Normal Force Stress Research Articles

Eigen Value Approach in Micropolar Elastic Medium with Voids

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.

The effect of thermal relaxation times on wave propagation of micropolar thermoelastic medium with voids due to various sources

PurposeThe purpose of this paper is to formulate a model of the equations of a two‐dimensional problem with the deformation of micropolar generalized thermoelastic medium with voids under the influence of various sources in the context of the Lord‐Shulman, Green‐Lindsay theories, as well as the classical dynamical coupled theory.Design/methodology/approachThe normal mode analysis was used to obtain the exact expressions of the displacement components, force stress, coupled stress, change in volume fraction field and temperature distribution. Numerical results were given and illustrated graphically when the volume source was applied.FindingsThe presence of voids plays a significant role on all the physical quantities. The value of normal displacement and normal force stress increases while the temperature, tangential force stress and the couple stress increase and then decrease due to the presence of voids. The value of all the physical quantities converges to zero with increase in distance z.Originality/valueComparisons are made with the results predicted by the three theories in the presence and the absence of material constants due to voids.

Transmission of stresses in static and sheared granular beds: The influence of particle size, shearing rate, layer thickness and sensor size

The spatial non-uniformities and temporal fluctuations in the normal stress transmitted across a sheared granular layer have been studied through a combination of experiments in a Jenike shear cell equipped with normal force (stress) transducers imbedded on the bottom shearing surface and discrete element method (DEM) simulations. Experiments were carried out with particles of different sizes and layers of different thicknesses; the normal stress was measured at several different shearing rates and at several positions on the bottom surface. The DEM simulations revealed a direct link between the spatial inhomogeneities and temporal fluctuations in the stress recorded in our measurements. We found that the dependence of the average normal stress on the bottom surface as a function of height mirrored that in Janssen's analysis of stresses in wall-bounded static assemblies.

Deformation Due to Mechanical and Thermal Sources in Magneto‐Micropolar Elastic Medium

The present investigation is concerned with a two‐dimensional problem in electromagnetic micropolar elasticity for a half‐space whose surface is subjected to mechanical or thermal source in the presence of a transverse magnetic field. Laplace and Fourier transform technique is used to solve the problem. As an application of the approach concentrated/continuous mechanical or thermal source has been taken. The integral transforms have been inverted by using a numerical technique to obtain the components of normal strain, temperature distribution, normal force stress and tangential couple stress in the physical domain. The expressions of these quantities have been given and illustrated graphically to depict the magnetic effect for two different theories of generalized thermoelasticity, Lord and Shulman (L‐S theory) and Green and Lindsay (G‐L theory). Some special cases of interest are also deduced from the present investigation.

Moving load response in micropolar thermoelastic medium without energy dissipation possessing cubic symmetry

The steady state response of a micropolar thermoelastic medium without energy dissipation possessing cubic symmetry due to a moving load has been studied. Fourier transform has been employed and the transform has been inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution have been compared for micropolar cubic crystal and micropolar isotropic solid. The numerical results are illustrated graphically for a particular material. Some special cases have also been deduced.

Deformation due to time harmonic sources in micropolar thermoelastic medium possessing cubic symmetry with two relaxation times

The response of a micropolar thermoelastic medium possessing cubic symmetry with two relaxation times due to time harmonic sources is investigated. Fourier transform is employed and the transform is inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution are compared for micropolar cubic crystal and micropolar isotropic solid. The numerical results are illustrated graphically for a particular material. Some special cases are also deduced.

Time harmonic sources at micropolar thermoelastic medium possessing cubic symmetry with one relaxation time

The response of a micropolar thermoelastic medium possessing cubic symmetry with one relaxation time due to time harmonic sources has been investigated. Fourier transform has been employed and the transform has been inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution have been compared for micropolar cubic crystal and isotropic micropolar solid. The numerical results are illustrated graphically for a particular material. Some special cases have also been deduced.

Deformation in micropolar cubic crystal due to various sources

The response of a micropolar cubic crystal due to various sources has been studied. The eigenvalue approach using Laplace and Fourier transforms has been employed to solve the problem. The integral transforms have been inverted by using a numerical technique to obtain the displacement, microrotation and stress components in the physical domain. The results of normal displacement, normal force stress and tangential couple stress have been compared for micropolar cubic crystal and micropolar isotropic solid and illustrated graphically.

Viscous effect at an orthotropic micropolar boundary surface

Steady state responses at viscous fluid/ orthotropic micropolar solid interfaces to moving point loads have been studied. An eigenvalue approach using the Fourier transform has been employed to solve the problem. The displacement, microrotation and stress components for the orthotropic micropolar solids so obtained in the physical domain are computed numerically by applying numerical inversion technique. Viscosity and anisotropy effects on normal displacement, normal force stress and tangential couple stress have been shown graphically for a particular model. Some special cases of interest have been presented.

Interaction due to mechanical sources in micropolar elastic medium with voids

The present paper is concerned with the dynamic problem of a homogeneous isotropic half-space with voids subjected to a set of normal point sources. The integral transforms have been inverted by using a numerical technique to obtain the normal force stress, normal displacement, tangential couple stress and volume fraction field in the physical domain for the two different sources. The expressions of these quantities have been given and illustrated graphically to depict the effect of micropolarity and voids.

RESPONSE OF ORTHOTROPIC MICROPOLAR ELASTIC MEDIUM DUE TO VARIOUS SOURCES

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

DISTURBANCE DUE TO MECHANICAL SOURCES IN MICROPOLAR ELASTIC MEDIUM WITH VOIDS

The dynamic response of a homogeneous isotropic micropolar half-space with voids subjected to a set of normal point sources is investigated. The integral transforms have been inverted by using a numerical technique to obtain the normal force stress, normal displacement, tangential force stress, tangential couple stress and volume fraction field in the physical domain for the two different sources. The results of these quantities for a magnesium crystal-like material are given and illustrated.

Dynamical Behaviour of Orthotropic Micropolar Elastic Medium

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.

Mechanical sources in orthotropic micropolar continua

The present paper is concerned with the problem of an orthotropic micropolar half-space subjected to concentrated and distributed loads. The disturbance due to normal and tangential loads are investigated by employing eigen-value 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 results of these quantities are given and illustrated graphically.

MECHANICAL AND THERMAL SOURCES IN A MICROPOLAR GENERALIZED THERMOELASTIC MEDIUM

The disturbance due to mechanical and thermal sources in a homogeneous, isotropic, micropolar generalized thermoelastic half-space is investigated by the use of Laplace– Fourier transform technique. The analytical expressions of displacement components, normal force stress, tangential force stress and temperature field so obtained have been inverted by using a numerical technique. Numerical results are presented graphically for a magnesium crystal like material.