation has been employed to find a general solution of the field equations in a generalized thermo microstretch elastic medium for an axisymmetric problem. An infinite space with the mechanical source has been applied to illustrate the utility of the approach. The integral transformations have been inverted by using a numerical inversion technique to obtain normal displacement, normal force stress, couple stress and microstress in the physical domain. Numerical results are shown graphically

Concentrated Forces on Shallow Cylindrical Shells

1970 ◽  
Vol 37 (2) ◽  
pp. 367-373 ◽  
Author(s):  
J. Lyell Sanders ◽  
J. G. Simmonds
Keyword(s):  
Cylindrical Shell ◽  
Bessel Functions ◽  
Normal Force ◽  
Tangential Force ◽  
Normal Displacement ◽  
Modified Bessel Functions ◽  
Elementary Functions ◽  
Concentrated Forces ◽  
Function Of Two Variables ◽  
Complete Investigation

Solutions for the normal displacement w and tangential displacements ux and uy for a shallow cylindrical shell subjected to concentrated forces are obtained in this paper. The normal force and the two tangential force cases are treated. The results for the displacements in all cases are expressible in terms of elementary functions, modified Bessel functions, and one new function of two variables. A reasonably complete investigation of this function is included.

An Elastic-Plastic Spherical Contact Model Under Combined Normal and Tangential Loading

2011 ◽  
Author(s):  
Aizhong Wu ◽  
Xi Shi ◽  
Andreas A. Polycarpou
Keyword(s):  
Coulomb Friction ◽  
Normal Force ◽  
Tangential Force ◽  
Element Model ◽  
Friction Model ◽  
Normal Displacement ◽  
Tangential Displacement ◽  
Spherical Contact ◽  
Elastic Plastic ◽  
Proposed Model

In this work, by utilizing the shear strength criterion for the sliding inception, a finite element model for obliquely loaded spherical contact has been developed, which realized a friction transition from perfect slip case to full stick case with increasing normal approach. Both tangential force and normal force during tangential loading were investigated using different models. It was found that with elastic-plastic normal displacement preload, there is an obvious normal force release during tangential loading. Furthermore, both Coulomb friction model and the proposed model predict a lower tangential force at the same tangential displacement compared to the full stick model. However, the Coulomb friction is more empirically determined with some arbitrary friction coefficient whereas the proposed model is based on physics parameters.

Thermomechanical Intereactions in Porous Generalized Thermoelastic Material Permeated with Heat Sources

2008 ◽  
Vol 4 (3) ◽  
pp. 237-254 ◽  
Author(s):  
Rajneesh Kumar ◽  
Savita Devi
Keyword(s):  
Boundary Conditions ◽  
Fourier Transforms ◽  
Volume Fraction ◽  
Stress Component ◽  
Boundary Surface ◽  
Heat Sources ◽  
Laplace And Fourier Transforms ◽  
Physical Form ◽  
Normal Stress Component ◽  
Generalized Thermoelastic

The Laplace and Fourier transforms have been employed to find the general solution to the fields equations in porous generalized thermoelastic medium subjected to thermomechanical boundary conditions permeated with various heat sources; in the transformed form. On the boundary surface, the distributed sources have been taken. To get the solution in the physical form, a numerical inversion technique has been used. The effect of continuous and moving heat sources with the thermomechanical boundary conditions; and the response of boundary sources (concentrated and continuous) with heat source varying with depth; on the normal stress component, change in volume fraction field and temperature distribution have been depicted graphically for a particular model. A particular case is also deduced from the present formulation.

scholarly journals Effect of Water-Based Nanolubricants in Ultrasonic Vibration Assisted Grinding

2018 ◽  
Vol 2 (4) ◽  
pp. 80 ◽  
Author(s):  
Mir Molaie ◽  
Ali Zahedi ◽  
Javad Akbari
Keyword(s):  
Surface Roughness ◽  
Specific Energy ◽  
Material Removal ◽  
Normal Force ◽  
Tangential Force ◽  
Process Efficiency ◽  
Multiwall Carbon Nanotube ◽  
Ultrasonic Vibrations ◽  
Mql Grinding ◽  
Water Based

Currently, because of stricter environmental standards and highly competitive markets, machining operations, as the main part of the manufacturing cycle, need to be rigorously optimized. In order to simultaneously maximize the production quality and minimize the environmental issues related to the grinding process, this research study evaluates the performance of minimum quantity lubrication (MQL) grinding using water-based nanofluids in the presence of horizontal ultrasonic vibrations (UV). In spite of the positive impacts of MQL using nanofluids and UV which are extensively reported in the literature, there is only a handful of studies on concurrent utilization of these two techniques. To this end, for this paper, five kinds of water-based nanofluids including multiwall carbon nanotube (MWCNT), graphite, Al2O3, graphene oxide (GO) nanoparticles, and hybrid Al2O3/graphite were employed as MQL coolants, and the workpiece was oscillated along the feed direction with 21.9 kHz frequency and 10 µm amplitude. Machining forces, specific energy, and surface quality were measured for determining the process efficiency. As specified by experimental results, the variation in the material removal nature made by ultrasonic vibrations resulted in a drastic reduction of the grinding normal force and surface roughness. In addition, the type of nanoparticles dispersed in water had a strong effect on the grinding tangential force. Hybrid Al2O3/graphite nanofluid through two different kinds of lubrication mechanisms—third body and slider layers—generated better lubrication than the other coolants, thereby having the lowest grinding forces and specific energy (40.13 J/mm3). It was also found that chemically exfoliating the graphene layers via oxidation and then purification prior to dispersion in water promoted their effectiveness. In conclusion, UV assisted MQL grinding increases operation efficiency by facilitating the material removal and reducing the use of coolants, frictional losses, and energy consumption in the grinding zone. Improvements up to 52%, 47%, and 61%, respectively, can be achieved in grinding normal force, specific energy, and surface roughness compared with conventional dry grinding.

scholarly journals Thermal Disturbances in Twinned Orthotropic Thermoelastic Material

2018 ◽  
Vol 23 (4) ◽  
pp. 897-910 ◽  
Author(s):  
L. Rani ◽  
V. Singh
Keyword(s):  
Fourier Transforms ◽  
Crystallographic Axis ◽  
Physical Domain ◽  
Matrix Differential Equation ◽  
Special Cases ◽  
Eigen Value ◽  
Basic Equations ◽  
Matrix Differential ◽  
Thermally Conducting ◽  
Vector Matrix

Abstract This paper deals with deformation in homogeneous, thermally conducting, single-crystal orthotropic twins, bounded symmetrically along a plane containing only one common crystallographic axis. The Fourier transforms technique is applied to basic equations to form a vector matrix differential equation, which is then solved by the eigen value approach. The solution obtained is applied to specific problems of an orthotropic twin crystal subjected to triangular loading. The components of displacement, stresses and temperature distribution so obtained in the physical domain are computed numerically. A numerical inversion technique has been used to obtain the components in the physical domain. Particular cases as quasi-static thermo-elastic and static thermoelastic as well as special cases are also discussed in the context of the problem.

Sign in / Sign up

Export Citation Format

Share Document