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.

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

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.

Dynamical Behaviour of Orthotropic Micropolar Elastic Medium

2002 ◽  
Vol 8 (8) ◽  
pp. 1053-1069 ◽  
Author(s):  
Rajneesh Kumar ◽  
Suman Choudhary
Keyword(s):  
Elastic Medium ◽  
Couple Stress ◽  
Normal Force ◽  
Numerical Technique ◽  
Integral Transforms ◽  
Dynamical Behaviour ◽  
Normal Displacement ◽  
Physical Domain ◽  
Elastic Solids ◽  
Eigenvalue Approach

The present paper is concerned with the plane strain problem in homogeneous micropolar orthotropic elastic solids. The disturbance due to continuous normal and tangential sources are investigated by employing eigenvalue approach. The integral transforms have been inverted by using a numerical technique to obtain the normal displacement, normal force stress and tangential couple stress in the physical domain. The expressions of these quantities are given and illustrated graphically.

scholarly journals Axisymmetric Vibration for Micropolar Porous Thermoelastic Circular Plate

2017 ◽  
Vol 22 (3) ◽  
pp. 583-600 ◽  
Author(s):  
R. Kumar ◽  
P. Kaushal ◽  
R. Sharma
Keyword(s):  
Circular Plate ◽  
Axisymmetric Problem ◽  
Volume Fraction ◽  
Hankel Transform ◽  
Specific Model ◽  
Axisymmetric Vibration ◽  
Physical Domain ◽  
Special Cases ◽  
Eigen Value ◽  
Field Temperature

AbstractThe present investigation is concerned with a two dimensional axisymmetric problem in a homogeneous isotropic micropolar porous thermoelastic circular plate by using the eigen value approach. The Laplace and Hankel transform are used to solve the problem. The expression of displacements, microrotation, volume fraction field, temperature distribution and stresses are obtained in the transformed domain subjected to thermomechanical sources. A computer algorithm is developed for numerical computations. To obtain the resulting quantities in a physical domain, a numerical inversion technique is used. The resulting quantities are depicted graphically for a specific model. Some special cases are also deduced.

Interaction due to Mechanical and Thermal Sources in Thermoelastic Half-Space with Voids

2005 ◽  
Vol 11 (4) ◽  
pp. 499-517 ◽  
Author(s):  
Rajneesh Kumar ◽  
Leena Rani
Keyword(s):  
Half Space ◽  
Normal Force ◽  
Volume Fraction ◽  
Thermal Source ◽  
Physical Domain ◽  
Coupled Thermoelasticity ◽  
Time Harmonic ◽  
The Fourier Transform ◽  
Mechanical And Thermal Sources ◽  
Thermal Sources

The dynamic response of a homogeneous, isotropic, thermoelastic half-space with voids subjected to time harmonic normal force and thermal source is investigated by applying the Fourier transform. The displacements, stresses, temperature distribution, and change in volume fraction field obtained in the physical domain are computed numerically and illustrated graphically. The numerical results of these quantities for magnesium crystal-like material are illustrated to depict the voids effect for the theory of coupled thermoelasticity and uncoupled thermoelasticity for an insulated boundary and temperature gradient boundary.

Axi-symmetric deformation in the micropolar porous generalized thermoelastic medium

2010 ◽  
Vol 58 (1) ◽  
pp. 129-139 ◽  
Author(s):  
R. Kumar ◽  
R. Gupta
Keyword(s):  
Normal Force ◽  
Volume Fraction ◽  
Specific Model ◽  
Numerical Inversion ◽  
Thermal Source ◽  
Field Equations ◽  
Thermoelastic Medium ◽  
Symmetric Deformation ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid

Axi-symmetric deformation in the micropolar porous generalized thermoelastic mediumIn the present article we studied the thermodynamical theory of micropolar porous material and derived the equations of the linear theory of microploar porous generalized thermoelastic solid. Then the general solution to the field equations for plane axi-symmetric problem are obtained. The Laplace and Hankel transforms have been employed to study the problem, which are inverted numerically by using numerical inversion technique. An application of normal force and thermal source has been taken to show the utility of the approach. The technique developed in the present paper is simple, straightforward and convenient for numerical computation. Effect of micropolarity and porosity on the components of stress, temperature distribution and volume fraction field together with the effect of generalized theory of thermoelasticity have been depicted graphically for a specific model. Some particular cases are also deduced from the present problem.

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.

scholarly journals Response due to mechanical source in second axisymmetric problem of micropolar elastic medium

2013 ◽  
Vol 18 (4) ◽  
pp. 1249-1261
Author(s):  
R. Singh
Keyword(s):  
Elastic Medium ◽  
Couple Stress ◽  
Axisymmetric Problem ◽  
Numerical Technique ◽  
Integral Transforms ◽  
Physical Domain ◽  
Concentrated Force ◽  
Infinite Space ◽  
Eigen Value ◽  
Displacement Force

Abstract The second axisymmetric problem in a micropolar elastic medium has been investigated by employing an eigen value approach after applying the Laplace and the Hankel transforms. An example of infinite space with concentrated force at the origin has been presented to illustrate the application of the approach. The integral transforms have been inversed by using a numerical technique to obtain the components of microrotation, displacement, force stress and couple stress in the physical domain. The results for these quantities are given and illustratred graphically.

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.

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