Multilevel functional preconditioning for shape optimisation

We study the application of a multi-level preconditioner to a practical optimal shape design problem. The preconditioner is based on the Bramble-Pasciak-Xu (BPX) series. We extend it to the unstructured parametrization of 3D shapes by using the volume–agglomeration heuristics. The choice of the smoothing parameter is analysed from functional arguments. Application to the shape design for optimising aerodynamic and sonic boom performances of a wing is demonstrated.     

Strength-optimal running surface contour for track links

The various stresses resulting from weight, driving and tracking forces are transmitted over the contact point between track roller and track link running surface which is, compared with the dimensions of a track-type undercarriage, very small. The design of this contact point and hence the running surface profile of a track link, therefore, is particularly important. References were analyzed with the aim of discussing theoretical diversions on contact problems between plain and curved bodies to get the basis for an optimized design of the running surface profile of track-type undercarriages. Therefore stresses at point and line contact, i.e. for curved and plane running surfaces, are compared by Hertz' theory. In the case of line contact, the maximum Hertzian stress and thus also the maximum effective stresses strongly depend on the actual tilted position of the track roller to the track link running surface. The lowest stress is applied in the case of ideal line contact which is only theoretically interesting. Already at small angles of misalignment, the stresses for line contact are higher than for point contact. In field operation, at constantly changing angles of misalignment, the edge stresses cause the formation of curved running surfaces due to plastic deformation. If track links are already designed with such a running surface contour, the result will be constant stresses over the whole service life which are largely independent of the angle of misalignment avoiding excessive stresses caused by roller misalignments.     

An improved analysis for thermal track buckling

In a previous analysis of track buckling by the author, a simplifying assumption was made that the axial resistance which the ballast exerts on the rail-tie structure is constant. In the present paper this assumption is dropped, by presenting the axial resistance as a bi-linear response, which agrees better with the corresponding test data over the entire range of axial displacements. The obtained analytical results were evaluated numerically for the track parameters currently in use and the results are compared with the results of previous analyses, in order to establish the effect of the introduced analytical improvement.     

Wings of minimum drag for given lift

The variational problem of determining the optimal shape (camber and twist) of the midsurface of a wing having minimum wavedrag is examined in the linear formulation. It is shown that for wings with supersonic leading edge and straight trailing edge, whose shape is given in the form of a double polynomial, the over-all aerodynamic characteristics can be simply expressed in terms of the equation for the leading edge of the wing. This makes it possible not only to solve the variational problem by the Ritz method and obtain the minimum wave drag [1] but also to find the optimal shape of the wing. As examples we consider delta and double-delta wings.     

Polymer track developments

This article summarizes the development of tracks for cross-country vehicles and emphasizes the importance of a very well defined specification of the needs to be able control the development work. It also points out that it is absolutely essential for the manufacturers involved to work very closely together to ascertain the most suitable design of track vehicle.     

Dielectric-barrier-discharge vortex generators: characterisation and optimisation for flow separation control

We investigated the use of dielectric-barrier-discharge plasma actuators as vortex generators for flow separation control applications. Plasma actuators were placed at a yaw angle to the oncoming flow, so that they produced a spanwise wall jet. Through interaction with the oncoming boundary layer, this created a streamwise longitudinal vortex. In this experimental investigation, the effect of yaw angle, actuator length and plasma-induced velocity ratio was studied. Particular attention was given to the vortex formation mechanism and its development downstream. The DBD plasma actuators were then applied in the form of co-rotating and counter-rotating vortex arrays to control flow separation over a trailing-edge ramp. It was found that the vortex generators were successful in reducing the separation region, even at plasma-to-free-stream velocity ratios of less than 10%.     

Patch repair design optimisation for fracture and fatigue improvements of cracked plates

The problem of improving fracture and/or fatigue life of structural components by means of patch repairs is addressed in the present paper by applying a biology-based method, known as the Genetic Algorithm. The optimum design procedure consists in evaluating the patch topology, to be applied to the highest stressed region, which maximises the fracture resistance or the expected fatigue life of the improved structural component by keeping constant the total patched area (constrained optimisation problem). The proposed procedure is implemented in a finite element code and some numerical simulations are carried out in order to assess its reliability. The method is applied to two simple cases of cracked plates under pure Mode I or Mode II: for such analysed configurations, the method allow to improve significantly the fracture or fatigue behaviour of structural components repaired by employing the optimised shape patches instead of a simple shape (e.g. square or rectangular) patches.     

Free-piston driver optimisation for simulation of high Mach number scramjet flow conditions

The University of Queensland (UQ) is currently developing high Mach number, high total pressure scramjet flow conditions in its X2 and X3 expansion tube facilities. These conditions involve shock-processing a high-density air test gas followed by its unsteady expansion into a low-pressure acceleration tube. This relatively slow shock-processing requires the driver to supply high pressure gas for a significantly greater duration than normally required for superorbital flow conditions. One technique to extend the duration is to operate a tuned free-piston driver. For X2, this involves the use of a very light piston at high speeds so that, following diaphragm rupture, the piston displacement substitutes for vented driver gas, thus maintaining driver pressure much longer. However, this presents challenges in terms of higher piston loading and also safely stopping the piston. This article discusses the tuned driver concept, the design of a very lightweight but highly stressed piston, and details the successful development of a new set of tuned free-piston driver conditions for X2.     

A minimum principle for microstructuring in rigid-viscoplastic crystalline solids

A minimum plastic power principle is proposed for a rigid-viscoplastic crystalline domain subdivided into two sets of lath-shaped regions, called bands. The lattice orientation in each band is assumed uniform and to differ infinitesimally from that in the other band. The proposed minimum principle yields the slip activity in the bands and semi-analytical expressions for the misorientation axis and orientation of band boundaries. These band boundary characteristics are predicted for f.c.c. lattice orientations near the ideal rolling texture components. Surprisingly, it found that the predicted band boundary characteristics closely match those of microstructural features called cell block boundaries reported in the experimental literature, except when the dislocations of activated slip systems are known to interact very strongly. This suggests that except when precluded by strong dislocation interactions, continuum extremum principles may also govern microstructural characteristics.     

Propagation of perturbances generated in classic track, and track with Y-type sleepers

Railway track with classic and Y-shaped sleepers or slab track is composed of two rails that are assumed to be infinitely long and joined with sleepers by viscoelastic pads. Numerous assumptions are used in railway-track modelling, leading to different simplifications. The two-dimensional periodic model of track consists of two parallel infinite Timoshenko beams (rails) coupled with equally spaced sleepers on a viscoelastic foundation. Nowadays the interest of engineers is focused on slab track and track with Y-shaped sleepers. The fundamental qualitative difference between the track with classic and Y-shaped sleepers is related to local longitudinal symmetric or antisymmetric features of the railway track. The sleeper spacing influences the periodicity of the foundation elasticity coefficient, mass density (rotational inertia) and the effective shear rigidity. Track with classic concrete sleepers is affected much more by rotational inertia and shear deflections than track with Y-shaped sleepers. The increase of the elastic-wave velocity in track with Y-shaped sleepers and more uniform load distribution will be proved by analysis and simulation. The analytical and numerical analyses allows us to evaluate the track properties in a range of moderate and high train speeds. However, the correct approach is not simple, since the structure of the track interacts with the wheels, wheelsets and vehicles, which constitute complex inertial loads. We note that the growth of amplitude in selected velocity ranges depends strongly on the track type.     

Analytical track models for ride dynamic simulation of tracked vehicles

This paper presents various modelling strategies to account for track in the ride dynamic simulation of high mobility tracked vehicles negotiating rough off-road terrains. Four analytical track representations of varying complexities are formulated in conjuction with an in-plane ride dynamic model of a typical tracked vehicle. These track models are conceived in view of the tracked vehicle kinematics while ignoring the track belt vibrations. The ride dynamic response of a conventional armoured personnel carrier is evaluated in conjunction with different track methods, and validated against field-measured ride data. The relative performances of these track models are thus assessed based on the accuracy of response predictions, and associated computational time.     

On the risk-based steam generator lifetime optimisation

A probabilistic fracture mechanics model is employed to estimate the failure probability of axially cracked steam generator tubes. The model estimates the failure probability from the random changes of the influencing parameters such as tube and crack geometry, material properties and non-destructive examination results, reliability and sizing accuracy and stable crack propagation. The performance of the model is illustrated by a numerical example. A steam generator tubing severely affected by the stress corrosion cracking is studied during most unfavourable accidental conditions. Two different plugging approaches are analyzed and the quality is compared, showing the superior performance of crack length oriented approach over tube wall thickness reduction both in terms of SG failure probability and extent of plugging. Thus, apart from setting the acceptable SG failure probability, all elements for the risk-based SG lifetime optimisation are provided on the example of stress corrosion cracking in the tube expansion transition zone.     

On kinematical minimum principles for rates and increments in plasticity

Summary The optimization approach for elastoplastic analysis is discussed showing that some minimum principles related to numerical methods can be derived by means of duality and penalization procedures. Three minimum principles for velocity and plastic multiplier rate fields are presented in the framework of perfect plasticity. The first one is the classical Greenberg formulation. The second one, due to Capurso in rates and to Maier in finite terms, is developed here with different motivation, and modified by penalization of constraints so as to arrive at a third principle for rates. The counterparts of these optimization formulations in terms of discrete increments of displacements and plastic multipliers are discussed. The third one of these minimum principles for finite increments is recognized to be closely related to Maier's formulation of holonomic plasticity.

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Sommario Un approccio per ottimizzazione all'analisi elastoplastica è discusso mostrando che alcuni principi di minimo collegati a metodi numerici possono essere ricavati mediante dualità e tecniche di penalizzazione. Tra principi di minimo per campi di spostamenti incrementali e moltiplicatori plastici incrementali sono presentati nel contesto della plasticità perfetta. Il primo è la formulazione classica di Greenberg; il secondo, dovuto a Capurso in termini incrementali ed a Maier in termini finiti, è qui sviluppato con diversa motivazione e modificato con penalizzazione dei vincoli in modo da giungere ad un terzo principio incrementale. Si discutono le corrispondenti formulazioni di estremo in termini di incrementi finiti, di spostamenti e di moltiplicatori plastici. Si trova che il terzo di questi principi di minimo per incrementi finiti è strettamente connesso alla formulazione di Maier della plasticità olonoma.

     

Existence theorem for a minimum problem with free discontinuity set

We study the variational problem Where is an open set in ⁿ ,n2gL ^q () L (), 1q<+, O<, <+ andH _n–1 is the (n–1)-dimensional Hausdorff Measure.