The influence of frame pitch and stiffness on the stress distribution in pressurised cylinders

An analysis is made of the stresses occurring in stringer reinforced cylinders due to the restraining action of the frames. Graphs are presented showing the effect of variation in frame pitch and stiffness, on the bending moment and shear force in the skins, and the hoop stress in the skins between frames. The results are used to show how the optimum structural geometry can be chosen for any given stress ratios

Optimum design of a band reinforced pressurised cylinder

The surface stresses in band reinforced cylindrical pressure vessels are examined, and an equivalent stress determined by using the Mises- Hencky criterion. By comparing the equivalent stress to the band stress, the efficiency of the structural material can be established, and by equating these stresses to their respective yield stresses, the theoretical maximum strength of the structure can be found. Once the material properties of the shell and the reinforcing bands have been specified, the optimum structural layout can be determined

An analysis of an unstiffened cylindrical shell subjected to internal pressure and axial loading

General equations are obtained for the deflections and stresses in long thin unreinforced cylinders, which are subjected to an axial load and internal pressure. By making suitable simplifying assumptions, results are presented which show the variation of the structural weight parameter with the structural axial loading index, for both pressurised and unpressurised shells. An allowance is made for the effects of shell initial eccentricities on the buckling stress coefficient K, in accordance with R. Ae.S. data sheet 04.01.01. Extreme cases are considered, in which the shell is assumed to be either fully effective (K = 0.6). 0:. completely ineffective (K = 0), in resisting axial compressive loads. For this latter case, complete pressure stabilisation of the shell is considered, and it is shown that the weight penalty involved in using this design philosophy, is negligible for a certain range of the structural loading index. A simple modification to the analysis for this case, i.e. K = 0, is made to allow for the effect of an external longitudinal bending moment

Linear buckling of an axially reinforced pressurised cylinder

An analysis is presented using small deflection theory for the buckling of a pressurised, axially reinforced cylinder, which is subjected to axial compression. Various approximations to the analysis are discussed and some results are presented which show the effects of internal pressure and various structural parameters on both panel buckling and overall buckling

Linear buckling of an axially reinforced pressurised cylinder

An analysis is presented using small deflection theory for the buckling of a pressurised, axially reinforced cylinder, which is subjected to axial compression. Various approximations to the analysis are discussed and some results are presented which show the effects of internal pressure and various structural parameters on both panel buckling and overall buckling

A note on the discontinuity stresses at the junction of a pressurised spherical shell and a cylinder

An analysis has been made of the forces and moments occurring at the junction of a pressurised spherical shell with an intersecting cylinder. The additional effects of having a temperature gradient along the length of the cylinder and the effect of a jointing ring have been considered

Homoclinic snaking in bounded domains

Homoclinic snaking is a term used to describe the back and forth oscillation of a branch of time-independent spatially localized states in a bistable, spatially reversible system as the localized structure grows in length by repeatedly adding rolls on either side. On the real line this process continues forever. In finite domains snaking terminates once the domain is filled but the details of how this occurs depend critically on the choice of boundary conditions. With periodic boundary conditions the snaking branches terminate on a branch of spatially periodic states. However, with non-Neumann boundary conditions they turn continuously into a large amplitude filling state that replaces the periodic state. This behavior, shown here in detail for the Swift-Hohenberg equation, explains the phenomenon of “snaking without bistability”, recently observed in simulations of binary fluid convection by Mercader, Batiste, Alonso and Knobloch (preprint)

Symmetric Skyrmions

We present candidates for the global minimum energy solitons of charge one to nine in the Skyrme model, generated using sophisticated numerical algorithms. Assuming the Skyrme model accurately represents the low energy limit of QCD, these configurations correspond to the classical nuclear ground states of the light elements. The solitons found are particularly symmetric, for example, the charge seven skyrmion has icosahedral symmetry, and the shapes are shown to fit a remarkable sequence defined by a geometric energy minimization (GEM) rule. We also calculate the energies and sizes to within at least a few percent accuracy. These calculations provide the basis for a future investigation of the low energy vibrational modes of skyrmions and hence the possibility of testing the Skyrme model against experiment.Comment: latex, 9 pages, 1 figure (fig1.gif

Surface Stress, Morphological Development, and Dislocation Nucleation During SixGe1-x Epitaxy

Utilizing Ge marker layer experiments combined with atomic number contrast (Z-contrast) imaging, we have studied the evolving surface morphology of SixGe1-x alloys during growth by molecular beam epitaxy. The marker layers map out the instability transition between planar two-dimensional (2D) growth and three-dimensional (3D) growth. The transition occurs via the gradual formation of a surface ripple as anticipated from instability theory. However, these undulations rapidly develop into crack-like surface instabilities which we simulate and explain by the mechanism of stress-driven surface diffusion. Finally, we model the large stresses associated with these features within a fracture mechanics formalism. This analysis demonstrates that crack-like instabilities provide ideal candidate sites for the nucleation of misfit dislocations

Single-Particle Green Functions in Exactly Solvable Models of Bose and Fermi Liquids

Based on a class of exactly solvable models of interacting bose and fermi liquids, we compute the single-particle propagators of these systems exactly for all wavelengths and energies and in any number of spatial dimensions. The field operators are expressed in terms of bose fields that correspond to displacements of the condensate in the bose case and displacements of the fermi sea in the fermi case. Unlike some of the previous attempts, the present attempt reduces the answer for the spectral function in any dimension in both fermi and bose systems to quadratures. It is shown that when only the lowest order sea-displacement terms are included, the random phase approximation in its many guises is recovered in the fermi case, and Bogoliubov's theory in the bose case. The momentum distribution is evaluated using two different approaches, exact diagonalisation and the equation of motion approach. The novelty being of course, the exact computation of single-particle properties including short wavelength behaviour.Comment: Latest version to be published in Phys. Rev. B. enlarged to around 40 page