On localised vibrations in incompressible pre-stressed transversely isotropic elastic solids

This paper is concerned with 2D localised vibration in incompressible pre-stressed fibre-reinforced elastic solids and the closely related problem of surface wave propagation in such materials. An appropriate constitutive model is derived and its stability discussed within the context of the strong ellipticity condition. Surface wave propagation in an associated half-space is considered, with the particular cases of propagation along a principal direction of primary deformation and that of almost inextensible fibres also investigated. The problems of free and forced edge vibration of a semi-infinite strip are analysed, revealing a link between the natural edge frequencies and the associated Rayleigh surface wave speed

A systematic review of Vancouver B2 and B3 periprosthetic femoral fractures

Aims The aim of this study was to investigate the outcomes of Vancouver type B2 and B3 fractures by performing a systematic review of the methods of surgical treatment which have been reported. Materials and Methods A systematic search was performed in Ovid MEDLINE, Embase and the Cochrane Central Register of Controlled Trials. For inclusion, studies required a minimum of ten patients with a Vancouver type B2 and/or ten patients with a Vancouver type B3 fracture, a minimum mean follow-up of two years and outcomes which were matched to the type of fracture. Studies were also required to report the rate of re-operation as an outcome measure. The protocol was registered in the PROSPERO database. Results A total of 22 studies were included based on the eligibility criteria, including 343 B2 fractures and 167 B3 fractures. The mean follow-up ranged from 32 months to 74 months. Of 343 Vancouver B2 fractures, the treatment in 298 (86.8%) involved revision arthroplasty and 45 (12.6%) were treated with internal fixation alone. A total of 37 patients (12.4%) treated with revision arthroplasty and six (13.3%) treated by internal fixation only underwent further re-operation. Of 167 Vancouver B3 fractures, the treatment in 160 (95.8%) involved revision arthroplasty and eight (4.8%) were treated with internal fixation without revision. A total of 23 patients (14.4%) treated with revision arthroplasty and two (28.6%) treated only with internal fixation required re-operation. Conclusion A significant proportion, particularly of B2 fractures, were treated without revision of the stem. These were associated with a higher rate of re-operation. The treatment of B3 fractures without revision of the stem resulted in a high rate of re-operation. This demonstrates the importance of careful evaluation and accurate characterisation of the fracture at the time of presentation to ensure the correct management. There is a need for improvement in the reporting of data in case series recording the outcome of the surgical treatment of periprosthetic fractures. We have suggested a minimum dataset to improve the quality of data in studies dealing with these fractures

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)

Effect of the relative shift between the electron density and temperature pedestal position on the pedestal stability in JET-ILW and comparison with JET-C

The electron temperature and density pedestals tend to vary in their relative radial positions, as observed in DIII-D (Beurskens et al 2011 Phys. Plasmas 18 056120) and ASDEX Upgrade (Dunne et al 2017 Plasma Phys. Control. Fusion 59 14017). This so-called relative shift has an impact on the pedestal magnetohydrodynamic (MHD) stability and hence on the pedestal height (Osborne et al 2015 Nucl. Fusion 55 063018). The present work studies the effect of the relative shift on pedestal stability of JET ITER-like wall (JET-ILW) baseline low triangularity (\u3b4) unseeded plasmas, and similar JET-C discharges. As shown in this paper, the increase of the pedestal relative shift is correlated with the reduction of the normalized pressure gradient, therefore playing a strong role in pedestal stability. Furthermore, JET-ILW tends to have a larger relative shift compared to JET carbon wall (JET-C), suggesting a possible role of the plasma facing materials in affecting the density profile location. Experimental results are then compared with stability analysis performed in terms of the peeling-ballooning model and with pedestal predictive model EUROPED (Saarelma et al 2017 Plasma Phys. Control. Fusion). Stability analysis is consistent with the experimental findings, showing an improvement of the pedestal stability, when the relative shift is reduced. This has been ascribed mainly to the increase of the edge bootstrap current, and to minor effects related to the increase of the pedestal pressure gradient and narrowing of the pedestal pressure width. Pedestal predictive model EUROPED shows a qualitative agreement with experiment, especially for low values of the relative shift

Some comments on the dispersion relation for periodically layered pre-stressed elastic media

In this paper the dispersion relation associated with harmonic waves propagating in a periodically layered structure is derived and analysed. Specifically, the structure is made up of repeating unit cells, with each layer composed of an incompressible, pre-stressed elastic material, each interface perfectly bonded and the upper and lower surfaces of the structure free of incremental traction. The complexity of the problem is reduced using an approach involving the Cayley-Hamilton theorem. A numerical method is also used which eliminates positive exponential functions, thereby considerably reducing the complexity of solving the dispersion relation numerically. Numerical solutions are presented in respect of both a two-ply and symmetric four-ply unit cell. An interesting feature of these solutions is the grouping together of harmonics as the number of unit cells increases. In the case of n unit cells, n-1 harmonics group together in the moderate wave number region, with an additional harmonic joining the group at a higher wave number

Two-dimensional motion in a Bell-constrained plate

The so-called Bell constraint has been used for several years in plasticity theory and has additionally been the subject to several investigations within an elastic context. In this paper the effects of the Bell constraint on the propagation of harmonic waves in a finitely deformed elastic plate are considered. Strong ellipticity conditions are first derived for the unbounded case, and are shown to be dependent on the scalar multiplier associated with the Bell constraint. The dispersion relation, associated with harmonic wave propagation in a plate composed of such a material with zero incremental surface traction, is derived in respect of an arbitrary strain energy function. Asymptotic expansions are then obtained for high and low wave number. These expansions, which give phase speed as a function of wave number, harmonic number and pre-stress, are shown to give excellent agreement with numerical solutions

Dispersion phenomena in symmetric pre-stressed layered elastic structures

The dispersion relation associated with a symmetric three layer structure, composed of compressible, pre-stressed elastic layers, is derived. This mathematically elaborate transcendental equation gives phase speed as an implicit function of wave number. Numerical solutions are established to show a wide range of dispersion behaviour which is delicately dependent on the material parameters and pre-stress in each layer. Particularly interesting behaviour is observed within the short wave (high wave number) regime, with six possible cases of short wave liming behaviour shown possible. Within each of these, a short wave asymptotic analysis is carried out, resulting in a set of approximations which provide explicit relationships between phase speed and wave number. It is envisaged that these approximations may prove helpful to approximate numerical truncation errors associated with impact response, as well as providing excellent first approximations for particularly (numerically) challenging sets of material parameters