A. Tyas

Layout optimization of large‐scale pin‐jointed frames

Computerized layout (or “topology”) optimization was pioneered almost four decades back. However, despite dramatic increases in available computer power and the application of increasingly efficient optimization algorithms, even now only relatively modest sized problems can be tackled using the traditional “ground structure” approach. This is because of the need, in general, for the latter to contain every conceivable member connecting together the nodes in a problem. A simple, but effective solution method capable of tackling problems with large numbers of potential members (e.g. >100,000,000) is presented. Though the method draws on the linear programming technique of “column generation”, since layout optimization specific heuristics are employed it is presented as an iterative “member adding” method. The method requires a ground structure with minimal connectivity to be used in the first iteration; members are then added as required in subsequent iterations until the (provably) optimal solution is found.

An investigation of frequency domain dispersion correction of pressure bar signals

Abstract The frequency-domain method has been used for several years for the correction of dispersed experimental pressure bar signals. However, the accuracy of this method has been assessed only against assumed force–time histories of the loading function, not against a priori known loads. Further, this method presently fails to take into account predictions from the Pochammer–Chree theory for both the variation of axial strain over the bar radius, and the relation between axial stress and strain. In the current work, a known force–time history is applied to the impact face of a finite element model of a pressure bar. The dispersed signal is recorded on the bar perimeter some way from the impact face, and the frequency domain correction method applied in an attempt to re-construct the undispersed forcing function. It is demonstrated that, even for signals containing moderately high frequencies, excellent reconstruction of the forcing function can be achieved if the Pochammer–Chree results for strain variation and stress–strain relation are incorporated in the dispersion correction method.

A large scale experimental approach to the measurement of spatially and temporally localised loading from the detonation of shallow-buried explosives

A large scale experimental approach to the direct measurement of the spatial and temporal variation in loading resulting from an explosive event has been developed. The approach utilises a fixed target plate through which Hopkinson pressure bars are inserted. This technique allows the pressure-time histories for an array of bars to be generated, giving data over a large area of interest. A numerical interpolation technique has also been developed to allow for the full pressure-time history for any point on the target plate to be estimated and hence total imparted impulse to be calculated. The principles underlying the design of the experimental equipment are discussed, along with the importance of carefully controlling the explosive preparation, and the method and location of the detonation initiation. Initial results showing the key features of the loading recorded and the consistency attainable by this method are presented along with the data interpolation routines used to estimate the loading on the entire face.

The Negative Phase of the Blast Load

Following the positive phase of a blast comes a period where the pressure falls below atmospheric pressure known as the negative phase. Whilst the positive phase of the blast is well understood, validation of the negative phase is rare in the literature, and as such it is often incorrectly treated or neglected altogether. Herein, existing methods of approximating the negative phase are summarised and recommendations of which form to use are made based on experimental validation. Also, through numerical simulations, the impact of incorrectly modelling the negative phase has been shown and its implications discussed.

Investigation of shock waves in explosive blasts using fibre optic pressure sensors

We describe miniature all-optical pressure sensors, fabricated by wafer etching techniques, less than 1 mm2 in overall cross-section with rise times in the µs regime and pressure ranges typically 900 kPa (9 bar). Their performance is suitable for experimental studies of the pressure–time history for test models exposed to shocks initiated by an explosive charge. The small size and fast response of the sensors promises higher quality data than has been previously available from conventional electrical sensors, with potential improvements to numerical models of blast effects. Results from blast tests are presented in which up to six sensors were multiplexed, embedded within test models in a range of orientations relative to the shock front.

A study of the effect of spatial variation of load in the pressure bar

The numerical pressure bar studies of previous authors are extended into a detailed frequency domain analysis. A finite element analysis is conducted, of the propagation of a strain pulse generated by the application of a spatially varying load to the face of a pressure bar. It is found that, for a sufficiently large propagation distance, the bar response is in good agreement with theoretical predictions derived from the Pochammer-Chree analysis; evidence of response attributable to the first two propagation modes is found. These results are extended to assess the accuracy of frequency domain dispersion correction for a concentrated load. It is demonstrated that a good prediction of the form and magnitude of the loading function can be obtained from the highly dispersed bar response.

A Numerical Investigation of Blast Loading and Clearing on Small Targets

When a blast wave strikes a finite target, diffraction of the blast wave around the free edge causes a rarefaction clearing wave to propagate along the loaded face and relieve the pressure acting at any point it passes over. For small targets, the time taken for this clearing wave to traverse the loaded face will be small in relation to the duration of loading. Previous studies have not shown what happens in the late-time stages of clearing relief, nor the mechanism by which the cleared reflected pressure decays to approach the incident pressure. Current design guidance assumes a series of interacting clearing waves propagate over the target face – this assumption is tested in this article by using numerical analysis to evaluate the blast pressure acting on small targets subjected to blast loads. It is shown that repeat propagations of the rarefaction waves do not occur and new model is proposed, based on an over-expanded region of air in front of the loaded face of the target.

Optimum structure to carry a uniform load between pinned supports: exact analytical solution

Recent numerical evidence indicates that a parabolic funicular is not necessarily the optimal structural form to carry a uniform load between pinned supports. When the constituent material is capable of resisting equal limiting tensile and compressive stresses, a more efficient structure can be identified, comprising a central parabolic section and networks of truss bars emerging from the supports. In the current article, a precise geometry for this latter structure is identified, avoiding the inconsistencies that render the parabolic form non-optimal. Explicit analytical expressions for the geometry, stress and virtual-displacement fields within and above the structure are presented. Furthermore, a suitable displacement field below the structure is computed numerically and shown to satisfy the Michell–Hemp optimality criteria, hence formally establishing the global optimality of this new structural form.

Full correction of first-mode Pochammer?Chree dispersion effects in experimental pressure bar signals

Frequency domain analysis of dispersed strain signals in pressure bars has been an active area of study for many years. Over the last two decades, methods have been developed for the correction of dispersed signals, by adjustment of the phase angles of the Fourier components of the signal. Recent work has shown that, theoretically, dispersion correction should be significantly improved by the application of additional correction factors to the amplitude of the Fourier components. This paper describes a study using experimental and related numerical work to further test these proposals.

Observations from Preliminary Experiments on Spatial and Temporal Pressure Measurements from Near-Field Free Air Explosions

It is self-evident that a crucial step in analysing the performance of protective structures is to be able to accurately quantify the blast load arising from a high explosive detonation. For structures located near to the source of a high explosive detonation, the resulting pressure is extremely high in magnitude and highly non-uniform over the face of the target. There exists very little direct measurement of blast parameters in the near-field, mainly attributed to the lack of instrumentation sufficiently robust to survive extreme loading events yet sensitive enough to capture salient features of the blast. Instead literature guidance is informed largely by early numerical analyses and parametric studies. Furthermore, the lack of an accurate, reliable data set has prevented subsequent numerical analyses from being validated against experimental trials. This paper presents an experimental methodology that has been developed in part to enable such experimental data to be gathered. The experimental apparatus comprises an array of Hopkinson pressure bars, fitted through holes in a target, with the loaded faces of the bars flush with the target face. Thus, the bars are exposed to the normally or obliquely reflected shocks from the impingement of the blast wave with the target. Pressure-time recordings are presented along with associated Arbitary-Langrangian-Eulerian modelling using the LS-DYNA explicit numerical code. Experimental results are corrected for the effects of dispersion of the propagating waves in the pressure bars, enabling accurate characterisation of the peak pressures and impulses from these loadings. The combined results are used to make comments on the mechanism of the pressure load for very near-field blast events.