Modeling of Polymer Clay Nanocomposite for a Multiscale Approach

The mechanical property enhancement of polymer reinforced with nano-thin clay platelets (of high aspect ratio) is associated with a high polymer-filler interfacial area per unit volume. The ideal case of fully separated (exfoliated) platelets is generally difficult to achieve in practice: a typical nanocomposite also contains multilayer stacks of intercalated platelets. Here we use numerical modelling to investigate how the platelet properties affect the overall mechanical properties. The configuration of platelets is modelled using a statistical interpretation of the Representative Volume Element (RVE) approach, in which an ensemble of "sample" heterogeneous material is generated (with periodic boundary conditions). A simple Monte Carlo algorithm is used to place non-intersecting platelets in the RVE according to a specified set of statistical distributions. The effective stiffness of the platelet-matrix system is determined by measuring the stress (using standard Finite Element analysis) produced as a result of applying a small deformation to the boundaries, and averaging over the entire statistical ensemble. In this work we determine the way in which the platelet properties (curvature, filling fraction, stiffness, aspect ratio) and the number of layers in the stack affect the overall stiffness enhancement of the nanocomposite. Thus, we bridge the gap between behaviour on the macroscopic scale with that on the scale of the nano-reinforcement, forming part of a multi-scale modelling framework.Comment: 39 pages, 19 figure

Strategies for producing fast finite element solutions of the incompressible Navier-Stokes equations on massively parallel architectures

To take advantage of the inherent flexibility of the finite element method in solving for flows within complex geometries, it is necessary to produce efficient implementations of the method. Segregation of the solution scheme and the use of parallel computers are two ways of doing this. Here, the optimisation of a sequential segregated finite element algorithm is discussed, together with the various strategies by which this is done. Furthermore, the implications of parallelising the code onto a massively parallel computer, the MasPar, are explored. This machine is of Single Instruction Multiple Data type and so modifications to the computer code have been necessary. A general methodology for the implementation of finite element programs is presented based on projecting the levels of data within the algorithm into a form which is ideal for parallelisation. Application of this methodology, in a high level language, has resulted in a code which runs at just under 30MFlops (in double precision). The computations are performed with minimal inter-processor communication and this represents an efficiency of 20% of the theoretical peak speed. Even though only high level language constructs have been used, this efficiency is comparable with other work using low level constructs on machines of this architecture. In particular, the use of data parallel arrays and the utilisation of the non-unique machine specific features of the computer architecture have produced an efficient, fast program

Global supply chains of high value low volume products

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Variational approach to relaxed topological optimization: closed form solutions for structural problems in a sequential pseudo-time framework

The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a non-smoothed characteristic function field as a topological design variable, (c) the consistent derivation of a relaxed topological derivative whose determination is simple, general and efficient, (d) formulation of the overall increasing cost function topological sensitivity as a suitable optimality criterion, and (e) consideration of a pseudo-time framework for the problem solution, ruled by the problem constraint evolution. In this setting, it is shown that the optimization problem can be analytically solved in a variational framework, leading to, nonlinear, closed-form algebraic solutions for the characteristic function, which are then solved, in every time-step, via fixed point methods based on a pseudo-energy cutting algorithm combined with the exact fulfillment of the constraint, at every iteration of the non-linear algorithm, via a bisection method. The issue of the ill-posedness (mesh dependency) of the topological solution, is then easily solved via a Laplacian smoothing of that pseudo-energy. In the aforementioned context, a number of (3D) topological structural optimization benchmarks are solved, and the solutions obtained with the explored closed-form solution method, are analyzed, and compared, with their solution through an alternative level set method. Although the obtained results, in terms of the cost function and topology designs, are very similar in both methods, the associated computational cost is about five times smaller in the closed-form solution method this possibly being one of its advantages. Some comments, about the possible application of the method to other topological optimization problems, as well as envisaged modifications of the explored method to improve its performance close the workPeer ReviewedPostprint (author's final draft

A coupled CFD approach for combustor-turbine interaction

The current approach in the industry to numerically investigate the flow in a gas turbine considers each component, such as combustor and turbine, as a stand-alone part, involving no or very minor interactions with other parts, mainly applied through static boundary conditions. Efficient and very specialised CFD codes have been developed in the past to address the different flow characteristic occurring in the different regions of the engine. In order to meet the future requirements in terms of fuel consumption and pollutants emissions, an integrated approach capable of capturing all the possible interactions between different components is necessary. An efficient and accurate way to achieve integrated simulations is to couple already existing specialised codes in a zonal type of coupling. In this Thesis work a methodology to couple an incompressible/low-Mach number pressure-based combustion code with a compressible density-based turbomachinery code for industrial application has been developed. In particular two different couplings have been implemented: the first, based on the exchange of existing boundary conditions through files, comes as a completely separated tools from the original codes, of which no modifications are required, and it is applied to steady state simulations; the second instead, based on the exchange of boundary conditions and body forces through message passing, requires some modifications of the source codes and it is applied to both steady and unsteady cases. A simple analysis shows that not all the primitive variables can be made continuous at the coupling interface between the two codes and a compromise was found that allows minor discontinuity in some of the variables while achieving mass flow conservation and continuity of the temperature profiles. The coupling methodology has been applied to a simplified but realistic industrial case, consisting of a RQL (Rich Burn - Quick quench - Lean burn) combustor coupled with the first stage of the HP turbine. The analysis of the steady case has shown that the combustor field is affected as far as 150% axial chord lengths upstream of the blades leading edge, affecting RTDF and OTDF at the interfaces. In the turbine stage significant differences in both efficiency and degree of reaction were found in the coupled cases with respect to standard standalone simulations using radial inlet profiles. The analysis of the unsteady simulation has instead shown the hot streaks behaviour across the turbine, that are only partially mitigated by the stator blades and, due to segregation effect of hot and cold gases, migrate towards the pressure side of the rotor blades

Description of a robotics-oriented relational positioning methodology

This paper presents a relational positioning methodology for flexibly and intuitively specifying offline programmed robot tasks, as well as for assisting the execution of teleoperated tasks demanding precise movements. In relational positioning, the movements of an object can be restricted totally or partially by specifying its allowed positions in terms of a set of geometric constraints. These allowed positions are found by means of a 3D sequential geometric constraint solver called PMF – Positioning Mobile with respect to Fixed. PMF exploits the fact that in a set of geometric constraints, the rotational component can often be separated from the translational one and solved independently