NEW SOLUTION TO THE PROBLEM OF A CRACK IN AN ORTHOTROPIC PLATE UNDER TENSION

Abstract— A classical plane problem of the theory of elasticity about a crack in a stretched orthotropic elastic unbounded plane is considered, which leads to a singular solution for stresses in the vicinity of the crack edge. The relations of the generalized theory of elasticity, including a small scale parameter, are given. The equations of the generalized theory are of a higher order than the equations of the classical theory and allow eliminating the singularity of the classical solution. The scale parameter is determined experimentally. The results obtained determine the effect of the crack length on the bearing capacity of the plate and are compared with the experimental results for plates made of fiberglass and carbon fiber reinforced plastic.

On non-perturbative unitarity in gravitational scattering

We argue that the tree-level graviton-scalar scattering in the Regge limit is unitarized by non-perturbative effects within General Relativity alone, that is without resorting to any extension thereof. At Planckian energy the back reaction of the incoming graviton on the background geometry produces a non-perturbative plane wave which softens the UV-behavior in turn. Our amplitude interpolates between the perturbative graviton-scalar scattering at low energy and scattering on a classical plane wave in the Regge limit that is bounded for all values of s.

Effect of vortex line distribution in superfluid plane Poiseuille flow instability

The hydrodynamic stability of plane Poiseuille flow of superfluid is studied using modal and non-modal analysis. Two modes of instability are predicted, in normal mode stability analysis of the normal fluid, one caused by viscosity similar to the classical mode and another due to mutual friction between superfluid and normal fluid. The mutual friction mode occurs at high wavenumbers, which are stable wavenumbers in classical plane Poiseuille flow. A high superfluid vortex line density alone is not enough to induce instability in normal fluid; a localization of vortex lines is shown to play a major role. The extent of vortex line concentration required to cause instability depends on the density itself. Non-modal instability analysis shows that oblique waves are stronger than streamwise waves, unlike the scenario in classical plane Poiseuille flow.

Features of the stress field at the surface of a flush shrink-fit shaft

The state of stress induced by a shrink-fitted circular shaft in an elastically similar half-space, positioned so that the end of the shaft is flush with the remainder of the free surface, is studied. At deep interior points the classical plane strain (Lamé) solution obtains, and the transition to the free surface state is found. It is found that a residual interfacial axial shear develops and the coefficient of friction needed to ensure adhesion along the interface is found. The effect of slip when a lower coefficient of friction is present is also found as a solution to an integral equation.

The Classical Plane Couette-Poiseuille Flow With Variable Fluid Properties

A theoretical study of the effect of variable viscosity and variable thermal conductivity on the classical plane Couette-Poiseuille flow is presented in this brief communication. The investigation concerns engine oil, air, and water taking into account the variation of these quantities with temperature. The results are obtained with the numerical simulation of the governing equations and cover large temperature differences. Velocity and temperature profiles are presented as well as the volume flow rate and the heat flux between the plates. It is found that temperature profiles are close to the straight line for oil and water and depart significantly from the straight line for air due to nonlinear thermal conductivity. Dynamic viscosity plays an important role on the results which depart significantly from those of a fluid with constant properties.