Absence Of Initial Stress Research Articles

ПРИМЕНЕНИЕ МЕТОДА ПЕРЕМЕННЫХ ПАРАМЕТРОВ УПРУГОСТИ ПРИ РЕШЕНИИ ЗАДАЧ ЗНАКОПЕРЕМЕННОГО УПРУГО-ПЛАСТИЧЕСКОГО НАГРУЖЕНИЯ МЕТАЛЛИЧЕСКИХ КОНСТРУКЦИЙ С УЧЕТОМ ОСТАТОЧНЫХ НАПРЯЖЕНИЙ.

When calculating metal structures, as a rule, assumptions are made that allow us to consider the complex nonlinear operation of the structure in a linear formulation, namely, the absence of initial stresses, the absence of kinematic and isotropic changes in the flow surface of the material during plastic deformations, the identity of the behavior of the material during loading and unloading, etc. This approach is laid down in regulatory documents and is due to the following arguments: self-balanced stresses affect the deformability of the section, but cannot affect the kinematic boundary of its strength under the assumption of an ideally elasticplastic behavior of the material; the design works for a single load; initial stresses in some zones slow down the development of plastic deformations, and in others accelerate, etc. These assumptions seem to be justified in the classical problems of structural strength, in which the development of plastic deformations is allowed. However, in some tasks, these assumptions can lead to a distorted or erroneous result. The article describes the addition of the method of variable elasticity parameters in the formulation of a nonlinear deformation model, which makes it possible to remove the above assumptions. The algorithm is implemented in Python and tested on two verification tasks, and the process of loading the I-beam section taking into account residual stresses is also considered. The results of numerical calculation showed similar values with analytical solutions and qualitatively correspond to well-known ideas about the cyclic operation of structures.

Some models for initially stressed and initially strained structurally anisotropic incompressible materials

In this paper, we determine the constitutive relations for structurally anisotropic materials from a reference with initial strain or initial stress. Using reference independence of strain energy density, we first deduce the relationship of various initial strain measures with material symmetry and determine the resulting structural tensors. We use these structural tensors to derive the necessary invariants for initially strained materials. We also Examine the polyconvexity of the derived invariants and determine constitutive relations for the initially strained Ogden model. Next, we determine the constitutive relation for a combination of initial stress-texture symmetry which may be a more popular approach of recent interest. We deduce four reference-independent constitutive relations for initially stressed transversely isotropic incompressible materials. The first two strain energy functions are linear in the left Cauchy stretch and its cofactor, respectively, in the stress-free state. In the absence of initial stress, the third strain energy function involves all standard invariants for transversely isotropy. To deduce this strain energy in the presence of initial stress, we invert a fourth-order tensor and perform several involved tensor calculations. Finally, we obtain the constitutive relation for an initially stressed transversely isotropic limited chain extensible (LCE) model. To determine the initial stretch in the preferred texture direction in terms of initial stress, we utilize the geometrical interpretation of the Almansi strain measure.

Love wave in porous layer under initial stress over heterogeneous elastic half-space under gravity and initial stress

In the present paper, effect of initial stresses and gravity on the propagation of Love waves has been studied in porous layer surface over a heterogeneous half-space. We have considered two types of boundary on free surfaces: (a) rigid boundary and (b) traction free boundary. The propagation of Love waves has been investigated under assumed media in both the cases of boundary and discusses a comparison study of two cases. The dispersion equations and phase velocities have been obtained in both the cases. The numerical calculations have been done and presented graphically. This study of Love waves in the assumed medium reveals that the presence of initial stress in the half-space and absence of initial stress in the layer, the displacement of phase velocity in rigid boundary is more than the traction free boundary.

Influence of Rigidity, Irregularity and Initial Stress on Shear Waves Propagation in Multilayered Media

The propagation of shear waves in an anisotropic fluid saturated porous layer over a prestressed semi-infinite homogeneous elastic half-space lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary has been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for shear waves is derived by using the perturbation technique followed by Fourier transformations. The dimensionless phase velocity is plotted against dimensionless wave number for the different size of ratios of depth of rectangular irregularity with the height of the layer and anisotropy parameters with the help of MATLAB graphical routines in presence and absence of initial stress. From the graphical results, it has been seen that the phase velocity is significantly influenced by the wave number, the depth of the irregularity, rigid boundary and initial stress. The acquired outcomes can be valuable for the investigation of geophysical prospecting and understanding the cause and evaluating of damage due to earthquakes.

A new features on S-waves propagation in a nonhomogeneous anisotropic incompressible medium under influence of gravity field and initial stress with and without electromagnetic field and rotation

ABSTRACTThe present article is concerned with the investigation of the propagation of shear waves in a nonhomogeneous anisotropic incompressible medium under the effect of the electromagnetic field, gravity field, rotation, and initial stress taking into account a comparison between presence and absence of magnetic field, initial stress, and rotation. Analytical analysis reveals that the velocity of propagation of the shear waves depends upon the direction of propagation, the anisotropy, magnetic field, rotation, gravity field, nonhomogeneity of the medium, and the initial stress. The frequency equation that determines the velocity of the shear waves has been obtained. Some special cases are also deduced from the present investigation. In fact, these equations are an agreement with the corresponding classical results when the medium is isotropic. Numerical results have been given and illustrated graphically in each case considered. The results indicate that the effects of gravity field, initial stress, magnetic field, electric field, anisotropy, and rotation are very pronounced. Also, the absence of initial stress, magnetic field, and rotation tends to increasing of the S-waves velocity compared with presence of them.

Quasi-P and quasi-S waves in a self–reinforced medium under initial stresses and under gravity

The present paper is concerned with the propagation of plane waves in self–reinforced media. The velocities of quasi-P and quasi-S waves in an unbounded self–reinforced medium under initial stresses and under gravity field have been derived. Also the reflection coefficients and the partition of energy of reflected quasi-P and quasi-SV waves due to incident quasi-P and quasi-SV waves have been obtained under the influence of initial stress and gravity field. It has been noticed that the velocities, reflection coefficients and energy coefficients not only depend on the initial stress and gravity but also on the direction of propagation. The results are in agreement with the classical case in the absence of initial stresses and gravity. In presence of initial stresses and gravity field, the velocities, reflection coefficients and energy coefficients of quasi-P and quasi-S waves are calculated numerically and are presented by means of graphs.

Effect of Rotation and Initial Stress onGeneralized Thermoelastic Medium with Two-Temperature under Three-Phase-Lag Model

Three-phase-lag theory of thermoelasticity is employed to study the deformation of thermoelastic solid half-space under hydrostatic initial stress and rotation with two- temperature. The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress, thermodynamic temperature and conductive temperature. The numerical results are given and presented graphically when mechanical and thermal force is applied. Comparisons are made with the results predicted by three phase lag, Green-Naghdi III and Lord-Shulman in the presence and absence of initial stress as well as rotation

Metrical Encoding in Adults Who Do and Do Not Stutter

The purpose of this study was to explore metrical aspects of phonological encoding (i.e., stress and syllable boundary assignment) in adults who do and do not stutter (AWS and AWNS, respectively). Participants monitored nonwords for target sounds during silent phoneme monitoring tasks across two distinct experiments. For Experiment 1, the 22 participants (11 AWNS, 11 AWS) silently monitored target phonemes in nonwords with initial stress. For Experiment 2, an additional cohort of 22 participants (11 AWNS, 11 AWS) silently monitored phonemes in nonwords with noninitial stress. In Experiment 1, AWNS and AWS silently monitored target phonemes in initial stress stimuli with similar speed and accuracy. In Experiment 2, AWS demonstrated a within-group effect that was not present for AWNS. They required additional time when monitoring phonemes immediately following syllable boundary assignment in stimuli with noninitial stress. There was also a between-groups effect, with AWS exhibiting significantly greater errors identifying phonemes in nonwords with noninitial stress than AWNS. Findings suggest metrical properties may affect the time course of phonological encoding in AWS in a manner distinct from AWNS. Specifically, in the absence of initial stress, metrical encoding of the syllable boundary may delay speech planning in AWS and contribute to breakdowns in fluent speech production.

Reflection of a plane magneto-thermoelastic wave at the boundary of a solid half-space in presence of initial stress

The paper studies the effects of the magnetic field and initial stress on the reflection of a plane magneto-thermoelastic wave from the boundary of a solid half-space. The basic dynamical equations of thermoelasticity in presence of Lorentz force and the heat conduction equation of Green–Lindsay theory have been solved to derive the wave equations for the reflected P-, SV- and thermal waves. By considering the boundary to be a stress-free and insulated one, the boundary equations that contain the ratios of the amplitude of the reflected components to that of the incident wave have been obtained. The analytical solution has been cast in matrix form for each of the incident plane waves at the boundary, namely the P-wave, SV-wave and thermal wave. The numerical calculations of the absolute values of the amplitude ratios for an incident SV-wave have been carried out for different values of both magnetic pressure number and initial stress parameter. The initial stress parameter shows a marked influence on the magnitude of the amplitude ratios. The reflection coefficients for different values of magnetic pressure number in absence of initial stress have also been included for the sake of comparison.

The effect of initial stress and magnetic field on wave propagation in human dry bones

The aim of the present paper is to study the influence of initial stress and magnetic field on the propagation of harmonic waves in a human long dry bone as transversely isotropic material, subject to the boundary conditions that the outer and inner surfaces are traction free. The equations of elastodynamics are solved in terms of displacements. The natural frequency of plane vibrations in the case of harmonic vibrations has been obtained. The frequencies and phase velocity are calculated numerically, the effects of initial stress and magnetic field are discussed. Comparisons are made with the result in the absence of initial stress and magnetic field.

Influence of heat and mass transfer, initial stress and radially varying magnetic field on the peristaltic flow in an annulus with gravity field

In this paper, the effects of both initial stress, radially varying and gravity field on the peristaltic flow of an incompressible MHD Newtonian fluid in a vertical annulus have been studied under the assumption of long wavelength and low-Reynolds number. The analytical solution has been derived for the temperature, concentration and velocity. The results for velocity, concentration and temperature obtained in the analytical form have been evaluated numerically and discussed briefly. The effect of the non-dimensional wave amplitude, the coefficient of viscosity, Sort number, Schmidt number, initial stress, gravitational field and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. The expressions for pressure rise, temperature, concentration field, velocity and pressure gradient are sketched for various embedded parameters and interpreted. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of initial stress and gravitational field.

SH-type waves dispersion in an isotropic medium sandwiched between an initially stressed orthotropic and heterogeneous semi-infinite media

The present paper studies the propagation of shear waves (SH-type waves) in an homogeneous isotropic medium sandwiched between two semi infinite media. The upper half-space is considered as orthotropic medium under initial stress and lower half-space considered as heterogeneous medium. We have obtained the dispersion equation of phase velocity for SH-type waves. The propagation of SH-type waves are influenced by inhomogeneity parameters and initial stress parameter. The velocity of SH-type wave has been computed for different cases. We have also obtained the dispersion equation of phase velocity in homogeneous media in the absence of initial stress. The velocities of SH-type waves are calculated numerically as a function of kH (non-dimensional wave number) and presented in a number of graphs. To study the effect of inhomogeneity parameters and initial stress parameter we have plotted the velocity of SH-type wave in several figure. We have observed that the velocity of wave increases with the increase inhomogeneity parameters. We found that in both homogeneous and inhomogeneous media the velocity of SH-type wave increases with the increase of initial stress parameter. The results may be useful for the study of seismic waves propagation during any earthquake and artificial explosions.

Dispersion of torsional surface waves in anisotropic layer over porous half space under gravity

AbstractIn this paper an attempt has been made to derive the frequency equation of torsional surface waves in initially stressed fiber reinforced layer lying over fluid saturated anisotropic porous half space under gravity. The dispersion equation has been obtained in terms of Whittaker function and its derivatives, which further expanded asymptotically and retain the terms upto second degree. The analysis of frequency equation bear out the pronounced effect of initial stress, transverse and longitudinal rigidity of reinforced material, gravity and porosity of the porous half space on the propagation of torsional surface waves. Moreover, it can be noted that in the absence of initial stress, reinforcement parameters, gravity and porosity, the frequency equation of torsional surface waves reduces to dispersion equation of Love waves in isotropic layer. This ensures the classical result that torsional surface waves do not propagate through isotropic homogeneous medium.

Effect of stress on reflection and refraction of plane wave at the interface between fluid and stressed rock

Reflection and refraction of plane wave through an interface between fluid and rock with elastic deformations on the basis of the acoustoelastic theory are considered. The effects of stress on the anisotropy and energy reflection and transmission coefficients are investigated. The incident wave plane can coincide with or deviate from planes of material symmetry. Elastic deformations are assumed to be locally homogeneous and to satisfy static boundary conditions. Numerical computations are carried out and comparisons are made with the results predicted in the presence and absence of initial stress. The changes in phase velocity, group velocity, and energy reflection and refraction coefficients due to the presence of stress are displayed graphically and discussed. The results show that the effect of stress depends on its magnitude, direction and form (uniaxial and biaxial).

On the problem of radial vibrations in non-homogeneity isotropic cylinder under influence of initial stress and magnetic field

In the present work, the effects of initial stress, magnetic field and non-homogeneity on wave propagation of free harmonic waves in isotropic material are discussed. The one-dimensional equation of elastodynamic is solved in terms of radial displacement and different cases of the boundary conditions for the hollow cylinder are considered. The determination is concerned with the eigenvalues of the natural frequencies of the radial vibrations for different boundary conditions in the case of harmonic vibrations. Numerical results are given and illustrated graphically for each case considered. Comparisons are made with the results in the absence of initial stress, magnetic field and non-homogeneity.

Relaxation effects on reflection of generalized magneto-thermoelastic waves

The paper studies the effects of the magnetic field and initial stress on the reflection of a plane magneto-thermoelastic wave from the boundary of a solid half-space. The basic dynamical equations of thermoelasticity in presence of Lorentz force and the heat conduction equation of Green–Lindsay theory have been solved to derive the wave equations for the reflected P-, SV- and thermal waves. By considering the boundary to be a stress-free and insulated one, the boundary equations that contain the ratios of the amplitude of the reflected components to that of the incident wave have been obtained. The analytical solution has been cast in matrix form for each of the incident plane waves at the boundary, namely the P-wave, SV-wave and thermal wave. The numerical calculations of the absolute values of the amplitude ratios for an incident SV-wave have been carried out for different values of both magnetic pressure number and initial stress parameter. The initial stress parameter shows a marked influence on the magnitude of the amplitude ratios. The reflection coefficients for different values of magnetic pressure number in absence of initial stress have also been included for the sake of comparison.

Transversely isoiropic beam under initial stress

Starting from Novozhilov's nonlinear equations of elasticity by appropriate simplification and integration over the beam cross-section, a linearized set of equations for a transversely isotropic beam under initial non-uniform state of stress is obtained. In the absence of initial stress, the obtained equations are reduced to well-known Timoshenko beam equations.

Complex potentials of the planar linearized problem of elasticity theory

1. The introduced representations of stresses and of displacements in terms of complex potentials for the planar problem of elasticity theory for compressible and incompressible bodies with uniform initial stresses transform to the well-known Kolosov-Muskhelishvili representations for equal roots of the basic equations in the case of absence of initial stresses. 2. Including the complex potentials introduced and the Cauchy-type integrals, a solution was obtained in closed form of the first and second basic problems for a semiplane with initial stresses, in agreement with [11]. 3. Using the Keldysh-Sedov equations, a solution was obtained of contact problems for a semiplane with initial stresses. 4. The numerical examples provided indicate the important effect of initial stresses for large (finite) initial deformations.