Optimal H2 order-one reduction by solving eigenproblems for polynomial equations

A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based search, and hence avoids the usual problems of local minima. We examine mostly the case when the model order is reduced by one, and when the original system has distinct poles. This case exhibits special structure which allows us to provide a complete solution. The problem is converted into linear algebra by exhibiting a finite-dimensional basis for a certain space, and can then be solved by eigenvalue calculations, following the methods developed by Stetter and Moeller. The use of Buchberger's algorithm is avoided by writing the first-order optimality conditions in a special form, from which a Groebner basis is immediately available. Compared with our previous work the method presented here has much smaller time and memory requirements, and can therefore be applied to systems of significantly higher McMillan degree. In addition, some hypotheses which were required in the previous work have been removed. Some examples are included.

Appraisal of PD6493:1991 fracture assessment procedures

PD6493:1991 fracture assessment have been performed for a range of large-scale fracture mechanics tests conducted at TWI in the past. These tests cover several material groups, including pressure vessel steels, pipeline steels, stainless steels and aluminium alloys, including parent material and weldments. Ninety-two wide plate and pressure vessel tests have been assessed, following Levels 1, 2 and 3 PD6493:1991 procedures. In total, over 400 assessments have been performed, examining many features of the fracture assessment procedure including toughness input, proof testing, residual stress assumptions and stress state (tension, bending and biaxial). In all cases the large scale tests have been assessed as one would actual structures: i.e., based on lower bound toughness values obtained from small scale fracture toughness specimens.

Some examples of multiple solutions in limiting flaw calculations using PD6493:1991 fracture mechanics analyses

The use of PC-based PD6493:1991 fracture assessment procedures has revealed that, under certain circumstances, flaws of different dimensions may be found as being limiting or critical for identical applied conditions. The main causes for multiple solutions are a steep applied stress gradient, residual stress relaxation and flaw re-characterisation. This work uses several case studies to illustrate some of the circumstances under which multiple solutions occurs.

Defect and disorder reduction by annealing in hydrogenated tetrahedral amorphous carbon

Hydrogenated tetrahedral amorphous carbon (ta-C:H) is a form of diamond-like carbon with a high sp3 content (>60%), grown here using a plasma beam source. Information on the behaviour of hydrogen upon annealing is obtained from effusion measurements, which show that hydrogen does not effuse significantly at temperatures less than 500 °C in films grown using methane and 700 °C in films grown using acetylene. Raman measurements show no significant structural changes at temperatures up to 300 °C. At higher temperatures, corresponding to the onset of effusion, the Raman spectra show a clustering of the sp2 phase. The density of states of ta-C:H is directly measured using scanning tunnelling spectroscopy. The measured gradients of the conduction and valence band tails increase up to 300 °C, confirming the occurrence of band tail sharpening. Examination of the photoluminescence background in the Raman spectra shows an increase in photoluminescence intensity with decreasing defect density, providing evidence that paramagnetic defects are the dominant non-radiative recombination centres in ta-C:H.

Reduction of porosity in RE1Ba2Cu3Oy pseudo crystals

The distribution of porosity in Y1Ba2Cu3Oy (Y-123) pseudo-crystals prepared by hot seeded melt growth of precursor pellet samples pre-sintered at elevated temperatures in air or vacuum has been investigated. The results demonstrate that the porosity within the Y-123 pseudo-crystal matrix could be reduced dramatically by pre-sintering in vacuum, compared with that for precursor pellets processed in air.

A cohesive approach to thin-shell fracture and fragmentation

We develop a finite-element method for the simulation of dynamic fracture and fragmentation of thin-shells. The shell is spatially discretized with subdivision shell elements and the fracture along the element edges is modeled with a cohesive law. In order to follow the propagation and branching of cracks, subdivision shell elements are pre-fractured ab initio and the crack opening is constrained prior to crack nucleation. This approach allows for shell fracture in an in-plane tearing mode, a shearing mode, or a bending of hinge mode. The good performance of the method is demonstrated through the simulation of petalling failure experiments in aluminum plates. © 2005 Elsevier B.V. All rights reserved.