Build Time Estimations for Large Scale Modelling

Achieving speedy results in model making is very much desired if not a necessity in ahnost any manufacturing industry. There is no doubt that rapid prototyping contributes to this process. It is generally considered that when compared to conventional machining techniques like nlilling, the current rapid prototyping systems appear to be much faster. This is certainly true for complex,slnall objects. I-Iowever, this is not alwaysa,pplicable to simple, large and bulky parts. There are a number of projects and systems concentrating on the fabrication of large models. Work is being carried out at the University ofHong Kong, using milling. along with slicing technology. This.report compares some ofthe rapid prototyping systems witl1milling. Milling is an established technology and recent developments in materials and nlachines used in Inilling nlake it a good alternative to rapid prototyping when itcomes to largesyale nl0delling.Mechanical Engineerin

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method

Approximation in LQG control of a thermoelastic rod

Control and estimator gains are computed for linear-quadratic-Gaussian (LQG) optimal control of the axial vibrations of a thermoelastic rod. The computations are based on a modal approximation of the partial differential equations representing the rod, and convergence of the approximations to control and estimator gains is the main issue

Rapid Prototyping Using 3-D Welding

Rapid prototyping systems are based, almost exclusively on polymer, or paper materials. The dimensions of the parts produced are limited by the volume of the processing area within the machine, and parts tend to warp or distort due to shrinkage and lack of support. Also the mechanical properties of the part are restricted to those of the processable materials and thus, in many cases, required 'engineering properties' cannot be obtainedMechanical Engineerin

The role of stellar radial motions in shaping galaxy surface brightness profiles

Aims. The physics driving features such as breaks observed in galaxy surface brightness (SB) profiles remains contentious. Here, we assess the importance of stellar radial motions in shaping their characteristics. Methods. We use the simulated Milky Way-mass cosmological discs from the Ramses Disc Environment Study (RaDES) to characterise the radial redistribution of stars in galaxies displaying type-I (pure exponentials), II (downbending), and III (upbending) SB profiles. We compare radial profiles of the mass fractions and the velocity dispersions of different sub-populations of stars according to their birth and current location. Results. Radial redistribution of stars is important in all galaxies regardless of their light profiles. Type-II breaks seem to be a consequence of the combined effects of outward-moving and accreted stars. The former produce shallower inner profiles (lack of stars in the inner disc) and accumulate material around the break radius and beyond, strengthening the break; the latter can weaken or even convert the break into a pure exponential. Further accretion from satellites can concentrate material in the outermost parts, leading to type-III breaks that can coexist with type-II breaks, but situated further out. Type-III galaxies would be the result of an important radial redistribution of material throughout the entire disc, as well as a concentration of accreted material in the outskirts. In addition, type-III galaxies display the most efficient radial redistribution and the largest number of accreted stars, followed by type-I and II systems, suggesting that type-I galaxies may be an intermediate case between types-II and III. In general, the velocity dispersion profiles of all galaxies tend to flatten or even increase around the locations where the breaks are found. The age and metallicity profiles are also affected, exhibiting different inner gradients depending on their SB profile, being steeper in the case of type-II systems (as found observationally). The steep type-II profiles might be inherent to their formation rather than acquired via radial redistribution