Stresses due to gravity in a notched elastic half-plane

Summary A method for the calculation of elastic stresses due to gravity in regions approximating a lower half-plane at infinity is presented. The method is based on an extension of familiar complex variable techniques. In principle the method fails for the case of a contour with corner points. However it is shown that an approximate solution for such regions can be obtained utilizing an approximate conformai transformation onto a unit circle. For a special case, results are given.

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Übersicht In der vorliegenden Arbeit werden die Spannungen berechnet, die durch das Gewicht des Materials in einem elastischen, im Unendlichen einer Halbebene ähnlichen Gebiet verursacht werden. Die Berechnungsmethode ist eine Verallgemeinerung bekannter funktionentheoretischer Verfahren. Die Methode ist ihrem Prinzip nach nicht für Gebiete mit Ecken anwendbar. Es wird jedoch angegeben, wie man in solchen Fällen eine Näherungslösung mit Hilfe einer näherungsweisen, konformen Abbildung auf den Einheitskreis finden kann. Für ein spezielles Beispiel werden Ergebnisse angegeben.

     

Stresses in a half space due to Newtonian gravitation

An efficient general solution is obtained for the problem of the elastic half space z > 0 with a traction-free surface experiencing gravitational attraction to an arbitrarily shaped body located in z < 0. Many components of the stress field can be written down immediately if the potential of the attracting body is known. Results are given for the case of attraction to a uniform sphere.     

Stresses in a human skull due to pulse loading

Summary Assuming the human skull to be an isotropic homogeneous viscoelastic prolate spheroidal shell and the brain to be a homogeneous viscoelastic fluid, the stresses in the skull due to three various types of pulse loading for different load-durations have been reported in the present paper.

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übersicht Unter der Annahme, da? die menschliche Sch?deldecke als isotrope, homogone, viskoelastische, flache sph?roidische Schale und das Gehirn als homogene, viskoelastische Flüssigkeit aufgefa?t werden k?nnen, werden in der vorliegenden Arbeit die Spannungen im Sch?del infolde dreier veschiedener Arten von Impulsbelastungen mit unterschiedlicher Lastdauer dargestellt.

     

Stresses in the human head generated due to thermogenesis

Of concern in the paper is a study of the stresses in a human head, developed due to thermogenesis. As in most of earlier studies, the human head is modelled as an elastic spherical shell. The temperature at any point of the skull has been considered to be a function of both the radial and angular coordinates. The analysis is carried out for a general power law variation of the heat produced in the head, so that the derived expressions can be used to study the response due to different environmental temperatures. The applicability of the analysis has been illustrated through an attempt to compute the stress-variation at different angular distances.     

Stresses in a welded diaphragm due to boundary contraction and normal uniform pressure

The boundary contraction of a small welded circular diaphragm is determined semi-experimentally by utilizing a theoretical relationship between boundary contraction, applied normal pressure and measured deflection. The relationship is nonlinear since large deflections have to be considered. Stresses are determined by a method that uses slope measurements on casts of the deflected diaphragm surface and the value of the boundary contraction as input. Radial and tangential membrane and bending stresses of a typical diaphragm are obtained as application example. The approach should particularly be useful in cases where boundary contraction cannot be measured directly because of design restrictions.     

Elastic indentation of a rough surface by a conical punch

In the contact of a cone with a rough plane the mean pressure in the contact area is constant. In particular, above a critical ratio of the opening angle of the cone with respect to the rms gradient of surface roughness, the mean pressure is the same of that for nominally flat contact, no matter how large is the normal load. We introduce a new variable, namely, the local density of contact area, whose integral over the smooth nominal contact domain gives the real contact area. The results given by the theoretical model agree with the numerical simulations of the same problem presented in the paper.     

Stresses produced in slightly compressible,finitely deformed elastic media due to a normal moving load

In this paper, the stresses developed in slightly compressible, finitely deformed half-space due to normal moving load has been discussed. It has been observed that this type of media have much effect on the existing normal and shearing stresses due to the load. The numerical calculations have been done for developed stresses at different depths. It has been observed that the stresses increase significantly in case of slightly compressible, deformed media.     

Stresses due to an adhesion crack in T-shaped junction of two orthotropic plates

The general solution of stresses is derived for a T-shaped junction of two thin plates with an adhesion crack.The plates are orthotropic.A shear force is applied on the crack surface.The analysis is based on the supposition that the stresses in each plate can be approximated by a plane stress condition.The results obtained are verified by numerical calculation of FEM.     

Stresses in a long hollow cylindrically aeolotropic circular cylinder with plane ends subjected to surface forces

In this paper the stress distribution at a point in a long hollow cylindrically aeolotropic circular cylinder whose plane ends are subjected to systems of forces each of which is statically equivalent to a couple and a longitudinal force, and whose curved surface is subjected to a uniform normal pressure has been studied. The solution of this static mixed Saint-Venant type problem provides results from which the corresponding results of isotropic, transversely isotropic circular cylindrical bodies can be readily deduced. In the end a simple practical application has been made with regard to a similar problem of a long hollow wood pole made up of species walnut.     

Free surface deformation due to a source or a sink in Stokes flow

Free surface shape and cusp formation are analyzed by considering two-dimensional viscous flow due to a line source or a line sink below the free surface where the strength of source/sink is given arbitrarily. In the analysis, the Stokes' approximation is used and surface tension effects are included, but gravity is neglected. The solution is obtained analytically by using conformal mapping and complex function theory. From the solution, shapes of the free surface are shown and the formation of a cusp on the free surface is discussed. As the capillary number decreases in negative, the free surface shape becomes singular and in a real fluid a cusp should form on the free surface below some negative critical capillary number. Typically, streamline patterns for some capillary numbers are also shown. As the small capillary number vanishes, the solution is reduced to a linearized potential flow solution.     

Unsteady boundary layer flow due to a stretching surface in a rotating fluid

The induced unsteady flow due to a stretching surface in a rotating fluid, where the unsteadiness is caused by the suddenly stretched surface is studied in this paper. After a similarity transformation, the unsteady Navier–Stokes equations have been solved numerically using the Keller-box method. Also, the perturbation solution for small times as well as the asymptotic solution for large times, when the flow becomes steady, has been obtained. It is found that there is a smooth transition from the small time solution to the large time or steady state solution.     

On the flow instabilities in the end-wall region of a surface mounted obstacle

Visualization of flow in the around a surface mounted obstacle revealed that the pressure gradients imposed on the boundary layer amplified the formation of turbulent spots in the end-wall region. It was observed that the juncture vortices exhibited Λ waveform instability even during the stretching phase that was followed by a rapid amplification and formation of a turbulent spot. The turbulent spot spread laterally as it convected past the attachment and corner region of the end-wall flow. At the Reynolds number used in this investigation the instabilities were always initiated in the region where the primary singular point is located.     

Refraction effects in the generation of helical surface waves on a cylindrical obstacle

We investigate the scattering of compressional waves from an infinite, circular-cylindrical obstacle, and the excitation during the scattering process of surface waves that propagate along helical paths over the cylinder surface. For the case of a rigid or soft obstacle, the surface waves are external, and are obtained via the use of a Watson transformation. For the case of a penetrable cylinder, additional internal, resonant surface waves are generated for which the phase and group velocity dispersion curves can be obtained from the Resonance Scattering Theory. We perform a detailed study of certain refraction effects which take place upon the generation of the surface waves by the incident plane wave.     

Hydromagnetic flow in a viscoelastic fluid due to the oscillatory stretching surface

An analysis is carried out to study the unsteady magnetohydrodynamic (MHD) two-dimensional boundary layer flow of a second grade viscoelastic fluid over an oscillatory stretching surface. The flow is induced due to an infinite elastic sheet which is stretched back and forth in its own plane. For the investigated problem, the governing equations are reduced to a non-linear partial differential equation by means of similarity transformations. This equation is solved both by a newly developed analytic technique, namely homotopy analysis method (HAM) and by a numerical method employing the finite difference scheme, in which a coordinate transformation is employed to transform the semi-infinite physical space to a bounded computational domain. The results obtained by means of both methods are then compared and show an excellent agreement. The effects of various parameters like visco-elastic parameter, the Hartman number and the relative frequency amplitude of the oscillatory sheet to the stretching rate on the velocity field are graphically illustrated and analysed. The values of wall shear stress for these parameters are also tabulated and discussed.     

Shallow-water waves on a rotating ocean due to oscillatory surface stresses

The initial-value problem of shallow-water waves due to an oscillatory surface stress distribution on a homogeneous rotating ocean is solved by the method of integral transforms. For the wave integral, an asymptotic analysis is given which is uniform across the line produced by the coalescing of the pole and the stationary point of the wave spectrum; the result, unlike previous findings, is non-singular when the circular frequency of oscillation equals the Coriolis parameter. Some limiting cases of interest are deduced and the asymptotic envelope of the progressive waves at the surface is illustrated graphically.     

On periodic indentation of a rigid solid occupying a wavy surface moving on multiferroic materials

The present article is concerned with a 2D dynamic contact problem of a rigid solid occupying a wavy surface moving on anisotropic multiferroic materials. Three bulk wave velocities for anisotropic multiferroic materials are obtained. Five harmonic functions are suggested to derive the general solutions of anisotropic multiferroic governing equations based on the generalized Almansi’s theorem. The contact length and various stresses, electric displacements, and magnetic inductions can be given in the whole half-plane analytically. Figures are plotted to gain an insight of how the velocity and the elastic coefficient influence the contact performance of anisotropic multiferroic materials. Numerical results show that the contact length can be enlarged by escalating the velocity of the rigid solid.     

Water entrainment due to spillway surface jets

Strong flow entrainment has been observed downstream of spillways constructed with flow deflectors. This water entrainment has important environmental and ecological impacts because it improves the mixing of powerhouse and spillway flows, but may negatively impact fish migration or create adverse flow conditions.

Most studies found in the literature attempt to explain this entrainment with turbulent mixing. Both reduced-scale hydraulic models and single-phase, isotropic RANS models grossly under-predict the degree of entrainment observed in prototypes. In this paper, an anisotropic model that accounts for the bubble volume fraction and attenuation of the normal velocity fluctuations at the free surface is presented. The model adequately predicts the main mechanisms causing water entrainment and compares well against experimental data for a round surface jet and for Brownlee Dam at model scale. It is shown that appropriate entrainment can only be captured if the turbulence anisotropy and the two-phase nature of the flow are modelled.